Showing papers in "IEEE Transactions on Evolutionary Computation in 2006"
TL;DR: The comprehensive learning particle swarm optimizer (CLPSO) is presented, which uses a novel learning strategy whereby all other particles' historical best information is used to update a particle's velocity.
Abstract: This paper presents a variant of particle swarm optimizers (PSOs) that we call the comprehensive learning particle swarm optimizer (CLPSO), which uses a novel learning strategy whereby all other particles' historical best information is used to update a particle's velocity. This strategy enables the diversity of the swarm to be preserved to discourage premature convergence. Experiments were conducted (using codes available from http://www.ntu.edu.sg/home/epnsugan) on multimodal test functions such as Rosenbrock, Griewank, Rastrigin, Ackley, and Schwefel and composition functions both with and without coordinate rotation. The results demonstrate good performance of the CLPSO in solving multimodal problems when compared with eight other recent variants of the PSO.
3,217Â citations
TL;DR: The results show that the algorithm with self-adaptive control parameter settings is better than, or at least comparable to, the standard DE algorithm and evolutionary algorithms from literature when considering the quality of the solutions obtained.
Abstract: We describe an efficient technique for adapting control parameter settings associated with differential evolution (DE). The DE algorithm has been used in many practical cases and has demonstrated good convergence properties. It has only a few control parameters, which are kept fixed throughout the entire evolutionary process. However, it is not an easy task to properly set control parameters in DE. We present an algorithm-a new version of the DE algorithm-for obtaining self-adaptive control parameter settings that show good performance on numerical benchmark problems. The results show that our algorithm with self-adaptive control parameter settings is better than, or at least comparable to, the standard DE algorithm and evolutionary algorithms from literature when considering the quality of the solutions obtained
2,820Â citations
TL;DR: This paper systematically review and analyze many problems from the EA literature, each belonging to the important class of real-valued, unconstrained, multiobjective test problems, and presents a flexible toolkit for constructing well-designed test problems.
Abstract: When attempting to better understand the strengths and weaknesses of an algorithm, it is important to have a strong understanding of the problem at hand. This is true for the field of multiobjective evolutionary algorithms (EAs) as it is for any other field. Many of the multiobjective test problems employed in the EA literature have not been rigorously analyzed, which makes it difficult to draw accurate conclusions about the strengths and weaknesses of the algorithms tested on them. In this paper, we systematically review and analyze many problems from the EA literature, each belonging to the important class of real-valued, unconstrained, multiobjective test problems. To support this, we first introduce a set of test problem criteria, which are in turn supported by a set of definitions. Our analysis of test problems highlights a number of areas requiring attention. Not only are many test problems poorly constructed but also the important class of nonseparable problems, particularly nonseparable multimodal problems, is poorly represented. Motivated by these findings, we present a flexible toolkit for constructing well-designed test problems. We also present empirical results demonstrating how the toolkit can be used to test an optimizer in ways that existing test suites do not
1,567Â citations
TL;DR: Results show that NSGA-II, a popular multiobjective evolutionary algorithm, performs well compared with random search, even within the restricted number of evaluations used.
Abstract: This paper concerns multiobjective optimization in scenarios where each solution evaluation is financially and/or temporally expensive. We make use of nine relatively low-dimensional, nonpathological, real-valued functions, such as arise in many applications, and assess the performance of two algorithms after just 100 and 250 (or 260) function evaluations. The results show that NSGA-II, a popular multiobjective evolutionary algorithm, performs well compared with random search, even within the restricted number of evaluations used. A significantly better performance (particularly, in the worst case) is, however, achieved on our test set by an algorithm proposed herein-ParEGO-which is an extension of the single-objective efficient global optimization (EGO) algorithm of Jones et al. ParEGO uses a design-of-experiments inspired initialization procedure and learns a Gaussian processes model of the search landscape, which is updated after every function evaluation. Overall, ParEGO exhibits a promising performance for multiobjective optimization problems where evaluations are expensive or otherwise restricted in number.
979Â citations
TL;DR: An algorithm for calculating hypervolume exactly, the Hypervolume by Slicing Objectives (HSO) algorithm, that is faster than any that has previously been published and increases the utility of hypervolume, both as a metric for general optimization algorithms and as a diversity mechanism for evolutionary algorithms.
