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Nowadays, the transport goods problem occupies an important place in the economic life of modern societies. The pickup and delivery problem with time windows (PDPTW) is one of the problems which a large part of the research was interested. In this paper, we present a a brief literature review of the VRP and the PDPTW, propose our multicriteria approach based on genetic algorithms which allows minimize the compromise between the vehicles number, the total tardiness time and the total travel cost. And this, by treating the case where a customer can have multiple suppliers and one supplier can have multiple customers
Approche Multicritère pour le Problème de Ramassage et de Livraison avec Fenêtres de Temps à Plusieurs Véhicules
6,000
Extending previous analyses on function classes like linear functions, we analyze how the simple (1+1) evolutionary algorithm optimizes pseudo-Boolean functions that are strictly monotone. Contrary to what one would expect, not all of these functions are easy to optimize. The choice of the constant $c$ in the mutation probability $p(n) = c/n$ can make a decisive difference. We show that if $c < 1$, then the (1+1) evolutionary algorithm finds the optimum of every such function in $\Theta(n \log n)$ iterations. For $c=1$, we can still prove an upper bound of $O(n^{3/2})$. However, for $c > 33$, we present a strictly monotone function such that the (1+1) evolutionary algorithm with overwhelming probability does not find the optimum within $2^{\Omega(n)}$ iterations. This is the first time that we observe that a constant factor change of the mutation probability changes the run-time by more than constant factors.
Optimizing Monotone Functions Can Be Difficult
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Sparse coding algorithms are about finding a linear basis in which signals can be represented by a small number of active (non-zero) coefficients. Such coding has many applications in science and engineering and is believed to play an important role in neural information processing. However, due to the computational complexity of the task, only approximate solutions provide the required efficiency (in terms of time). As new results show, under particular conditions there exist efficient solutions by minimizing the magnitude of the coefficients (`$l_1$-norm') instead of minimizing the size of the active subset of features (`$l_0$-norm'). Straightforward neural implementation of these solutions is not likely, as they require \emph{a priori} knowledge of the number of active features. Furthermore, these methods utilize iterative re-evaluation of the reconstruction error, which in turn implies that final sparse forms (featuring `population sparseness') can only be reached through the formation of a series of non-sparse representations, which is in contrast with the overall sparse functioning of the neural systems (`lifetime sparseness'). In this article we present a novel algorithm which integrates our previous `$l_0$-norm' model on spike based probabilistic optimization for sparse coding with ideas coming from novel `$l_1$-norm' solutions. The resulting algorithm allows neurally plausible implementation and does not require an exactly defined sparseness level thus it is suitable for representing natural stimuli with a varying number of features. We also demonstrate that the combined method significantly extends the domain where optimal solutions can be found by `$l_1$-norm' based algorithms.
Sparse and silent coding in neural circuits
6,002
This paper details the application of a genetic programming framework for classification of decision tree of Soil data to classify soil texture. The database contains measurements of soil profile data. We have applied GATree for generating classification decision tree. GATree is a decision tree builder that is based on Genetic Algorithms (GAs). The idea behind it is rather simple but powerful. Instead of using statistic metrics that are biased towards specific trees we use a more flexible, global metric of tree quality that try to optimize accuracy and size. GATree offers some unique features not to be found in any other tree inducers while at the same time it can produce better results for many difficult problems. Experimental results are presented which illustrate the performance of generating best decision tree for classifying soil texture for soil data set.
Soil Classification Using GATree
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Evolutionary algorithms (EAs) are heuristic algorithms inspired by natural evolution. They are often used to obtain satisficing solutions in practice. In this paper, we investigate a largely underexplored issue: the approximation performance of EAs in terms of how close the solution obtained is to an optimal solution. We study an EA framework named simple EA with isolated population (SEIP) that can be implemented as a single- or multi-objective EA. We analyze the approximation performance of SEIP using the partial ratio, which characterizes the approximation ratio that can be guaranteed. Specifically, we analyze SEIP using a set cover problem that is NP-hard. We find that in a simple configuration, SEIP efficiently achieves an $H_n$-approximation ratio, the asymptotic lower bound, for the unbounded set cover problem. We also find that SEIP efficiently achieves an $(H_k-\frac{k-1}/{8k^9})$-approximation ratio, the currently best-achievable result, for the k-set cover problem. Moreover, for an instance class of the k-set cover problem, we disclose how SEIP, using either one-bit or bit-wise mutation, can overcome the difficulty that limits the greedy algorithm.
On the approximation ability of evolutionary optimization with application to minimum set cover
6,004
This paper introduces a novel type of memetic algorithm based Topology and Weight Evolving Artificial Neural Network (TWEANN) system called DX Neural Network (DXNN). DXNN implements a number of interesting features, amongst which is: a simple and database friendly tuple based encoding method, a 2 phase neuroevolutionary approach aimed at removing the need for speciation due to its intrinsic population diversification effects, a new "Targeted Tuning Phase" aimed at dealing with "the curse of dimensionality", and a new Random Intensity Mutation (RIM) method that removes the need for crossover algorithms. The paper will discuss DXNN's architecture, mutation operators, and its built in feature selection method that allows for the evolved systems to expand and incorporate new sensors and actuators. I then compare DXNN to other state of the art TWEANNs on the standard double pole balancing benchmark, and demonstrate its superior ability to evolve highly compact solutions faster than its competitors. Then a set of oblation experiments is performed to demonstrate how each feature of DXNN effects its performance, followed by a set of experiments which demonstrate the platform's ability to create NN populations with exceptionally high diversity profiles. Finally, DXNN is used to evolve artificial robots in a set of two dimensional open-ended food gathering and predator-prey simulations, demonstrating the system's ability to produce ever more complex Neural Networks, and the system's applicability to the domain of robotics, artificial life, and coevolution.
DXNN Platform: The Shedding of Biological Inefficiencies
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We extend the work of Lehre and Witt (GECCO 2010) on the unbiased black-box model by considering higher arity variation operators. In particular, we show that already for binary operators the black-box complexity of \leadingones drops from $\Theta(n^2)$ for unary operators to $O(n \log n)$. For \onemax, the $\Omega(n \log n)$ unary black-box complexity drops to O(n) in the binary case. For $k$-ary operators, $k \leq n$, the \onemax-complexity further decreases to $O(n/\log k)$.
Faster Black-Box Algorithms Through Higher Arity Operators
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Differential evolution (DE) is a population based evolutionary algorithm widely used for solving multidimensional global optimization problems over continuous spaces. However, the design of its operators makes it unsuitable for many real-life constrained combinatorial optimization problems which operate on binary space. On the other hand, the quantum inspired evolutionary algorithm (QEA) is very well suitable for handling such problems by applying several quantum computing techniques such as Q-bit representation and rotation gate operator, etc. This paper extends the concept of differential operators with adaptive parameter control to the quantum paradigm and proposes the adaptive quantum-inspired differential evolution algorithm (AQDE). The performance of AQDE is found to be significantly superior as compared to QEA and a discrete version of DE on the standard 0-1 knapsack problem for all the considered test cases.
An Adaptive Quantum-inspired Differential Evolution Algorithm for 0-1 Knapsack Problem
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In this work, we introduce multiplicative drift analysis as a suitable way to analyze the runtime of randomized search heuristics such as evolutionary algorithms. We give a multiplicative version of the classical drift theorem. This allows easier analyses in those settings where the optimization progress is roughly proportional to the current distance to the optimum. To display the strength of this tool, we regard the classical problem how the (1+1) Evolutionary Algorithm optimizes an arbitrary linear pseudo-Boolean function. Here, we first give a relatively simple proof for the fact that any linear function is optimized in expected time $O(n \log n)$, where $n$ is the length of the bit string. Afterwards, we show that in fact any such function is optimized in expected time at most ${(1+o(1)) 1.39 \euler n\ln (n)}$, again using multiplicative drift analysis. We also prove a corresponding lower bound of ${(1-o(1))e n\ln(n)}$ which actually holds for all functions with a unique global optimum. We further demonstrate how our drift theorem immediately gives natural proofs (with better constants) for the best known runtime bounds for the (1+1) Evolutionary Algorithm on combinatorial problems like finding minimum spanning trees, shortest paths, or Euler tours.
Multiplicative Drift Analysis
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Spectrum scarceness is one of the major challenges that the present world is facing. The efficient use of existing licensed spectrum is becoming most critical as growing demand of the radio spectrum. Different researches show that the use of licensed are not utilized inefficiently. It has been also shown that primary user does not use more than 70% of the licensed frequency band most of the time. Many researchers are trying to found the techniques that efficiently utilize the under-utilized licensed spectrum. One of the approaches is the use of "Cognitive Radio". This allows the radio to learn from its environment, changing certain parameters. Based on this knowledge the radio can dynamically exploit the spectrum holes in the licensed band of the spectrum. This paper w i l l focus on the performance of spectrum allocation technique, based on popular meta-heuristics Genetics Algorithm and analyzing the performance of this technique using Mat Lab.
Spectrum Management for Cognitive Radio based on Genetics Algorithm
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Multi-Objective Evolutionary Algorithms (MOEAs) have been proved efficient to deal with Multi-objective Optimization Problems (MOPs). Until now tens of MOEAs have been proposed. The unified mode would provide a more systematic approach to build new MOEAs. Here a new model is proposed which includes two sub-models based on two classes of different schemas of MOEAs. According to the new model, some representatives algorithms are decomposed and some interesting issues are discussed.
New Model for Multi-Objective Evolutionary Algorithms
6,010
Several genetic programming systems are created, each solving a different problem. In these systems, the median number of generations G needed to evolve a working program is measured. The behavior of G is observed as the difficulty of the problem is increased. In these systems, the density D of working programs in the universe of all possible programs is measured. The relationship G ~ 1/sqrt(D) is observed to approximately hold for two program-like systems. For parallel systems (systems that look like several independent programs evolving in parallel), the relationship G ~ 1/(n ln n) is observed to approximately hold. Finally, systems that are anti-parallel are considered.