Abstract: We present an algorithm for calculating hypervolume exactly, the Hypervolume by Slicing Objectives (HSO) algorithm, that is faster than any that has previously been published. HSO processes objectives instead of points, an idea that has been considered before but that has never been properly evaluated in the literature. We show that both previously studied exact hypervolume algorithms are exponential in at least the number of objectives and that although HSO is also exponential in the number of objectives in the worst case, it runs in significantly less time, i.e., two to three orders of magnitude less for randomly generated and benchmark data in three to eight objectives. Thus, HSO increases the utility of hypervolume, both as a metric for general optimization algorithms and as a diversity mechanism for evolutionary algorithms.
697Â citations
TL;DR: The extensive use of the uncertainty information of predictions for screening the candidate solutions makes it possible to significantly reduce the computational cost of singleand multiobjective EA.
Abstract: This paper presents and analyzes in detail an efficient search method based on evolutionary algorithms (EA) assisted by local Gaussian random field metamodels (GRFM). It is created for the use in optimization problems with one (or many) computationally expensive evaluation function(s). The role of GRFM is to predict objective function values for new candidate solutions by exploiting information recorded during previous evaluations. Moreover, GRFM are able to provide estimates of the confidence of their predictions. Predictions and their confidence intervals predicted by GRFM are used by the metamodel assisted EA. It selects the promising members in each generation and carries out exact, costly evaluations only for them. The extensive use of the uncertainty information of predictions for screening the candidate solutions makes it possible to significantly reduce the computational cost of singleand multiobjective EA. This is adequately demonstrated in this paper by means of mathematical test cases and a multipoint airfoil design in aerodynamics
639Â citations
TL;DR: The potential and effectiveness of the newly developed Pareto-based multiobjective evolutionary algorithms (MOEA) for solving a real-world power system multi objective nonlinear optimization problem are comprehensively discussed and evaluated.
Abstract: The potential and effectiveness of the newly developed Pareto-based multiobjective evolutionary algorithms (MOEA) for solving a real-world power system multiobjective nonlinear optimization problem are comprehensively discussed and evaluated in this paper. Specifically, nondominated sorting genetic algorithm, niched Pareto genetic algorithm, and strength Pareto evolutionary algorithm (SPEA) have been developed and successfully applied to an environmental/economic electric power dispatch problem. A new procedure for quality measure is proposed in this paper in order to evaluate different techniques. A feasibility check procedure has been developed and superimposed on MOEA to restrict the search to the feasible region of the problem space. A hierarchical clustering algorithm is also imposed to provide the power system operator with a representative and manageable Pareto-optimal set. Moreover, an approach based on fuzzy set theory is developed to extract one of the Pareto-optimal solutions as the best compromise one. These multiobjective evolutionary algorithms have been individually examined and applied to the standard IEEE 30-bus six-generator test system. Several optimization runs have been carried out on different cases of problem complexity. The results of MOEA have been compared to those reported in the literature. The results confirm the potential and effectiveness of MOEA compared to the traditional multiobjective optimization techniques. In addition, the results demonstrate the superiority of the SPEA as a promising multiobjective evolutionary algorithm to solve different power system multiobjective optimization problems.
631Â citations
TL;DR: An improved particle swarm optimizer using the notion of species to determine its neighborhood best values for solving multimodal optimization problems and for tracking multiple optima in a dynamic environment is proposed.
Abstract: This paper proposes an improved particle swarm optimizer using the notion of species to determine its neighborhood best values for solving multimodal optimization problems and for tracking multiple optima in a dynamic environment. In the proposed species-based particle swam optimization (SPSO), the swarm population is divided into species subpopulations based on their similarity. Each species is grouped around a dominating particle called the species seed. At each iteration step, species seeds are identified from the entire population, and then adopted as neighborhood bests for these individual species groups separately. Species are formed adaptively at each step based on the feedback obtained from the multimodal fitness landscape. Over successive iterations, species are able to simultaneously optimize toward multiple optima, regardless of whether they are global or local optima. Our experiments on using the SPSO to locate multiple optima in a static environment and a dynamic SPSO (DSPSO) to track multiple changing optima in a dynamic environment have demonstrated that SPSO is very effective in dealing with multimodal optimization functions in both environments
528Â citations
TL;DR: New variants of particle swarm optimization (PSO) specifically designed to work well in dynamic environments are explored, showing that the new multiswarm optimizer significantly outperforms previous approaches.