Toward Measuring the Scaling of Genetic Programming
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This work is focused on improving the character recognition capability of feed-forward back-propagation neural network by using one, two and three hidden layers and the modified additional momentum term. 182 English letters were collected for this work and the equivalent binary matrix form of these characters was applied to the neural network as training patterns. While the network was getting trained, the connection weights were modified at each epoch of learning. For each training sample, the error surface was examined for minima by computing the gradient descent. We started the experiment by using one hidden layer and the number of hidden layers was increased up to three and it has been observed that accuracy of the network was increased with low mean square error but at the cost of training time. The recognition accuracy was improved further when modified additional momentum term was used.
Improving the character recognition efficiency of feed forward BP neural network
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A way to enhance the performance of a model that combines genetic algorithms and fuzzy logic for feature selection and classification is proposed. Early diagnosis of any disease with less cost is preferable. Diabetes is one such disease. Diabetes has become the fourth leading cause of death in developed countries and there is substantial evidence that it is reaching epidemic proportions in many developing and newly industrialized nations. In medical diagnosis, patterns consist of observable symptoms along with the results of diagnostic tests. These tests have various associated costs and risks. In the automated design of pattern classification, the proposed system solves the feature subset selection problem. It is a task of identifying and selecting a useful subset of pattern-representing features from a larger set of features. Using fuzzy rule-based classification system, the proposed system proves to improve the classification accuracy.
Cost effective approach on feature selection using genetic algorithms and fuzzy logic for diabetes diagnosis
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This paper is an extension to the memory retrieval procedure of the B-Matrix approach [6],[17] to neural network learning. The B-Matrix is a part of the interconnection matrix generated from the Hebbian neural network, and in memory retrieval, the B-matrix is clamped with a small fragment of the memory. The fragment gradually enlarges by means of feedback, until the entire vector is obtained. In this paper, we propose the use of delta learning to enhance the retrieval rate of the stored memories.
Memory Retrieval in the B-Matrix Neural Network
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In this work we provide a formal model for the different time-dependent components that can appear in dynamic multi-objective optimization problems, along with a classification of these components. Four main classes are identified, corresponding to the influence of the parameters, objective functions, previous states of the dynamic system and, last, environment changes, which in turn lead to online optimization problems. For illustration purposes, examples are provided for each class identified - by no means standing as the most representative ones or exhaustive in scope.
Design and classification of dynamic multi-objective optimization problems
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Genetic Programming (GP) has found various applications. Understanding this type of algorithm from a theoretical point of view is a challenging task. The first results on the computational complexity of GP have been obtained for problems with isolated program semantics. With this paper, we push forward the computational complexity analysis of GP on a problem with dependent program semantics. We study the well-known sorting problem in this context and analyze rigorously how GP can deal with different measures of sortedness.
Computational Complexity Results for Genetic Programming and the Sorting Problem
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A genetic programming system is created. A first fitness function f1 is used to evolve a program that implements a first feature. Then the fitness function is switched to a second function f2, which is used to evolve a program that implements a second feature while still maintaining the first feature. The median number of generations G1 and G2 needed to evolve programs that work as defined by f1 and f2 are measured. The behavior of G1 and G2 are observed as the difficulty of the problem is increased. In these systems, the density D1 of programs that work (for fitness function f1) is measured in the general population of programs. The relationship G1~1/sqrt(D1) is observed to approximately hold. Also, the density D2 of programs that work (for fitness function f2) is measured in the general population of programs. The relationship G2~1/sqrt(D2) is observed to approximately hold.
Evolving a New Feature for a Working Program
6,017
Team pursuit track cycling is a bicycle racing sport held on velodromes and is part of the Summer Olympics. It involves the use of strategies to minimize the overall time that a team of cyclists needs to complete a race. We present an optimisation framework for team pursuit track cycling and show how to evolve strategies using metaheuristics for this interesting real-world problem. Our experimental results show that these heuristics lead to significantly better strategies than state-of-art strategies that are currently used by teams of cyclists.
Evolving Pacing Strategies for Team Pursuit Track Cycling
6,018
This paper explores an idealized dynamic population sizing strategy for solving additive decomposable problems of uniform scale. The method is designed on top of the foundations of existing population sizing theory for this class of problems, and is carefully compared with an optimal fixed population sized genetic algorithm. The resulting strategy should be close to a lower bound in terms of what can be achieved, performance-wise, by self-adjusting population sizing algorithms for this class of problems.
Idealized Dynamic Population Sizing for Uniformly Scaled Problems
6,019
In the present paper, an effort has been made for storing and recalling images with Hopfield Neural Network Model of auto-associative memory. Images are stored by calculating a corresponding weight matrix. Thereafter, starting from an arbitrary configuration, the memory will settle on exactly that stored image, which is nearest to the starting configuration in terms of Hamming distance. Thus given an incomplete or corrupted version of a stored image, the network is able to recall the corresponding original image. The storing of the objects has been performed according to the Hopfield algorithm explained below. Once the net has completely learnt this set of input patterns, a set of testing patterns containing degraded images will be given to the net. Then the Hopfield net will tend to recall the closest matching pattern for the given degraded image. The simulated results show that Hopfield model is the best for storing and recalling images.
Recalling of Images using Hopfield Neural Network Model
6,020
The genetic algorithm (GA) is an optimization and search technique based on the principles of genetics and natural selection. A GA allows a population composed of many individuals to evolve under specified selection rules to a state that maximizes the "fitness" function. In that process, crossover operator plays an important role. To comprehend the GAs as a whole, it is necessary to understand the role of a crossover operator. Today, there are a number of different crossover operators that can be used in GAs. However, how to decide what operator to use for solving a problem? A number of test functions with various levels of difficulty has been selected as a test polygon for determine the performance of crossover operators. In this paper, a novel crossover operator called 'ring crossover' is proposed. In order to evaluate the efficiency and feasibility of the proposed operator, a comparison between the results of this study and results of different crossover operators used in GAs is made through a number of test functions with various levels of difficulty. Results of this study clearly show significant differences between the proposed operator and the other crossover operators.
A Novel Crossover Operator for Genetic Algorithms: Ring Crossover
6,021
The risk of diseases such as heart attack and high blood pressure could be reduced by adequate physical activity. However, even though majority of general population claims to perform some physical exercise, only a minority exercises enough to keep a healthy living style. Thus, physical inactivity has become one of the major concerns of public health in the past decade. Research shows that the highest decrease in physical activity is noticed from high school to college. Thus, it is of great importance to quickly identify college students at health risk due to physical inactivity. Research also shows that the level of physical activity of an individual is highly correlated to demographic features such as race and gender, as well as self motivation and support from family and friends. This information could be collected from each student via a 20 minute questionnaire, but the time needed to distribute and analyze each questionnaire is infeasible on a collegiate campus. Thus, we propose an automatic identifier of students at risk, so that these students could easier be targeted by collegiate campuses and physical activity promotion departments. We present in this paper preliminary results of a supervised backpropagation multilayer neural network for classifying students into at-risk or not at-risk group.
Neural network to identify individuals at health risk
6,022
In this paper, we present an empirical study on convergence nature of Differential Evolution (DE) variants to solve unconstrained global optimization problems. The aim is to identify the competitive nature of DE variants in solving the problem at their hand and compare. We have chosen fourteen benchmark functions grouped by feature: unimodal and separable, unimodal and nonseparable, multimodal and separable, and multimodal and nonseparable. Fourteen variants of DE were implemented and tested on fourteen benchmark problems for dimensions of 30. The competitiveness of the variants are identified by the Mean Objective Function value, they achieved in 100 runs. The convergence nature of the best and worst performing variants are analyzed by measuring their Convergence Speed (Cs) and Quality Measure (Qm).
Convergence Analysis of Differential Evolution Variants on Unconstrained Global Optimization Functions
6,023
Ant Colony Optimization (ACO) is a very popular metaheuristic for solving computationally hard combinatorial optimization problems. Runtime analysis of ACO with respect to various pseudo-boolean functions and different graph based combinatorial optimization problems has been taken up in recent years. In this paper, we investigate the runtime behavior of an MMAS*(Max-Min Ant System) ACO algorithm on some well known hypergraph covering problems that are NP-Hard. In particular, we have addressed the Minimum Edge Cover problem, the Minimum Vertex Cover problem and the Maximum Weak- Independent Set problem. The influence of pheromone values and heuristic information on the running time is analysed. The results indicate that the heuristic information has greater impact towards improving the expected optimization time as compared to pheromone values. For certain instances of hypergraphs, we show that the MMAS* algorithm gives a constant order expected optimization time when the dominance of heuristic information is suitably increased.
Ant Colony Optimization and Hypergraph Covering Problems
6,024
A schema is a naturally defined subset of the space of fixed-length binary strings. The Holland Schema Theorem gives a lower bound on the expected fraction of a population in a schema after one generation of a simple genetic algorithm. This paper gives formulas for the exact expected fraction of a population in a schema after one generation of the simple genetic algorithm. Holland's schema theorem has three parts, one for selection, one for crossover, and one for mutation. The selection part is exact, whereas the crossover and mutation parts are approximations. This paper shows how the crossover and mutation parts can be made exact. Holland's schema theorem follows naturally as a corollary. There is a close relationship between schemata and the representation of the population in the Walsh basis. This relationship is used in the derivation of the results, and can also make computation of the schema averages more efficient. This paper gives a version of the Vose infinite population model where crossover and mutation are separated into two functions rather than a single "mixing" function.