Abstract: Many real-world problems are dynamic, requiring an optimization algorithm which is able to continuously track a changing optimum over time. In this paper, we explore new variants of particle swarm optimization (PSO) specifically designed to work well in dynamic environments. The main idea is to split the population of particles into a set of interacting swarms. These swarms interact locally by an exclusion parameter and globally through a new anti-convergence operator. In addition, each swarm maintains diversity either by using charged or quantum particles. This paper derives guidelines for setting the involved parameters and evaluates the multiswarm algorithms on a variety of instances of the multimodal dynamic moving peaks benchmark. Results are also compared with other PSO and evolutionary algorithm approaches from the literature, showing that the new multiswarm optimizer significantly outperforms previous approaches
525Â citations
TL;DR: The empirical evidence suggests that the new approach is robust, efficient, and generic when handling linear/nonlinear equality/inequality constraints and the best, mean, and worst objective function values and the standard deviations.
Abstract: A considerable number of constrained optimization evolutionary algorithms (COEAs) have been proposed due to increasing interest in solving constrained optimization problems (COPs) by evolutionary algorithms (EAs). In this paper, we first review existing COEAs. Then, a novel EA for constrained optimization is presented. In the process of population evolution, our algorithm is based on multiobjective optimization techniques, i.e., an individual in the parent population may be replaced if it is dominated by a nondominated individual in the offspring population. In addition, three models of a population-based algorithm-generator and an infeasible solution archiving and replacement mechanism are introduced. Furthermore, the simplex crossover is used as a recombination operator to enrich the exploration and exploitation abilities of the approach proposed. The new approach is tested on 13 well-known benchmark functions, and the empirical evidence suggests that it is robust, efficient, and generic when handling linear/nonlinear equality/inequality constraints. Compared with some other state-of-the-art algorithms, our algorithm remarkably outperforms them in terms of the best, mean, and worst objective function values and the standard deviations. It is noteworthy that our algorithm does not require the transformation of equality constraints into inequality constraints
365Â citations
TL;DR: Simulation results confirm the prediction from theory that stability of the particle dynamics requires increasing the maximum value of the random parameter when the inertia factor is reduced.
Abstract: Previous stability analysis of the particle swarm optimizer was restricted to the assumption that all parameters are nonrandom, in effect a deterministic particle swarm optimizer. We analyze the stability of the particle dynamics without this restrictive assumption using Lyapunov stability analysis and the concept of passive systems. Sufficient conditions for stability are derived, and an illustrative example is given. Simulation results confirm the prediction from theory that stability of the particle dynamics requires increasing the maximum value of the random parameter when the inertia factor is reduced.
TL;DR: The results presented demonstrate the role of mutation and genotype length in the evolvability of the graph-based Cartesian genetic programming system and find that the most evolvable representations occur when the genotype is extremely large and in which over 95% of the genes are inactive.
Abstract: The graph-based Cartesian genetic programming system has an unusual genotype representation with a number of advantageous properties. It has a form of redundancy whose role has received little attention in the published literature. The representation has genes that can be activated or deactivated by mutation operators during evolution. It has been demonstrated that this "junk" has a useful role and is very beneficial in evolutionary search. The results presented demonstrate the role of mutation and genotype length in the evolvability of the representation. It is found that the most evolvable representations occur when the genotype is extremely large and in which over 95% of the genes are inactive.
TL;DR: A genetic algorithm is proposed that uses a variable population size and periodic partial reinitialization of the population in the form of a saw-tooth function to enhance the overall performance of the algorithm relying on the dynamics of evolution of the GA and the synergy of the combined effects of population size variation and reinitalization.
Abstract: A genetic algorithm (GA) is proposed that uses a variable population size and periodic partial reinitialization of the population in the form of a saw-tooth function. The aim is to enhance the overall performance of the algorithm relying on the dynamics of evolution of the GA and the synergy of the combined effects of population size variation and reinitialization. Preliminary parametric studies to test the validity of these assertions are performed for two categories of problems, a multimodal function and a unimodal function with different features. The proposed scheme is compared with the conventional GA and micro GA (/spl mu/GA) of equal computing cost and guidelines for the selection of effective values of the involved parameters are given, which facilitate the implementation of the algorithm. The proposed algorithm is tested for a variety of benchmark problems and a problem generator from which it becomes evident that the saw-tooth scheme enhances the overall performance of GAs.