The Exact Schema Theorem
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This paper analises distributed evolutionary computation based on the Representational State Transfer (REST) protocol, which overlays a farming model on evolutionary computation. An approach to evolutionary distributed optimisation of multilayer perceptrons (MLP) using REST and language Perl has been done. In these experiments, a master-slave based evolutionary algorithm (EA) has been implemented, where slave processes evaluate the costly fitness function (training a MLP to solve a classification problem). Obtained results show that the parallel version of the developed programs obtains similar or better results using much less time than the sequential version, obtaining a good speedup.
Distributed Evolutionary Computation using REST
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In this paper, a high-level comparison of both SOAP (Simple Object Access Protocol) and REST (Representational State Transfer) is made. These are the two main approaches for interfacing to the web with web services. Both approaches are different and present some advantages and disadvantages for interfacing to web services: SOAP is conceptually more difficult (has a steeper learning curve) and more "heavy-weight" than REST, although it lacks of standards support for security. In order to test their eficiency (in time), two experiments have been performed using both technologies: a client-server model implementation and a master-slave based genetic algorithm (GA). The results obtained show clear differences in time between SOAP and REST implementations. Although both techniques are suitable for developing parallel systems, SOAP is heavier than REST, mainly due to the verbosity of SOAP communications (XML increases the time taken to parse the messages).
SOAP vs REST: Comparing a master-slave GA implementation
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We reconsider stochastic convergence analyses of particle swarm optimisation, and point out that previously obtained parameter conditions are not always sufficient to guarantee mean square convergence to a local optimum. We show that stagnation can in fact occur for non-trivial configurations in non-optimal parts of the search space, even for simple functions like SPHERE. The convergence properties of the basic PSO may in these situations be detrimental to the goal of optimisation, to discover a sufficiently good solution within reasonable time. To characterise optimisation ability of algorithms, we suggest the expected first hitting time (FHT), i.e., the time until a search point in the vicinity of the optimum is visited. It is shown that a basic PSO may have infinite expected FHT, while an algorithm introduced here, the Noisy PSO, has finite expected FHT on some functions.
Finite First Hitting Time versus Stochastic Convergence in Particle Swarm Optimisation
6,028
Evolution is one of the major omnipresent powers in the universe that has been studied for about two centuries. Recent scientific and technical developments make it possible to make the transition from passively understanding to actively mastering evolution. As of today, the only area where human experimenters can design and manipulate evolutionary processes in full is that of Evolutionary Computing, where evolutionary processes are carried out in a digital space, inside computers, in simulation. We argue that in the near future it will be possible to move evolutionary computing outside such imaginary spaces and make it physically embodied. In other words, we envision the "Evolution of Things", rather than just the evolution of code, leading to a new field of Embodied Artificial Evolution (EAE). The main objective of the present paper is to offer an umbrella term and vision in order to aid the development of this high potential research area. To this end, we introduce the notion of EAE, discuss a few examples and applications, and elaborate on the expected benefits as well as the grand challenges this developing field will have to address.
Evolution of Things
6,029
Estimating of the overhead costs of building construction projects is an important task in the management of these projects. The quality of construction management depends heavily on their accurate cost estimation. Construction costs prediction is a very difficult and sophisticated task especially when using manual calculation methods. This paper uses Artificial Neural Network (ANN) approach to develop a parametric cost-estimating model for site overhead cost in Egypt. Fifty-two actual real-life cases of building projects constructed in Egypt during the seven year period 2002-2009 were used as training materials. The neural network architecture is presented for the estimation of the site overhead costs as a percentage from the total project price.
A Neural Network Model for Construction Projects Site Overhead Cost Estimating in Egypt
6,030
Although the traditional permute matrix coming along with Hopfield is able to describe many common problems, it seems to have limitation in solving more complicated problem with more constrains, like resource leveling which is actually a NP problem. This paper tries to find a better solution for it by using neural network. In order to give the neural network description of resource leveling problem, a new description method called Augmented permute matrix is proposed by expending the ability of the traditional one. An Embedded Hybrid Model combining Hopfield model and SA are put forward to improve the optimization in essence in which Hopfield servers as State Generator for the SA. The experiment results show that Augmented permute matrix is able to completely and appropriately describe the application. The energy function and hybrid model given in this study are also highly efficient in solving resource leveling problem.
Using Hopfield to Solve Resource-Leveling Problem
6,031
In this paper, we present a novel computational framework for nonlinear dimensionality reduction which is specifically suited to process large data sets: the Exploratory Inspection Machine (XIM). XIM introduces a conceptual cross-link between hitherto separate domains of machine learning, namely topographic vector quantization and divergence-based neighbor embedding approaches. There are three ways to conceptualize XIM, namely (i) as the inversion of the Exploratory Observation Machine (XOM) and its variants, such as Neighbor Embedding XOM (NE-XOM), (ii) as a powerful optimization scheme for divergence-based neighbor embedding cost functions inspired by Stochastic Neighbor Embedding (SNE) and its variants, such as t-distributed SNE (t-SNE), and (iii) as an extension of topographic vector quantization methods, such as the Self-Organizing Map (SOM). By preserving both global and local data structure, XIM combines the virtues of classical and advanced recent embedding methods. It permits direct visualization of large data collections without the need for prior data reduction. Finally, XIM can contribute to many application domains of data analysis and visualization important throughout the sciences and engineering, such as pattern matching, constrained incremental learning, data clustering, and the analysis of non-metric dissimilarity data.
A Computational Framework for Nonlinear Dimensionality Reduction of Large Data Sets: The Exploratory Inspection Machine (XIM)
6,032
Biclustering is a two way clustering approach involving simultaneous clustering along two dimensions of the data matrix. Finding biclusters of web objects (i.e. web users and web pages) is an emerging topic in the context of web usage mining. It overcomes the problem associated with traditional clustering methods by allowing automatic discovery of browsing pattern based on a subset of attributes. A coherent bicluster of clickstream data is a local browsing pattern such that users in bicluster exhibit correlated browsing pattern through a subset of pages of a web site. This paper proposed a new application of biclustering to web data using a combination of heuristics and meta-heuristics such as K-means, Greedy Search Procedure and Genetic Algorithms to identify the coherent browsing pattern. Experiment is conducted on the benchmark clickstream msnbc dataset from UCI repository. Results demonstrate the efficiency and beneficial outcome of the proposed method by correlating the users and pages of a web site in high degree.This approach shows excellent performance at finding high degree of overlapped coherent biclusters from web data.
Evolutionary Biclustering of Clickstream Data
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This work presents, the classification of user activities such as Rest, Walk and Run, on the basis of frequency component present in the acceleration data in a wireless sensor network environment. As the frequencies of the above mentioned activities differ slightly for different person, so it gives a more accurate result. The algorithm uses just one parameter i.e. the frequency of the body acceleration data of the three axes for classifying the activities in a set of data. The algorithm includes a normalization step and hence there is no need to set a different value of threshold value for magnitude for different test person. The classification is automatic and done on a block by block basis.
Frequency based Classification of Activities using Accelerometer Data
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This paper presents the designing of a neural network for the classification of Human activity. A Triaxial accelerometer sensor, housed in a chest worn sensor unit, has been used for capturing the acceleration of the movements associated. All the three axis acceleration data were collected at a base station PC via a CC2420 2.4GHz ISM band radio (zigbee wireless compliant), processed and classified using MATLAB. A neural network approach for classification was used with an eye on theoretical and empirical facts. The work shows a detailed description of the designing steps for the classification of human body acceleration data. A 4-layer back propagation neural network, with Levenberg-marquardt algorithm for training, showed best performance among the other neural network training algorithms.
High Accuracy Human Activity Monitoring using Neural network
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Artificial Neural Networks (ANN) comprise important symmetry properties, which can influence the performance of Monte Carlo methods in Neuroevolution. The problem of the symmetries is also known as the competing conventions problem or simply as the permutation problem. In the literature, symmetries are mainly addressed in Genetic Algoritm based approaches. However, investigations in this direction based on other Evolutionary Algorithms (EA) are rare or missing. Furthermore, there are different and contradictionary reports on the efficacy of symmetry breaking. By using a novel viewpoint, we offer a possible explanation for this issue. As a result, we show that a strategy which is invariant to the global optimum can only be successfull on certain problems, whereas it must fail to improve the global convergence on others. We introduce the \emph{Minimum Global Optimum Proximity} principle as a generalized and adaptive strategy to symmetry breaking, which depends on the location of the global optimum. We apply the proposed principle to Differential Evolution (DE) and Covariance Matrix Adaptation Evolution Strategies (CMA-ES), which are two popular and conceptually different global optimization methods. Using a wide range of feedforward ANN problems, we experimentally illustrate significant improvements in the global search efficiency by the proposed symmetry breaking technique.
Symmetry Breaking in Neuroevolution: A Technical Report
6,036
Black-box complexity is a complexity theoretic measure for how difficult a problem is to be optimized by a general purpose optimization algorithm. It is thus one of the few means trying to understand which problems are tractable for genetic algorithms and other randomized search heuristics. Most previous work on black-box complexity is on artificial test functions. In this paper, we move a step forward and give a detailed analysis for the two combinatorial problems minimum spanning tree and single-source shortest paths. Besides giving interesting bounds for their black-box complexities, our work reveals that the choice of how to model the optimization problem is non-trivial here. This in particular comes true where the search space does not consist of bit strings and where a reasonable definition of unbiasedness has to be agreed on.
Black-Box Complexities of Combinatorial Problems
6,037
We investigate Turing's notion of an A-type artificial neural network. We study a refinement of Turing's original idea, motivated by work of Teuscher, Bull, Preen and Copeland. Our A-types can process binary data by accepting and outputting sequences of binary vectors; hence we can associate a function to an A-type, and we say the A-type {\em represents} the function. There are two modes of data processing: clamped and sequential. We describe an evolutionary algorithm, involving graph-theoretic manipulations of A-types, which searches for A-types representing a given function. The algorithm uses both mutation and crossover operators. We implemented the algorithm and applied it to three benchmark tasks. We found that the algorithm performed much better than a random search. For two out of the three tasks, the algorithm with crossover performed better than a mutation-only version.
Evolving A-Type Artificial Neural Networks
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In this paper, a novel mutation operator of differential evolution algorithm is proposed. A new algorithm called divergence differential evolution algorithm (DDEA) is developed by combining the new mutation operator with divergence operator and assimilation operator (divergence operator divides population, and, assimilation operator combines population), which can detect multiple solutions and robustness in noisy environment. The new algorithm is applied to optimize Michalewicz Function and to track changing of rain-induced-attenuation process. The results based on DDEA are compared with those based on Differential Evolution Algorithm (DEA). It shows that DDEA algorithm gets better results than DEA does in the same premise. The new algorithm is significant for optimizing and tracking the characteristics of MIMO (Multiple Input Multiple Output) channel at millimeter waves.
A Novel and Robust Evolution Algorithm for Optimizing Complicated Functions
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We present a number of bounds on convergence time for two elitist population-based Evolutionary Algorithms using a recombination operator k-Bit-Swap and a mainstream Randomized Local Search algorithm. We study the effect of distribution of elite species and population size.
Convergence Properties of Two (μ + λ) Evolutionary Algorithms On OneMax and Royal Roads Test Functions
6,040
We present an analysis of the performance of an elitist Evolutionary algorithm using a recombination operator known as 1-Bit-Swap on the Royal Roads test function based on a population. We derive complete, approximate and asymptotic convergence rates for the algorithm. The complete model shows the benefit of the size of the population and re- combination pool.
Convergence of a Recombination-Based Elitist Evolutionary Algorithm on the Royal Roads Test Function
6,041
The analysis of randomized search heuristics on classes of functions is fundamental for the understanding of the underlying stochastic process and the development of suitable proof techniques. Recently, remarkable progress has been made in bounding the expected optimization time of the simple (1+1) EA on the class of linear functions. We improve the best known bound in this setting from $(1.39+o(1))en\ln n$ to $en\ln n+O(n)$ in expectation and with high probability, which is tight up to lower-order terms. Moreover, upper and lower bounds for arbitrary mutations probabilities $p$ are derived, which imply expected polynomial optimization time as long as $p=O((\ln n)/n)$ and which are tight if $p=c/n$ for a constant $c$. As a consequence, the standard mutation probability $p=1/n$ is optimal for all linear functions, and the (1+1) EA is found to be an optimal mutation-based algorithm. The proofs are based on adaptive drift functions and the recent multiplicative drift theorem.
Tight Bounds on the Optimization Time of the (1+1) EA on Linear Functions
6,042
Population-based evolutionary algorithms (EAs) have been widely applied to solve various optimization problems. The question of how the performance of a population-based EA depends on the population size arises naturally. The performance of an EA may be evaluated by different measures, such as the average convergence rate to the optimal set per generation or the expected number of generations to encounter an optimal solution for the first time. Population scalability is the performance ratio between a benchmark EA and another EA using identical genetic operators but a larger population size. Although intuitively the performance of an EA may improve if its population size increases, currently there exist only a few case studies for simple fitness functions. This paper aims at providing a general study for discrete optimisation. A novel approach is introduced to analyse population scalability using the fundamental matrix. The following two contributions summarize the major results of the current article. (1) We demonstrate rigorously that for elitist EAs with identical global mutation, using a lager population size always increases the average rate of convergence to the optimal set; and yet, sometimes, the expected number of generations needed to find an optimal solution (measured by either the maximal value or the average value) may increase, rather than decrease. (2) We establish sufficient and/or necessary conditions for the superlinear scalability, that is, when the average convergence rate of a $(\mu+\mu)$ EA (where $\mu\ge2$) is bigger than $\mu$ times that of a $(1+1)$ EA.
Novel Analysis of Population Scalability in Evolutionary Algorithms
6,043
Most transformer failures are attributed to bushings failures. Hence it is necessary to monitor the condition of bushings. In this paper three methods are developed to monitor the condition of oil filled bushing. Multi-layer perceptron (MLP), Radial basis function (RBF) and Rough Set (RS) models are developed and combined through majority voting to form a committee. The MLP performs better that the RBF and the RS is terms of classification accuracy. The RBF is the fasted to train. The committee performs better than the individual models. The diversity of models is measured to evaluate their similarity when used in the committee.
Ant Colony Optimization of Rough Set for HV Bushings Fault Detection
6,044
Most transformer failures are attributed to bushings failures. Hence it is necessary to monitor the condition of bushings. In this paper three methods are developed to monitor the condition of oil filled bushing. Multi-layer perceptron (MLP), Radial basis function (RBF) and Rough Set (RS) models are developed and combined through majority voting to form a committee. The MLP performs better that the RBF and the RS is terms of classification accuracy. The RBF is the fasted to train. The committee performs better than the individual models. The diversity of models is measured to evaluate their similarity when used in the committee.
Artificial Neural Network and Rough Set for HV Bushings Condition Monitoring
6,045
One of the problems in applying Genetic Algorithm is that there is some situation where the evolutionary process converges too fast to a solution which causes it to be trapped in local optima. To overcome this problem, a proper diversity in the candidate solutions must be determined. Most existing diversity-maintenance mechanisms require a problem specific knowledge to setup parameters properly. This work proposes a method to control diversity of the population without explicit parameter setting. A self-adaptation mechanism is proposed based on the competition of preference characteristic in mating. It can adapt the population toward proper diversity for the problems. The experiments are carried out to measure the effectiveness of the proposed method based on nine well-known test problems. The performance of the adaptive method is comparable to traditional Genetic Algorithm with the best parameter setting.
Self-Adaptation Mechanism to Control the Diversity of the Population in Genetic Algorithm
6,046
In India many people are now dependent on online banking. This raises security concerns as the banking websites are forged and fraud can be committed by identity theft. These forged websites are called as Phishing websites and created by malicious people to mimic web pages of real websites and it attempts to defraud people of their personal information. Detecting and identifying phishing websites is a really complex and dynamic problem involving many factors and criteria. This paper discusses about the prediction of phishing websites using neural networks. A neural network is a multilayer system which reduces the error and increases the performance. This paper describes a framework to better classify and predict the phishing sites using neural networks.
A Framework for Predicting Phishing Websites using Neural Networks
6,047
In this paper, a complete preprocessing methodology for discovering patterns in web usage mining process to improve the quality of data by reducing the quantity of data has been proposed. A dynamic ART1 neural network clustering algorithm to group users according to their Web access patterns with its neat architecture is also proposed. Several experiments are conducted and the results show the proposed methodology reduces the size of Web log files down to 73-82% of the initial size and the proposed ART1 algorithm is dynamic and learns relatively stable quality clusters.
An Efficient Preprocessing Methodology for Discovering Patterns and Clustering of Web Users using a Dynamic ART1 Neural Network
6,048
We present a new method for proving lower bounds on the expected running time of evolutionary algorithms. It is based on fitness-level partitions and an additional condition on transition probabilities between fitness levels. The method is versatile, intuitive, elegant, and very powerful. It yields exact or near-exact lower bounds for LO, OneMax, long k-paths, and all functions with a unique optimum. Most lower bounds are very general: they hold for all evolutionary algorithms that only use bit-flip mutation as variation operator---i.e. for all selection operators and population models. The lower bounds are stated with their dependence on the mutation rate. These results have very strong implications. They allow to determine the optimal mutation-based algorithm for LO and OneMax, i.e., which algorithm minimizes the expected number of fitness evaluations. This includes the choice of the optimal mutation rate.
A New Method for Lower Bounds on the Running Time of Evolutionary Algorithms
6,049
Evolutionary algorithms are popular heuristics for solving various combinatorial problems as they are easy to apply and often produce good results. Island models parallelize evolution by using different populations, called islands, which are connected by a graph structure as communication topology. Each island periodically communicates copies of good solutions to neighboring islands in a process called migration. We consider the speedup gained by island models in terms of the parallel running time for problems from combinatorial optimization: sorting (as maximization of sortedness), shortest paths, and Eulerian cycles. Different search operators are considered. The results show in which settings and up to what degree evolutionary algorithms can be parallelized efficiently. Along the way, we also investigate how island models deal with plateaus. In particular, we show that natural settings lead to exponential vs. logarithmic speedups, depending on the frequency of migration.
Analysis of Speedups in Parallel Evolutionary Algorithms for Combinatorial Optimization
6,050
In this paper we propose a crossover operator for evolutionary algorithms with real values that is based on the statistical theory of population distributions. The operator is based on the theoretical distribution of the values of the genes of the best individuals in the population. The proposed operator takes into account the localization and dispersion features of the best individuals of the population with the objective that these features would be inherited by the offspring. Our aim is the optimization of the balance between exploration and exploitation in the search process. In order to test the efficiency and robustness of this crossover, we have used a set of functions to be optimized with regard to different criteria, such as, multimodality, separability, regularity and epistasis. With this set of functions we can extract conclusions in function of the problem at hand. We analyze the results using ANOVA and multiple comparison statistical tests. As an example of how our crossover can be used to solve artificial intelligence problems, we have applied the proposed model to the problem of obtaining the weight of each network in a ensemble of neural networks. The results obtained are above the performance of standard methods.