TL;DR: A cooperative coevolutionary algorithm (CCEA) for multiobjective optimization, which applies the divide-and-conquer approach to decompose decision vectors into smaller components and evolves multiple solutions in the form of cooperative subpopulations is presented.
Abstract: Recent advances in evolutionary algorithms show that coevolutionary architectures are effective ways to broaden the use of traditional evolutionary algorithms. This paper presents a cooperative coevolutionary algorithm (CCEA) for multiobjective optimization, which applies the divide-and-conquer approach to decompose decision vectors into smaller components and evolves multiple solutions in the form of cooperative subpopulations. Incorporated with various features like archiving, dynamic sharing, and extending operator, the CCEA is capable of maintaining archive diversity in the evolution and distributing the solutions uniformly along the Pareto front. Exploiting the inherent parallelism of cooperative coevolution, the CCEA can be formulated into a distributed cooperative coevolutionary algorithm (DCCEA) suitable for concurrent processing that allows inter-communication of subpopulations residing in networked computers, and hence expedites the computational speed by sharing the workload among multiple computers. Simulation results show that the CCEA is competitive in finding the tradeoff solutions, and the DCCEA can effectively reduce the simulation runtime without sacrificing the performance of CCEA as the number of peers is increased
TL;DR: This paper presents a novel evolutionary algorithm based on the combination of a max-min optimization strategy with a Baldwinian trust-region framework employing local surrogate models for reducing the computational cost associated with robust design problems.
Abstract: Solving design optimization problems using evolutionary algorithms has always been perceived as finding the optimal solution over the entire search space. However, the global optima may not always be the most desirable solution in many real-world engineering design problems. In practice, if the global optimal solution is very sensitive to uncertainties, for example, small changes in design variables or operating conditions, then it may not be appropriate to use this highly sensitive solution. In this paper, we focus on combining evolutionary algorithms with function approximation techniques for robust design. In particular, we investigate the application of robust genetic algorithms to problems with high dimensions. Subsequently, we present a novel evolutionary algorithm based on the combination of a max-min optimization strategy with a Baldwinian trust-region framework employing local surrogate models for reducing the computational cost associated with robust design problems. Empirical results are presented for synthetic test functions and aerodynamic shape design problems to demonstrate that the proposed algorithm converges to robust optimum designs on a limited computational budget
TL;DR: A fuzzy neural network combined with a chaos-search genetic algorithm (CGA) and simulated annealing (SA) applied to short-term power-system load forecasting as a sample test demonstrates an encouraging degree of accuracy superior to other commonly used forecasting methods available.
Abstract: A fuzzy neural network combined with a chaos-search genetic algorithm (CGA) and simulated annealing (SA), hereafter called the FCS method, or simply the FCS, applied to short-term power-system load forecasting as a sample test is proposed in this paper. A fuzzy hyperrectangular composite neural network (FHCNN) is adopted for the initial load forecasting. An integrated CGA and fuzzy system (CGF) and SA is then used to find the optimal FHCNN parameters instead of the ones with the back propagation method. The CGF method will generate a set of parameters for a feasible solution. The CGF method holds good global search capability but poor local search ability. On the contrary, the SA method possesses a good local optimal search capability. We hence propose in this paper to combine the two methods to exploit their advantages and, furthermore, to eliminate the known downside of the traditional artificial neural network. The proposed FCS is next applied to power-system load forecasting as a sample test, which demonstrates an encouraging degree of accuracy superior to other commonly used forecasting methods available. The forecasting results are tabulated and partially converted into bar charts for evaluation and clear comparisons.
TL;DR: This paper aims at investigating the performance of multiobjective evolutionary algorithms (MOEAs) on solving large instances of the mapping problem and shows that MOEAs provide the designer with a highly accurate set of solutions in a reasonable amount of time.