CIXL2: A Crossover Operator for Evolutionary Algorithms Based on Population Features
6,051
Spiking neural networks have been referred to as the third generation of artificial neural networks where the information is coded as time of the spikes. There are a number of different spiking neuron models available and they are categorized based on their level of abstraction. In addition, there are two known learning methods, unsupervised and supervised learning. This thesis focuses on supervised learning where a new algorithm is proposed, based on genetic algorithms. The proposed algorithm is able to train both synaptic weights and delays and also allow each neuron to emit multiple spikes thus taking full advantage of the spatial-temporal coding power of the spiking neurons. In addition, limited synaptic precision is applied; only six bits are used to describe and train a synapse, three bits for the weights and three bits for the delays. Two limited precision schemes are investigated. The proposed algorithm is tested on the XOR classification problem where it produces better results for even smaller network architectures than the proposed ones. Furthermore, the algorithm is benchmarked on the Fisher iris classification problem where it produces higher classification accuracies compared to SpikeProp, QuickProp and Rprop. Finally, a hardware implementation on a microcontroller is done for the XOR problem as a proof of concept. Keywords: Spiking neural networks, supervised learning, limited synaptic precision, genetic algorithms, hardware implementation.
Developing a supervised training algorithm for limited precision feed-forward spiking neural networks
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This is a preprint of a book chapter from the Handbook of Memetic Algorithms, Studies in Computational Intelligence, Vol. 379, ISBN 978-3-642-23246-6, Springer, edited by F. Neri, C. Cotta, and P. Moscato. It is devoted to the parametrization of memetic algorithms and how to find a good balance between global and local search.
Memetic Algorithms: Parametrization and Balancing Local and Global Search
6,053
Evolvable hardware (EHW) is a set of techniques that are based on the idea of combining reconfiguration hardware systems with evolutionary algorithms. In other word, EHW has two sections; the reconfigurable hardware and evolutionary algorithm where the configurations are under the control of an evolutionary algorithm. This paper, suggests a method to design and optimize the synchronous sequential circuits. Genetic algorithm (GA) was applied as evolutionary algorithm. In this approach, for building input combinational logic circuit of each DFF, and also output combinational logic circuit, the cell arrays have been used. The obtained results show that our method can reduce the average number of generations by limitation the search space.
Using Genetic Algorithm in the Evolutionary Design of Sequential Logic Circuits
6,054
Evolutionary algorithms (EAs), simulating the evolution process of natural species, are used to solve optimization problems. Crossover (also called recombination), originated from simulating the chromosome exchange phenomena in zoogamy reproduction, is widely employed in EAs to generate offspring solutions, of which the effectiveness has been examined empirically in applications. However, due to the irregularity of crossover operators and the complicated interactions to mutation, crossover operators are hard to analyze and thus have few theoretical results. Therefore, analyzing crossover not only helps in understanding EAs, but also helps in developing novel techniques for analyzing sophisticated metaheuristic algorithms. In this paper, we derive the General Markov Chain Switching Theorem (GMCST) to facilitate theoretical studies of crossover-enabled EAs. The theorem allows us to analyze the running time of a sophisticated EA from an easy-to-analyze EA. Using this tool, we analyze EAs with several crossover operators on the LeadingOnes and OneMax problems, which are noticeably two well studied problems for mutation-only EAs but with few results for crossover-enabled EAs. We first derive the bounds of running time of the (2+2)-EA with crossover operators; then we study the running time gap between the mutation-only (2:2)-EA and the (2:2)-EA with crossover operators; finally, we develop strategies that apply crossover operators only when necessary, which improve from the mutation-only as well as the crossover-all-the-time (2:2)-EA. The theoretical results are verified by experiments.
Towards Analyzing Crossover Operators in Evolutionary Search via General Markov Chain Switching Theorem
6,055
The quadratic assignment problem (QAP) is one of the most difficult combinatorial optimization problems. One of the most powerful and commonly used heuristics to obtain approximations to the optimal solution of the QAP is simulated annealing (SA). We present an efficient implementation of the SA heuristic which performs more than 100 times faster then existing implementations for large problem sizes and a large number of SA iterations.
An efficient implementation of the simulated annealing heuristic for the quadratic assignment problem
6,056
Power dissipation in sequential circuits is due to increased toggling count of Circuit under Test, which depends upon test vectors applied. If successive test vectors sequences have more toggling nature then it is sure that toggling rate of flip flops is higher. Higher toggling for flip flops results more power dissipation. To overcome this problem, one method is to use GA to have test vectors of high fault coverage in short interval, followed by Hamming distance management on test patterns. This approach is time consuming and needs more efforts. Another method which is purposed in this paper is a PSO based Frame Work to optimize power dissipation. Here target is to set the entire test vector in a frame for time period 'T', so that the frame consists of all those vectors strings which not only provide high fault coverage but also arrange vectors in frame to produce minimum toggling.
Particle Swarm Optimization Framework for Low Power Testing of VLSI Circuits
6,057
Mixed strategy EAs aim to integrate several mutation operators into a single algorithm. However few theoretical analysis has been made to answer the question whether and when the performance of mixed strategy EAs is better than that of pure strategy EAs. In theory, the performance of EAs can be measured by asymptotic convergence rate and asymptotic hitting time. In this paper, it is proven that given a mixed strategy (1+1) EAs consisting of several mutation operators, its performance (asymptotic convergence rate and asymptotic hitting time)is not worse than that of the worst pure strategy (1+1) EA using one mutation operator; if these mutation operators are mutually complementary, then it is possible to design a mixed strategy (1+1) EA whose performance is better than that of any pure strategy (1+1) EA using one mutation operator.
Pure Strategy or Mixed Strategy?
6,058
Customer Relationship Management becomes a leading business strategy in highly competitive business environment. It aims to enhance the performance of the businesses by improving the customer satisfaction and loyalty. The objective of this paper is to improve customer satisfaction on product's colors and design with the help of the expert system developed by using Artificial Neural Networks. The expert system's role is to capture the knowledge of the experts and the data from the customer requirements, and then, process the collected data and form the appropriate rules for choosing product's colors and design. In order to identify the hidden pattern of the customer's needs, the Artificial Neural Networks technique has been applied to classify the colors and design based upon a list of selected information. Moreover, the expert system has the capability to make decisions in ranking the scores of the colors and design presented in the selection. In addition, the expert system has been validated with a different customer types.
The Expert System Designed to Improve Customer Satisfaction
6,059
The rapid advances in the field of optimization methods in many pure and applied science pose the difficulty of keeping track of the developments as well as selecting an appropriate technique that best suits the problem in-hand. From a practitioner point of view is rightful to wander "which optimization method is the best for my problem?". Looking at the optimization process as a "system" of intercon- nected parts, in this paper are collected some ideas about how to tackle an optimization problem using a class of tools from evolutionary computations called Genetic Algorithms. Despite the number of optimization techniques available nowadays the author of this paper thinks that Genetic Algorithms still play a central role for their versatility, robustness, theoretical framework and simplicity of use. The paper can be considered a "collection of tips" (from literature and personal experience) for the non-computer-scientist that has to deal with optimization problems both in the science and engineering practice. No original methods or algorithms are proposed.
Between theory and practice: guidelines for an optimization scheme with genetic algorithms - Part I: single-objective continuous global optimization
6,060
Two complementary techniques for analyzing search spaces are proposed: (i) an algorithm to detect search points with potential to be local optima; and (ii) a slightly adjusted Wang-Landau sampling algorithm to explore larger search spaces. The detection algorithm assumes that local optima are points which are easier to reach and harder to leave by a slow adaptive walker. A slow adaptive walker moves to a nearest fitter point. Thus, points with larger outgoing step sizes relative to incoming step sizes are marked using the local optima score formulae as potential local optima points (PLOPs). Defining local optima in these more general terms allows their detection within the closure of a subset of a search space, and the sampling of a search space unshackled by a particular move set. Tests are done with NK and HIFF problems to confirm that PLOPs detected in the manner proposed retain characteristics of local optima, and that the adjusted Wang-Landau samples are more representative of the search space than samples produced by choosing points uniformly at random. While our approach shows promise, more needs to be done to reduce its computation cost that it may pave a way toward analyzing larger search spaces of practical meaning.
Search space analysis with Wang-Landau sampling and slow adaptive walks
6,061
Robot design complexity is increasing day by day especially in automated industries. In this paper we propose biologically inspired design framework for robots in dynamic world on the basis of Co-Evolution, Virtual Ecology, Life time learning which are derived from biological creatures. We have created a virtual khepera robot in Framsticks and tested its operational credibility in terms hardware and software components by applying the above suggested techniques. Monitoring complex and non complex behaviors in different environments and obtaining the parameters that influence software and hardware design of the robot that influence anticipated and unanticipated failures, control programs of robot generation are the major concerns of our techniques.
Biologically inspired design framework for Robot in Dynamic Environments using Framsticks
6,062
This short paper introduces a new way by which to design production system rules. An indirect encoding scheme is presented which views such rules as protein complexes produced by the temporal behaviour of an artificial genetic regulatory network. This initial study begins by using a simple Boolean regulatory network to produce traditional ternary-encoded rules before moving to a fuzzy variant to produce real-valued rules. Competitive performance is shown with related genetic regulatory networks and rule-based systems on benchmark problems.
Production System Rules as Protein Complexes from Genetic Regulatory Networks
6,063
We investigate the self-organising behaviour of Digital Ecosystems, because a primary motivation for our research is to exploit the self-organising properties of biological ecosystems. We extended a definition for the complexity, grounded in the biological sciences, providing a measure of the information in an organism's genome. Next, we extended a definition for the stability, originating from the computer sciences, based upon convergence to an equilibrium distribution. Finally, we investigated a definition for the diversity, relative to the selection pressures provided by the user requests. We conclude with a summary and discussion of the achievements, including the experimental results.