Abstract: Sesame is a software framework that aims at developing a modeling and simulation environment for the efficient design space exploration of heterogeneous embedded systems. Since Sesame recognizes separate application and architecture models within a single system simulation, it needs an explicit mapping step to relate these models for cosimulation. The design tradeoffs during the mapping stage, namely, the processing time, power consumption, and architecture cost, are captured by a multiobjective nonlinear mixed integer program. This paper aims at investigating the performance of multiobjective evolutionary algorithms (MOEAs) on solving large instances of the mapping problem. With two comparative case studies, it is shown that MOEAs provide the designer with a highly accurate set of solutions in a reasonable amount of time. Additionally, analyses for different crossover types, mutation usage, and repair strategies for the purpose of constraints handling are carried out. Finally, a number of multiobjective optimization results are simulated for verification.
TL;DR: This paper proposes to construct local approximate models of the fitness function and then use these approximate models to estimate expected fitness and variance and demonstrates empirically that this approach significantly outperforms the implicit averaging approach, as well as the explicit averaging approaches using existing estimation techniques reported in the literature.
Abstract: For many real-world optimization problems, the robustness of a solution is of great importance in addition to the solution's quality. By robustness, we mean that small deviations from the original design, e.g., due to manufacturing tolerances, should be tolerated without a severe loss of quality. One way to achieve that goal is to evaluate each solution under a number of different scenarios and use the average solution quality as fitness. However, this approach is often impractical, because the cost for evaluating each individual several times is unacceptable. In this paper, we present a new and efficient approach to estimating a solution's expected quality and variance. We propose to construct local approximate models of the fitness function and then use these approximate models to estimate expected fitness and variance. Based on a variety of test functions, we demonstrate empirically that our approach significantly outperforms the implicit averaging approach, as well as the explicit averaging approaches using existing estimation techniques reported in the literature
TL;DR: The implicit and explicit knowledge representation mechanisms for evolutionary algorithms (EAs) are discussed and offline and online metaheuristics as examples of explicit methods to leverage this knowledge are described.
Abstract: We discuss implicit and explicit knowledge representation mechanisms for evolutionary algorithms (EAs). We also describe offline and online metaheuristics as examples of explicit methods to leverage this knowledge. We illustrate the benefits of this approach with four real-world applications. The first application is automated insurance underwriting-a discrete classification problem, which requires a careful tradeoff between the percentage of insurance applications handled by the classifier and its classification accuracy. The second application is flexible design and manufacturing-a combinatorial assignment problem, where we optimize design and manufacturing assignments with respect to time and cost of design and manufacturing for a given product. Both problems use metaheuristics as a way to encode domain knowledge. In the first application, the EA is used at the metalevel, while in the second application, the EA is the object-level problem solver. In both cases, the EAs use a single-valued fitness function that represents the required tradeoffs. The third application is a lamp spectrum optimization that is formulated as a multiobjective optimization problem. Using domain customized mutation operators, we obtain a well-sampled Pareto front showing all the nondominated solutions. The fourth application describes a scheduling problem for the maintenance tasks of a constellation of 25 low earth orbit satellites. The domain knowledge in this application is embedded in the design of a structured chromosome, a collection of time-value transformations to reflect static constraints, and a time-dependent penalty function to prevent schedule collisions.
TL;DR: Experimental results show that it can be very effective and robust even in the presence of noise and missing values, and when correlating the gene expression microarray data with DNA sequences, it was able to uncover significant biological binding sites (both previously known and unknown) in each cluster discovered by EvoCluster.
Abstract: Clustering is concerned with the discovery of interesting groupings of records in a database. Many algorithms have been developed to tackle clustering problems in a variety of application domains. In particular, some of them have been used in bioinformatics research to uncover inherent clusters in gene expression microarray data. In this paper, we show how some popular clustering algorithms have been used for this purpose. Based on experiments using simulated and real data, we also show that the performance of these algorithms can be further improved. For more effective clustering of gene expression microarray data, which is typically characterized by a lot of noise, we propose a novel evolutionary algorithm called evolutionary clustering (EvoCluster). EvoCluster encodes an entire cluster grouping in a chromosome so that each gene in the chromosome encodes one cluster. Based on such encoding scheme, it makes use of a set of reproduction operators to facilitate the exchange of grouping information between chromosomes. The fitness function that the EvoCluster adopts is able to differentiate between how relevant a feature value is in determining a particular cluster grouping. As such, instead of just local pairwise distances, it also takes into consideration how clusters are arranged globally. Unlike many popular clustering algorithms, EvoCluster does not require the number of clusters to be decided in advance. Also, patterns hidden in each cluster can be explicitly revealed and presented for easy interpretation even by casual users. For performance evaluation, we have tested EvoCluster using both simulated and real data. Experimental results show that it can be very effective and robust even in the presence of noise and missing values. Also, when correlating the gene expression microarray data with DNA sequences, we were able to uncover significant biological binding sites (both previously known and unknown) in each cluster discovered by EvoCluster.