Self-Organisation of Evolving Agent Populations in Digital Ecosystems
6,064
In the last decades, complex networks theory significantly influenced other disciplines on the modeling of both static and dynamic aspects of systems observed in nature. This work aims to investigate the effects of networks' topological features on the dynamics of an evolutionary algorithm, considering in particular the ability to find a large number of optima on multi-modal problems. We introduce a novel spatially-structured evolutionary algorithm and we apply it on two combinatorial problems: ONEMAX and the multi-modal NMAX. Considering three different network models we investigate the relationships between their features, algorithm's convergence and its ability to find multiple optima (for the multi-modal problem). In order to perform a deeper analysis we investigate the introduction of weighted graphs with time-varying weights. The results show that networks with a large Average Path Length lead to an higher number of optima and a consequent slow exploration dynamics (i.e. low First Hitting Time). Furthermore, the introduction of weighted networks shows the possibility to tune algorithm's dynamics during its execution with the parameter related with weights' change. This work gives a first answer about the effects of various graph topologies on the diversity of evolutionary algorithms and it describes a simple but powerful algorithmic framework which allows to investigate many aspects of ssEAs dynamics.
Influence of Topological Features on Spatially-Structured Evolutionary Algorithms Dynamics
6,065
Nowadays hybrid evolutionary algorithms, i.e, heuristic search algorithms combining several mutation operators some of which are meant to implement stochastically a well known technique designed for the specific problem in question while some others playing the role of random search, have become rather popular for tackling various NP-hard optimization problems. While empirical studies demonstrate that hybrid evolutionary algorithms are frequently successful at finding solutions having fitness sufficiently close to the optimal, many fewer articles address the computational complexity in a mathematically rigorous fashion. This paper is devoted to a mathematically motivated design and analysis of a parameterized family of evolutionary algorithms which provides a polynomial time approximation scheme for one of the well-known NP-hard combinatorial optimization problems, namely the "single machine scheduling problem without precedence constraints". The authors hope that the techniques and ideas developed in this article may be applied in many other situations.
A Polynomial Time Approximation Scheme for a Single Machine Scheduling Problem Using a Hybrid Evolutionary Algorithm
6,066
Applications of ACO algorithms to obtain better solutions for combinatorial optimization problems have become very popular in recent years. In ACO algorithms, group of agents repeatedly perform well defined actions and collaborate with other ants in order to accomplish the defined task. In this paper, we introduce new mechanisms for selecting the Elite ants dynamically based on simple statistical tools. We also investigate the performance of newly proposed mechanisms.
Statistical Approach for Selecting Elite Ants
6,067
Handwritten Numeral recognition plays a vital role in postal automation services especially in countries like India where multiple languages and scripts are used Discrete Hidden Markov Model (HMM) and hybrid of Neural Network (NN) and HMM are popular methods in handwritten word recognition system. The hybrid system gives better recognition result due to better discrimination capability of the NN. A major problem in handwriting recognition is the huge variability and distortions of patterns. Elastic models based on local observations and dynamic programming such HMM are not efficient to absorb this variability. But their vision is local. But they cannot face to length variability and they are very sensitive to distortions. Then the SVM is used to estimate global correlations and classify the pattern. Support Vector Machine (SVM) is an alternative to NN. In Handwritten recognition, SVM gives a better recognition result. The aim of this paper is to develop an approach which improve the efficiency of handwritten recognition using artificial neural network
Handwritten digit Recognition using Support Vector Machine
6,068
We show that for all $1<k \leq \log n$ the $k$-ary unbiased black-box complexity of the $n$-dimensional $\onemax$ function class is $O(n/k)$. This indicates that the power of higher arity operators is much stronger than what the previous $O(n/\log k)$ bound by Doerr et al. (Faster black-box algorithms through higher arity operators, Proc. of FOGA 2011, pp. 163--172, ACM, 2011) suggests. The key to this result is an encoding strategy, which might be of independent interest. We show that, using $k$-ary unbiased variation operators only, we may simulate an unrestricted memory of size $O(2^k)$ bits.
Reducing the Arity in Unbiased Black-Box Complexity
6,069
The computational complexity analysis of genetic programming (GP) has been started recently by analyzing simple (1+1) GP algorithms for the problems ORDER and MAJORITY. In this paper, we study how taking the complexity as an additional criteria influences the runtime behavior. We consider generalizations of ORDER and MAJORITY and present a computational complexity analysis of (1+1) GP using multi-criteria fitness functions that take into account the original objective and the complexity of a syntax tree as a secondary measure. Furthermore, we study the expected time until population-based multi-objective genetic programming algorithms have computed the Pareto front when taking the complexity of a syntax tree as an equally important objective.
Computational Complexity Analysis of Multi-Objective Genetic Programming
6,070
In this paper, we present a new mutation operator, Hybrid Mutation (HPRM), for a genetic algorithm that generates high quality solutions to the Traveling Salesman Problem (TSP). The Hybrid Mutation operator constructs an offspring from a pair of parents by hybridizing two mutation operators, PSM and RSM. The efficiency of the HPRM is compared as against some existing mutation operators; namely, Reverse Sequence Mutation (RSM) and Partial Shuffle Mutation (PSM) for BERLIN52 as instance of TSPLIB. Experimental results show that the new mutation operator is better than the RSM and PSM.
Hybridizing PSM and RSM Operator for Solving NP-Complete Problems: Application to Travelling Salesman Problem
6,071
The hardness of fitness functions is an important research topic in the field of evolutionary computation. In theory, the study can help understanding the ability of evolutionary algorithms. In practice, the study may provide a guideline to the design of benchmarks. The aim of this paper is to answer the following research questions: Given a fitness function class, which functions are the easiest with respect to an evolutionary algorithm? Which are the hardest? How are these functions constructed? The paper provides theoretical answers to these questions. The easiest and hardest fitness functions are constructed for an elitist (1+1) evolutionary algorithm to maximise a class of fitness functions with the same optima. It is demonstrated that the unimodal functions are the easiest and deceptive functions are the hardest in terms of the time-fitness landscape. The paper also reveals that the easiest fitness function to one algorithm may become the hardest to another algorithm, and vice versa.
On the Easiest and Hardest Fitness Functions
6,072
Today, robotics is an auspicious and fast-growing branch of technology that involves the manufacturing, design, and maintenance of robot machines that can operate in an autonomous fashion and can be used in a wide variety of applications including space exploration, weaponry, household, and transportation. More particularly, in space applications, a common type of robots has been of widespread use in the recent years. It is called planetary rover which is a robot vehicle that moves across the surface of a planet and conducts detailed geological studies pertaining to the properties of the landing cosmic environment. However, rovers are always impeded by obstacles along the traveling path which can destabilize the rover's body and prevent it from reaching its goal destination. This paper proposes an ANN model that allows rover systems to carry out autonomous path-planning to successfully navigate through challenging planetary terrains and follow their goal location while avoiding dangerous obstacles. The proposed ANN is a multilayer network made out of three layers: an input, a hidden, and an output layer. The network is trained in offline mode using back-propagation supervised learning algorithm. A software-simulated rover was experimented and it revealed that it was able to follow the safest trajectory despite existing obstacles. As future work, the proposed ANN is to be parallelized so as to speed-up the execution time of the training process.
Neural Network Model for Path-Planning of Robotic Rover Systems
6,073
Today, a wide variety of probabilistic and expert AI systems used to analyze real world inputs such as unstructured text, sounds, images, and statistical data. However, all these systems exist on different platforms, with different implementations, and with very different, often very specific goals in mind. This paper introduces a concept for a mediator framework for such systems and seeks to show several architectures which would support it, potential benefits in combining the signals of disparate networks for formalized, high level logic and signal processing, and its possible academic and industrial uses.
Managing contextual artificial neural networks with a service-based mediator
6,074
Spike-Timing Dependent Plasticity (STDP) is believed to play an important role in learning and the formation of computational function in the brain. The classical model of STDP which considers the timing between pairs of pre-synaptic and post-synaptic spikes (p-STDP) is incapable of reproducing synaptic weight changes similar to those seen in biological experiments which investigate the effect of either higher order spike trains (e.g. triplet and quadruplet of spikes), or, simultaneous effect of the rate and timing of spike pairs on synaptic plasticity. In this paper, we firstly investigate synaptic weight changes using a p-STDP circuit and show how it fails to reproduce the mentioned complex biological experiments. We then present a new STDP VLSI circuit which acts based on the timing among triplets of spikes (t-STDP) that is able to reproduce all the mentioned experimental results. We believe that our new STDP VLSI circuit improves upon previous circuits, whose learning capacity exceeds current designs due to its capability of mimicking the outcomes of biological experiments more closely; thus plays a significant role in future VLSI implementation of neuromorphic systems.
Efficient Design of Triplet Based Spike-Timing Dependent Plasticity
6,075
This paper describes the application of a real coded genetic algorithm (GA) to align two or more 2-D images by means of image registration. The proposed search strategy is a transformation parameters-based approach involving the affine transform. The real coded GA uses Simulated Binary Crossover (SBX), a parent-centric recombination operator that has shown to deliver a good performance in many optimization problems in the continuous domain. In addition, we propose a new technique for matching points between a warped and static images by using a randomized ordering when visiting the points during the matching procedure. This new technique makes the evaluation of the objective function somewhat noisy, but GAs and other population-based search algorithms have been shown to cope well with noisy fitness evaluations. The results obtained are competitive to those obtained by state-of-the-art classical methods in image registration, confirming the usefulness of the proposed noisy objective function and the suitability of SBX as a recombination operator for this type of problem.
Affine Image Registration Transformation Estimation Using a Real Coded Genetic Algorithm with SBX
6,076
This paper presents a novel mechanism to adapt surrogate-assisted population-based algorithms. This mechanism is applied to ACM-ES, a recently proposed surrogate-assisted variant of CMA-ES. The resulting algorithm, saACM-ES, adjusts online the lifelength of the current surrogate model (the number of CMA-ES generations before learning a new surrogate) and the surrogate hyper-parameters. Both heuristics significantly improve the quality of the surrogate model, yielding a significant speed-up of saACM-ES compared to the ACM-ES and CMA-ES baselines. The empirical validation of saACM-ES on the BBOB-2012 noiseless testbed demonstrates the efficiency and the scalability w.r.t the problem dimension and the population size of the proposed approach, that reaches new best results on some of the benchmark problems.