TL;DR: This work presents a framework for efficient design space exploration during high-level synthesis of datapaths for data-dominated applications using a genetic algorithm to concurrently perform scheduling and allocation with the aim of finding schedules and module combinations that lead to superior designs while considering user-specified latency and area constraints.
Abstract: High-level synthesis is comprised of interdependent tasks such as scheduling, allocation, and module selection. For today's very large-scale integration (VLSI) designs, the cost of solving the combined scheduling, allocation, and module selection problem by exhaustive search is prohibitive. However, to meet design objectives, an extensive design space exploration is often critical to obtaining superior designs. We present a framework for efficient design space exploration during high-level synthesis of datapaths for data-dominated applications. The framework uses a genetic algorithm (GA) to concurrently perform scheduling and allocation with the aim of finding schedules and module combinations that lead to superior designs while considering user-specified latency and area constraints. The GA uses a multichromosome representation to encode datapath schedules and module allocations and efficient heuristics to minimize functional and storage area costs, while minimizing circuit latencies. The framework provides the flexibility to perform resource-constrained scheduling, time-constrained scheduling, or a combination of the two, using a simple and fast list-scheduling technique. A graded penalty function is used as an objective function in evaluating the quality of designs to enable the GA to quickly reach areas of the search space where designs meeting user specified criteria are most likely to be found. Since GAs are population-based search heuristics, a unique feature of our framework is its ability to offer a large number of alternative datapath designs, all of which meet design specifications but differ in module, register, and interconnect configurations. Many experiments on well-known benchmarks show the effectiveness of our approach.
TL;DR: This paper proposes a landscape (test-problem) generator that can be used to generate optimization problem instances for continuous, bound-constrained optimization problems and analyzes some simple, continuous estimation of distribution algorithms, and gains new insights into the behavior of these algorithms using the landscape generator.
Abstract: The research literature on metaheuristic and evolutionary computation has proposed a large number of algorithms for the solution of challenging real-world optimization problems. It is often not possible to study theoretically the performance of these algorithms unless significant assumptions are made on either the algorithm itself or the problems to which it is applied, or both. As a consequence, metaheuristics are typically evaluated empirically using a set of test problems. Unfortunately, relatively little attention has been given to the development of methodologies and tools for the large-scale empirical evaluation and/or comparison of metaheuristics. In this paper, we propose a landscape (test-problem) generator that can be used to generate optimization problem instances for continuous, bound-constrained optimization problems. The landscape generator is parameterized by a small number of parameters, and the values of these parameters have a direct and intuitive interpretation in terms of the geometric features of the landscapes that they produce. An experimental space is defined over algorithms and problems, via a tuple of parameters for any specified algorithm and problem class (here determined by the landscape generator). An experiment is then clearly specified as a point in this space, in a way that is analogous to other areas of experimental algorithmics, and more generally in experimental design. Experimental results are presented, demonstrating the use of the landscape generator. In particular, we analyze some simple, continuous estimation of distribution algorithms, and gain new insights into the behavior of these algorithms using the landscape generator
TL;DR: This paper explores evolutionary algorithms that use combinatorial graphs to limit possible crossover partners and finds the optimal choice of graph improved solution time as much as 63-fold with typical impact being in the range of 15% to 100% variation.
Abstract: Evolutionary algorithms use crossover to combine information from pairs of solutions and use selection to retain the best solutions. Ideally, crossover takes distinct good features from each of the two structures involved. This process creates a conflict: progress results from crossing over structures with different features, but crossover produces new structures that are like their parents and so reduces the diversity on which it depends. As evolution continues, the algorithm searches a smaller and smaller portion of the search space. Mutation can help maintain diversity but is not a panacea for diversity loss. This paper explores evolutionary algorithms that use combinatorial graphs to limit possible crossover partners. These graphs limit the speed and manner in which information can spread giving competing solutions time to mature. This use of graphs is a computationally inexpensive method of picking a global level of tradeoff between exploration and exploitation. The results of using 26 graphs with a diverse collection of graphical properties are presented. The test problems used are: one-max, the De Jong functions, the Griewangk function in three to seven dimensions, the self-avoiding random walk problem in 9, 12, 16, 20, 25, 30, and 36 dimensions, the plus-one-recall-store (PORS) problem with n=15,16, and 17, location of length-six one-error-correcting DNA barcodes, and solving a simple differential equation semi-symbolically. The choice of combinatorial graph has a significant effect on the time-to-solution. In the cases studied, the optimal choice of graph improved solution time as much as 63-fold with typical impact being in the range of 15% to 100% variation. The graph yielding superior performance is found to be problem dependent. In general, the optimal graph diameter increases and the optimal average degree decreases with the complexity and difficulty of the fitness landscape. The use of diverse graphs as population structures for a collection of problems also permits a classification of the problems. A phylogenetic analysis of the problems using normalized time to solution on each graph groups the numerical problems as a clade together with one-max; self-avoiding walks form a clade with the semisymbolic differential equation solution; and the PORS and DNA barcode problems form a superclade with the numerical problems but are substantially distinct from them. This novel form of analysis has the potential to aid researchers choosing problems for a test suite
TL;DR: This work biasing a cooperative CEA in such a way that the fitness of an individual is based partly on the result of interactions with other individuals, and partly on an estimate of the best possible reward for that individual if partnered with its optimal collaborator.
Abstract: Cooperative coevolutionary algorithms (CEAs) offer great potential for concurrent multiagent learning domains and are of special utility to domains involving teams of multiple agents Unfortunately, they also exhibit pathologies resulting from their game-theoretic nature, and these pathologies interfere with finding solutions that correspond to optimal collaborations of interacting agents We address this problem by biasing a cooperative CEA in such a way that the fitness of an individual is based partly on the result of interactions with other individuals (as is usual), and partly on an estimate of the best possible reward for that individual if partnered with its optimal collaborator We justify this idea using existing theoretical models of a relevant subclass of CEAs, demonstrate how to apply biasing in a way that is robust with respect to parameterization, and provide some experimental evidence to validate the biasing approach We show that it is possible to bias coevolutionary methods to better search for optimal multiagent behaviors
TL;DR: A new classification algorithm, organizational coevolutionary algorithm for classification (OCEC), is proposed with the intrinsic properties of classification in mind, and its use of a bottom-up search mechanism shows that OCEC obtains a good scalability.
Abstract: Taking inspiration from the interacting process among organizations in human societies, a new classification algorithm, organizational coevolutionary algorithm for classification (OCEC), is proposed with the intrinsic properties of classification in mind. The main difference between OCEC and the available classification approaches based on evolutionary algorithms (EAs) is its use of a bottom-up search mechanism. OCEC causes the evolution of sets of examples, and at the end of the evolutionary process, extracts rules from these sets. These sets of examples form organizations. Because organizations are different from the individuals in traditional EAs, three evolutionary operators and a selection mechanism are devised for realizing the evolutionary operations performed on organizations. This method can avoid generating meaningless rules during the evolutionary process. An evolutionary method is also devised for determining the significance of each attribute, on the basis of which, the fitness function for organizations is defined. In experiments, the effectiveness of OCEC is first evaluated by multiplexer problems. Then, OCEC is compared with several well-known classification algorithms on 12 benchmarks from the UCI repository datasets and multiplexer problems. Moreover, OCEC is applied to a practical case, radar target recognition problems. All results show that OCEC achieves a higher predictive accuracy and a lower computational cost. Finally, the scalability of OCEC is studied on synthetic datasets. The number of training examples increases from 100 000 to 10 million, and the number of attributes increases from 9 to 400. The results show that OCEC obtains a good scalability.
TL;DR: This work proposes a new selection scheme, which is uniform in the fitness values and generates selection pressure toward sparsely populated fitness regions, not necessarily toward higher fitness, as is the case for all other selection schemes.