Self-Adaptive Surrogate-Assisted Covariance Matrix Adaptation Evolution Strategy
6,077
The placement of wind turbines on a given area of land such that the wind farm produces a maximum amount of energy is a challenging optimization problem. In this article, we tackle this problem, taking into account wake effects that are produced by the different turbines on the wind farm. We significantly improve upon existing results for the minimization of wake effects by developing a new problem-specific local search algorithm. One key step in the speed-up of our algorithm is the reduction in computation time needed to assess a given wind farm layout compared to previous approaches. Our new method allows the optimization of large real-world scenarios within a single night on a standard computer, whereas weeks on specialized computing servers were required for previous approaches.
A Fast and Effective Local Search Algorithm for Optimizing the Placement of Wind Turbines
6,078
The capability of discretization of matrix elements in the problem of quadratic functional minimization with linear member built on matrix in N-dimensional configuration space with discrete coordinates is researched. It is shown, that optimal procedure of replacement matrix elements by the integer quantities with the limited number of gradations exist, and the efficient of minimization does not reduce. Parameter depends on matrix properties, which allows estimate the capability of using described procedure for given type of matrix, is found. Computational complexities of algorithm and RAM requirements are reduced by 16 times, correct using of integer elements allows increase minimization algorithm speed by the orders.
Discretization of a matrix in the problem of quadratic functional binary minimization
6,079
A large part of the workforce, and growing every day, is originally from India. India one of the second largest populations in the world, they have a lot to offer in terms of jobs. The sheer number of IT workers makes them a formidable travelling force as well, easily picking up employment in English speaking countries. The beginning of the economic crises since 2008 September, many Indians have return homeland, and this has had a substantial impression on the Indian Rupee (INR) as liken to the US Dollar (USD). We are using numerational knowledge based techniques for forecasting has been proved highly successful in present time. The purpose of this paper is to examine the effects of several important neural network factors on model fitting and forecasting the behaviours. In this paper, Artificial Neural Network has successfully been used for exchange rate forecasting. This paper examines the effects of the number of inputs and hidden nodes and the size of the training sample on the in-sample and out-of-sample performance. The Indian Rupee (INR) / US Dollar (USD) is used for detailed examinations. The number of input nodes has a greater impact on performance than the number of hidden nodes, while a large number of observations do reduce forecast errors.
Forecasting of Indian Rupee (INR) / US Dollar (USD) Currency Exchange Rate Using Artificial Neural Network
6,080
This paper explores the theoretical basis of the covariance matrix adaptation evolution strategy (CMA-ES) from the information geometry viewpoint. To establish a theoretical foundation for the CMA-ES, we focus on a geometric structure of a Riemannian manifold of probability distributions equipped with the Fisher metric. We define a function on the manifold which is the expectation of fitness over the sampling distribution, and regard the goal of update of the parameters of sampling distribution in the CMA-ES as maximization of the expected fitness. We investigate the steepest ascent learning for the expected fitness maximization, where the steepest ascent direction is given by the natural gradient, which is the product of the inverse of the Fisher information matrix and the conventional gradient of the function. Our first result is that we can obtain under some types of parameterization of multivariate normal distribution the natural gradient of the expected fitness without the need for inversion of the Fisher information matrix. We find that the update of the distribution parameters in the CMA-ES is the same as natural gradient learning for expected fitness maximization. Our second result is that we derive the range of learning rates such that a step in the direction of the exact natural gradient improves the parameters in the expected fitness. We see from the close relation between the CMA-ES and natural gradient learning that the default setting of learning rates in the CMA-ES seems suitable in terms of monotone improvement in expected fitness. Then, we discuss the relation to the expectation-maximization framework and provide an information geometric interpretation of the CMA-ES.
Theoretical foundation for CMA-ES from information geometric perspective
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In this paper, we study the performance of IPOP-saACM-ES, recently proposed self-adaptive surrogate-assisted Covariance Matrix Adaptation Evolution Strategy. The algorithm was tested using restarts till a total number of function evaluations of $10^6D$ was reached, where $D$ is the dimension of the function search space. The experiments show that the surrogate model control allows IPOP-saACM-ES to be as robust as the original IPOP-aCMA-ES and outperforms the latter by a factor from 2 to 3 on 6 benchmark problems with moderate noise. On 15 out of 30 benchmark problems in dimension 20, IPOP-saACM-ES exceeds the records observed during BBOB-2009 and BBOB-2010.
Black-box optimization benchmarking of IPOP-saACM-ES on the BBOB-2012 noisy testbed
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The Artificial Bee Colony (ABC) is the name of an optimization algorithm that was inspired by the intelligent behavior of a honey bee swarm. It is widely recognized as a quick, reliable, and efficient methods for solving optimization problems. This paper proposes a hybrid ABC (HABC) algorithm for graph 3-coloring, which is a well-known discrete optimization problem. The results of HABC are compared with results of the well-known graph coloring algorithms of today, i.e. the Tabucol and Hybrid Evolutionary algorithm (HEA) and results of the traditional evolutionary algorithm with SAW method (EA-SAW). Extensive experimentations has shown that the HABC matched the competitive results of the best graph coloring algorithms, and did better than the traditional heuristics EA-SAW when solving equi-partite, flat, and random generated medium-sized graphs.
A Hybrid Artificial Bee Colony Algorithm for Graph 3-Coloring
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Prior studies have generally suggested that Artificial Neural Networks (ANNs) are superior to conventional statistical models in predicting consumer buying behavior. There are, however, contradicting findings which raise question over usefulness of ANNs. This paper discusses development of three neural networks for modeling consumer e-commerce behavior and compares the findings to equivalent logistic regression models. The results showed that ANNs predict e-commerce adoption slightly more accurately than logistic models but this is hardly justifiable given the added complexity. Further, ANNs seem to be highly adaptive, particularly when a small sample is coupled with a large number of nodes in hidden layers which, in turn, limits the neural networks' generalisability.
On applying Neuro - Computing in E-com Domain
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The paper introduces a connectionist network approach to find numerical solutions of Diophantine equations as an attempt to address the famous Hilbert's tenth problem. The proposed methodology uses a three layer feed forward neural network with back propagation as sequential learning procedure to find numerical solutions of a class of Diophantine equations. It uses a dynamically constructed network architecture where number of nodes in the input layer is chosen based on the number of variables in the equation. The powers of the given Diophantine equation are taken as input to the input layer. The training of the network starts with initial random integral weights. The weights are updated based on the back propagation of the error values at the output layer. The optimization of weights is augmented by adding a momentum factor into the network. The optimized weights of the connection between the input layer and the hidden layer are taken as numerical solution of the given Diophantine equation. The procedure is validated using different Diophantine Equations of different number of variables and different powers.
A Connectionist Network Approach to Find Numerical Solutions of Diophantine Equations
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We present a new method for analyzing the running time of parallel evolutionary algorithms with spatially structured populations. Based on the fitness-level method, it yields upper bounds on the expected parallel running time. This allows to rigorously estimate the speedup gained by parallelization. Tailored results are given for common migration topologies: ring graphs, torus graphs, hypercubes, and the complete graph. Example applications for pseudo-Boolean optimization show that our method is easy to apply and that it gives powerful results. In our examples the possible speedup increases with the density of the topology. Surprisingly, even sparse topologies like ring graphs lead to a significant speedup for many functions while not increasing the total number of function evaluations by more than a constant factor. We also identify which number of processors yield asymptotically optimal speedups, thus giving hints on how to parametrize parallel evolutionary algorithms.
General Upper Bounds on the Running Time of Parallel Evolutionary Algorithms
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An algorithm (bliss) is proposed to speed up the construction of slow adaptive walks. Slow adaptive walks are adaptive walks biased towards closer points or smaller move steps. They were previously introduced to explore a search space, e.g. to detect potential local optima or to assess the ruggedness of a fitness landscape. To avoid the quadratic cost of computing Hamming distance (HD) for all-pairs of strings in a set in order to find the set of closest strings for each string, strings are sorted and clustered by bliss such that similar strings are more likely to get paired off for HD computation. To efficiently arrange the strings by similarity, bliss employs the idea of shared non-overlapping position specific subsequences between strings which is inspired by an alignment-free protein sequence comparison algorithm. Tests are performed to evaluate the quality of b-walks, i.e. slow adaptive walks constructed from the output of bliss, on enumerated search spaces. Finally, b-walks are applied to explore larger search spaces with the help of Wang-Landau sampling.
Speeding up the construction of slow adaptive walks
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In this research paper, the problem of optimization of quadratic forms associated with the dynamics of Hopfield-Amari neural network is considered. An elegant (and short) proof of the states at which local/global minima of quadratic form are attained is provided. A theorem associated with local/global minimization of quadratic energy function using the Hopfield-Amari neural network is discussed. The results are generalized to a "Complex Hopfield neural network" dynamics over the complex hypercube (using a "complex signum function"). It is also reasoned through two theorems that there is no loss of generality in assuming the threshold vector to be a zero vector in the case of real as well as a "Complex Hopfield neural network". Some structured quadratic forms like Toeplitz form and Complex Toeplitz form are discussed.
Optimization of Real, Hermitian Quadratic Forms: Real, Complex Hopfield-Amari Neural Network
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In this paper, we study the performance of IPOP-saACM-ES and BIPOP-saACM-ES, recently proposed self-adaptive surrogate-assisted Covariance Matrix Adaptation Evolution Strategies. Both algorithms were tested using restarts till a total number of function evaluations of $10^6D$ was reached, where $D$ is the dimension of the function search space. We compared surrogate-assisted algorithms with their surrogate-less versions IPOP-saACM-ES and BIPOP-saACM-ES, two algorithms with one of the best overall performance observed during the BBOB-2009 and BBOB-2010. The comparison shows that the surrogate-assisted versions outperform the original CMA-ES algorithms by a factor from 2 to 4 on 8 out of 24 noiseless benchmark problems, showing the best results among all algorithms of the BBOB-2009 and BBOB-2010 on Ellipsoid, Discus, Bent Cigar, Sharp Ridge and Sum of different powers functions.