Abstract: In evolutionary algorithms, the fitness of a population increases with time by mutating and recombining individuals and by a biased selection of fitter individuals. The right selection pressure is critical in ensuring sufficient optimization progress on the one hand and in preserving genetic diversity to be able to escape from local optima on the other hand. Motivated by a universal similarity relation on the individuals, we propose a new selection scheme, which is uniform in the fitness values. It generates selection pressure toward sparsely populated fitness regions, not necessarily toward higher fitness, as is the case for all other selection schemes. We show analytically on a simple example that the new selection scheme can be much more effective than standard selection schemes. We also propose a new deletion scheme which achieves a similar result via deletion and show how such a scheme preserves genetic diversity more effectively than standard approaches. We compare the performance of the new schemes to tournament selection and random deletion on an artificial deceptive problem and a range of NP hard problems: traveling salesman, set covering, and satisfiability
TL;DR: It is seen that while overall, the assumption of Gaussian noise in previous studies is less severe than might have been expected, some significant differences do arise when considering noise that is of unbounded variance, skew, or biased.
Abstract: Most studies concerned with the effects of noise on the performance of optimization strategies, in general, and on evolutionary approaches, in particular, have assumed a Gaussian noise model. However, practical optimization strategies frequently face situations where the noise is not Gaussian. Noise distributions may be skew or biased, and outliers may be present. The effects of non-Gaussian noise are largely unexplored, and it is unclear whether the insights gained and the recommendations with regard to the sizing of strategy parameters that have been made under the assumption of Gaussian noise bear relevance to more general situations. In this paper, the behavior of a powerful class of recombinative evolution strategies is studied on the sphere model under the assumption of a very general noise model. A performance law is derived, its implications are studied both analytically and numerically, and comparisons with the case of Gaussian noise are drawn. It is seen that while overall, the assumption of Gaussian noise in previous studies is less severe than might have been expected, some significant differences do arise when considering noise that is of unbounded variance, skew, or biased
TL;DR: The differential evolution approach in particular, when appropriately augmented with local optimization methods, is shown to have significant potential for improving both the reliability and efficiency of the current industrial flight clearance process.
Abstract: The application of two evolutionary optimization methods, namely, differential evolution and genetic algorithms, to the clearance of nonlinear flight control laws for highly augmented aircraft is described. The algorithms are applied to the problem of evaluating a nonlinear handling quality clearance criterion for a simulation model of a high-performance aircraft with a delta canard configuration and a full-authority flight control law. Hybrid versions of both algorithms, incorporating local gradient-based optimization, are also developed and evaluated. Statistical comparisons of computational cost and global convergence properties reveal the benefits of hybridization for both algorithms. The differential evolution approach in particular, when appropriately augmented with local optimization methods, is shown to have significant potential for improving both the reliability and efficiency of the current industrial flight clearance process
TL;DR: It is shown that by using a different tree-based representation and local (insertion and deletion) structural modification operators, that this problem can be almost eliminated even with trivial (stochastic hill-climbing) search methods.
Abstract: Standard tree-based genetic programming suffers from a structural difficulty problem in that it is unable to search effectively for solutions requiring very full or very narrow trees. This deficiency has been variously explained as a consequence of restrictions imposed by the tree structure or as a result of the numerical distribution of tree shapes. We show that by using a different tree-based representation and local (insertion and deletion) structural modification operators, that this problem can be almost eliminated even with trivial (stochastic hill-climbing) search methods, thus eliminating the above explanations. We argue, instead, that structural difficulty is a consequence of the large step size of the operators in standard genetic programming, which is itself a consequence of the fixed-arity property embodied in its representation.
TL;DR: A novel tree representation which is suitable for the analysis of RLC (i.e., resistor, inductor, and capacitor) circuits is proposed and can effectively generate parsimonious filters of very high order where conventional methods fail.
Abstract: This paper proposes a novel tree representation which is suitable for the analysis of RLC (i.e., resistor, inductor, and capacitor) circuits. Genetic programming (GP) based on the tree representation is applied to passive filter synthesis problems. The GP is optimized and then incorporated into an algorithm which can automatically find parsimonious solutions without predetermining the number of the required circuit components. The experimental results show the proposed method is efficient in three aspects. First, the GP-evolved circuits are more parsimonious than those resulting from traditional design methods in many cases. Second, the proposed method is faster than previous work and can effectively generate parsimonious filters of very high order where conventional methods fail. Third, when the component values are restricted to a set of preferred values, the GP method can generate compliant solutions by means of novel circuit topology.