Black-box optimization benchmarking of IPOP-saACM-ES and BIPOP-saACM-ES on the BBOB-2012 noiseless testbed
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The all-pairs shortest path problem is the first non-artificial problem for which it was shown that adding crossover can significantly speed up a mutation-only evolutionary algorithm. Recently, the analysis of this algorithm was refined and it was shown to have an expected optimization time (w.r.t. the number of fitness evaluations) of $\Theta(n^{3.25}(\log n)^{0.25})$. In contrast to this simple algorithm, evolutionary algorithms used in practice usually employ refined recombination strategies in order to avoid the creation of infeasible offspring. We study extensions of the basic algorithm by two such concepts which are central in recombination, namely \emph{repair mechanisms} and \emph{parent selection}. We show that repairing infeasible offspring leads to an improved expected optimization time of $\mathord{O}(n^{3.2}(\log n)^{0.2})$. As a second part of our study we prove that choosing parents that guarantee feasible offspring results in an even better optimization time of $\mathord{O}(n^{3}\log n)$. Both results show that already simple adjustments of the recombination operator can asymptotically improve the runtime of evolutionary algorithms.
More Effective Crossover Operators for the All-Pairs Shortest Path Problem
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A significantly under-explored area of evolutionary optimization in the literature is the study of optimization methodologies that can evolve along with the problems solved. Particularly, present evolutionary optimization approaches generally start their search from scratch or the ground-zero state of knowledge, independent of how similar the given new problem of interest is to those optimized previously. There has thus been the apparent lack of automated knowledge transfers and reuse across problems. Taking the cue, this paper introduces a novel Memetic Computational Paradigm for search, one that models after how human solves problems, and embarks on a study towards intelligent evolutionary optimization of problems through the transfers of structured knowledge in the form of memes learned from previous problem-solving experiences, to enhance future evolutionary searches. In particular, the proposed memetic search paradigm is composed of four culture-inspired operators, namely, Meme Learning, Meme Selection, Meme Variation and Meme Imitation. The learning operator mines for memes in the form of latent structures derived from past experiences of problem-solving. The selection operator identifies the fit memes that replicate and transmit across problems, while the variation operator introduces innovations into the memes. The imitation operator, on the other hand, defines how fit memes assimilate into the search process of newly encountered problems, thus gearing towards efficient and effective evolutionary optimization. Finally, comprehensive studies on two widely studied challenging well established NP-hard routing problem domains, particularly, the capacitated vehicle routing (CVR) and capacitated arc routing (CAR), confirm the high efficacy of the proposed memetic computational search paradigm for intelligent evolutionary optimization of problems.
Meme as Building Block for Evolutionary Optimization of Problem Instances
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Partial classification popularly known as nugget discovery comes under descriptive knowledge discovery. It involves mining rules for a target class of interest. Classification "If-Then" rules are the most sought out by decision makers since they are the most comprehensible form of knowledge mined by data mining techniques. The rules have certain properties namely the rule metrics which are used to evaluate them. Mining rules with user specified properties can be considered as a multi-objective optimization problem since the rules have to satisfy more than one property to be used by the user. Cultural algorithm (CA) with its knowledge sources have been used in solving many optimization problems. However research gap exists in using cultural algorithm for multi-objective optimization of rules. In the current study a multi-objective cultural algorithm is proposed for partial classification. Results of experiments on benchmark data sets reveal good performance.
Nugget Discovery with a Multi-objective Cultural Algorithm
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The last decade has seen the parallel emergence in computational neuroscience and machine learning of neural network structures which spread the input signal randomly to a higher dimensional space; perform a nonlinear activation; and then solve for a regression or classification output by means of a mathematical pseudoinverse operation. In the field of neuromorphic engineering, these methods are increasingly popular for synthesizing biologically plausible neural networks, but the "learning method" - computation of the pseudoinverse by singular value decomposition - is problematic both for biological plausibility and because it is not an online or an adaptive method. We present an online or incremental method of computing the pseudoinverse, which we argue is biologically plausible as a learning method, and which can be made adaptable for non-stationary data streams. The method is significantly more memory-efficient than the conventional computation of pseudoinverses by singular value decomposition.
Learning the Pseudoinverse Solution to Network Weights
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We have employed a recent implementation of genetic algorithms to study a range of standard benchmark functions for global optimization. It turns out that some of them are not very useful as challenging test functions, since they neither allow for a discrimination between different variants of genetic operators nor exhibit a dimensionality scaling resembling that of real-world problems, for example that of global structure optimization of atomic and molecular clusters. The latter properties seem to be simulated better by two other types of benchmark functions. One type is designed to be deceptive, exemplified here by Lunacek's function. The other type offers additional advantages of markedly increased complexity and of broad tunability in search space characteristics. For the latter type, we use an implementation based on randomly distributed Gaussians. We advocate the use of the latter types of test functions for algorithm development and benchmarking.
Empirical review of standard benchmark functions using evolutionary global optimization
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VEGAS (Varying Evolvability-Guided Adaptive Search) is a new methodology proposed to deal with the neutrality property of some optimization problems. ts main feature is to consider the whole neutral network rather than an arbitrary solution. Moreover, VEGAS is designed to escape from plateaus based on the evolvability of solution and a multi-armed bandit. Experiments are conducted on NK-landscapes with neutrality. Results show the importance of considering the whole neutral network and of guiding the search cleverly. The impact of the level of neutrality and of the exploration-exploitation trade-off are deeply analyzed.
The Road to VEGAS: Guiding the Search over Neutral Networks
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The field of evolutionary computation is inspired by the achievements of natural evolution, in which there is no final objective. Yet the pursuit of objectives is ubiquitous in simulated evolution. A significant problem is that objective approaches assume that intermediate stepping stones will increasingly resemble the final objective when in fact they often do not. The consequence is that while solutions may exist, searching for such objectives may not discover them. This paper highlights the importance of leveraging human insight during search as an alternative to articulating explicit objectives. In particular, a new approach called novelty-assisted interactive evolutionary computation (NA-IEC) combines human intuition with novelty search for the first time to facilitate the serendipitous discovery of agent behaviors. In this approach, the human user directs evolution by selecting what is interesting from the on-screen population of behaviors. However, unlike in typical IEC, the user can now request that the next generation be filled with novel descendants. The experimental results demonstrate that combining human insight with novelty search finds solutions significantly faster and at lower genomic complexities than fully-automated processes, including pure novelty search, suggesting an important role for human users in the search for solutions.
Exploring Promising Stepping Stones by Combining Novelty Search with Interactive Evolution
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Designing a fast and efficient optimization method with local optima avoidance capability on a variety of optimization problems is still an open problem for many researchers. In this work, the concept of a new global optimization method with an open implementation area is introduced as a Curved Space Optimization (CSO) method, which is a simple probabilistic optimization method enhanced by concepts of general relativity theory. To address global optimization challenges such as performance and convergence, this new method is designed based on transformation of a random search space into a new search space based on concepts of space-time curvature in general relativity theory. In order to evaluate the performance of our proposed method, an implementation of CSO is deployed and its results are compared on benchmark functions with state-of-the art optimization methods. The results show that the performance of CSO is promising on unimodal and multimodal benchmark functions with different search space dimension sizes.
Curved Space Optimization: A Random Search based on General Relativity Theory
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The utilization of populations is one of the most important features of evolutionary algorithms (EAs). There have been many studies analyzing the impact of different population sizes on the performance of EAs. However, most of such studies are based computational experiments, except for a few cases. The common wisdom so far appears to be that a large population would increase the population diversity and thus help an EA. Indeed, increasing the population size has been a commonly used strategy in tuning an EA when it did not perform as well as expected for a given problem. He and Yao (2002) showed theoretically that for some problem instance classes, a population can help to reduce the runtime of an EA from exponential to polynomial time. This paper analyzes the role of population further in EAs and shows rigorously that large populations may not always be useful. Conditions, under which large populations can be harmful, are discussed in this paper. Although the theoretical analysis was carried out on one multi-modal problem using a specific type of EAs, it has much wider implications. The analysis has revealed certain problem characteristics, which can be either the problem considered here or other problems, that lead to the disadvantages of large population sizes. The analytical approach developed in this paper can also be applied to analyzing EAs on other problems.
A Large Population Size Can Be Unhelpful in Evolutionary Algorithms
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Very recently new genetic operators, called geometric semantic operators, have been defined for genetic programming. Contrarily to standard genetic operators, which are uniquely based on the syntax of the individuals, these new operators are based on their semantics, meaning with it the set of input-output pairs on training data. Furthermore, these operators present the interesting property of inducing a unimodal fitness landscape for every problem that consists in finding a match between given input and output data (for instance regression and classification). Nevertheless, the current definition of these operators has a serious limitation: they impose an exponential growth in the size of the individuals in the population, so their use is impossible in practice. This paper is intended to overcome this limitation, presenting a new genetic programming system that implements geometric semantic operators in an extremely efficient way. To demonstrate the power of the proposed system, we use it to solve a complex real-life application in the field of pharmacokinetic: the prediction of the human oral bioavailability of potential new drugs. Besides the excellent performances on training data, which were expected because the fitness landscape is unimodal, we also report an excellent generalization ability of the proposed system, at least for the studied application. In fact, it outperforms standard genetic programming and a wide set of other well-known machine learning methods.
An Efficient Genetic Programming System with Geometric Semantic Operators and its Application to Human Oral Bioavailability Prediction
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