Parameters Of Evolutionary Algorithm Research Articles

Self-adjusting Population Sizes for Non-elitist Evolutionary Algorithms: Why Success Rates Matter

Evolutionary algorithms (EAs) are general-purpose optimisers that come with several parameters like the sizes of parent and offspring populations or the mutation rate. It is well known that the performance of EAs may depend drastically on these parameters. Recent theoretical studies have shown that self-adjusting parameter control mechanisms that tune parameters during the algorithm run can provably outperform the best static parameters in EAs on discrete problems. However, the majority of these studies concerned elitist EAs and we do not have a clear answer on whether the same mechanisms can be applied for non-elitist EAs. We study one of the best-known parameter control mechanisms, the one-fifth success rule, to control the offspring population size λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda $$\\end{document} in the non-elitist (1,λ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${(1,\\lambda )}$$\\end{document} EA. It is known that the (1,λ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${(1,\\lambda )}$$\\end{document} EA has a sharp threshold with respect to the choice of λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda $$\\end{document} where the expected runtime on the benchmark function OneMax changes from polynomial to exponential time. Hence, it is not clear whether parameter control mechanisms are able to find and maintain suitable values of λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda $$\\end{document}. For OneMax we show that the answer crucially depends on the success rate s (i. e. a one-(s+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(s+1)$$\\end{document}-th success rule). We prove that, if the success rate is appropriately small, the self-adjusting (1,λ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${(1,\\lambda )}$$\\end{document} EA optimises OneMax in O(n) expected generations and O(nlogn)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(n \\log n)$$\\end{document} expected evaluations, the best possible runtime for any unary unbiased black-box algorithm. A small success rate is crucial: we also show that if the success rate is too large, the algorithm has an exponential runtime on OneMax and other functions with similar characteristics.

Population Diversity of Nonelitist Evolutionary Algorithms in the Exploration Phase

This paper discusses the genetic diversity of real-coded populations processed by an evolutionary algorithm (EA). Diversity is expressed as a variance or a covariance matrix of individuals contained in the population, in one- or multi-dimensional cases, respectively. We focus on the exploration stage of the optimization, therefore, the fitness function is modeled as noise. We prove that the expected value of genetic diversity achieves a level proportional to the mutation covariance matrix. The proportionality coefficient depends solely on the EA parameters. Formulas are derived to predict the diversity for fitness proportionate, tournament, and truncation selection, with and without arithmetic crossover and with Gaussian mutation. Experimental validation of the multidimensional case shows that prediction accuracy is satisfactory in a broad spectrum of settings of EA parameters.

Parameter Tuning for S-ABCPK

QoS-aware service composition problem has been drawn great attention in recent years. As an NP-hard problem, high time complexity is inevitable if global optimization algorithms (such as integer programming) are adopted. Researchers applied various evolutionary algorithms to decrease the time complexity by looking for a near-optimum solution. However, each evolutionary algorithm has two or more parameters, the values of which are to be assigned by algorithm designers and likely have impacts on the optimization results (primarily time complexity and optimality). The authors' experiments show that there are some dependencies between the features of a service composition problem, the values of an evolutionary algorithm's parameters, and the optimization results. In this article, the authors propose an improved algorithm called Service-Oriented Artificial Bee Colony algorithm considering Priori Knowledge (S-ABCPK) to solve service composition problem and focus on the S-ABCPK's parameter turning issue. The objective is to identify the potential dependency for designers of a service composition algorithm easily setting up the values of S-ABCPK parameters to obtain a preferable composition solution without many times of tedious attempts. Eight features of the service composition problem and the priori knowledge, five S-ABCPK parameters and two metrics of the final solution are identified. Based on a large volume of experiment data, S-ABCPK parameter tuning for a given service composition problem is conducted using C4.5 algorithm and the dependency between problem features and S-ABCPK parameters are established using the neural network method. An experiment on a validation dataset shows the feasibility of the approach.

Types of creativity.

Imagine the impact if we were to understand, and thus could reliably enhance, something - anything - about how creativity works in the brain. The fact that this prospect is not anywhere in sight makes it clear that no reliable progress has been made on the mechanisms underlying creativity over the last half century. Indeed, with the divergent thinking paradigm shown to be theoretically incoherent for neuroscience, there currently is no viable experimental approach to tackle the problem. Given that creativity is a complex and multifaceted concept, the obvious way forward is to parse it into subtypes. This paper presents a theoretical framework that divides the concept of creativity into three distinct types: a deliberate mode, a spontaneous mode, and a flow mode. Unlike previous attempts, the three creativity types are explicitly defined and delineated from one another based on established concepts in cognitive psychology and neuroscience. Moreover, to maximize the framework's heuristic value, this is done separately at three different levels of description: (A) neuroanatomy, (B) processes, and (C) evolutionary algorithms (EAs), or, more precisely, different parameters of EAs. This new theoretical framework advances the field in two significant ways. First, by defining the subtypes in terms of concepts that exist in mainstream psychology and neuroscience, they are valid subtypes, as they can be theoretically defended. Second, by providing a solid theoretical rationale to investigate a more circumscribed aspect of the larger problem, the framework provides a more targeted, and realistic, line of attack that will eventually lead to more meaningful data about the neural mechanisms of creativity.

Unveiling evolutionary algorithm representation with DU maps

Evolutionary algorithms (EAs) have proven to be effective in tackling problems in many different domains. However, users are often required to spend a significant amount of effort in fine-tuning the EA parameters in order to make the algorithm work. In principle, visualization tools may be of great help in this laborious task, but current visualization tools are either EA-specific, and hence hardly available to all users, or too general to convey detailed information. In this work, we study the Diversity and Usage map (DU map), a compact visualization for analyzing a key component of every EA, the representation of solutions. In a single heat map, the DU map visualizes for entire runs how diverse the genotype is across the population and to which degree each gene in the genotype contributes to the solution. We demonstrate the generality of the DU map concept by applying it to six EAs that use different representations (bit and integer strings, trees, ensembles of trees, and neural networks). We present the results of an online user study about the usability of the DU map which confirm the suitability of the proposed tool and provide important insights on our design choices. By providing a visualization tool that can be easily tailored by specifying the diversity (D) and usage (U) functions, the DU map aims at being a powerful analysis tool for EAs practitioners, making EAs more transparent and hence lowering the barrier for their use.

A selection hyper-heuristic with online learning for control of genetic algorithm ensemble

Evolutionary algorithms (EAs), in general, and genetic algorithms (GAs), in particular, are popular and efficient search metaheuristics, which have been applied for many complex optimization problems. At the same time, the performance of EAs depends on appropriate choice of the EA's structure and parameters. One of the ways to automate the EA design is to apply a hyper-heuristic approach. The hyper-heuristic is a high-level approach that can select and apply an appropriate low-level heuristic at each decision point. In this paper, we present a selection hyper-heuristic with online learning that is used to design and adaptively control an ensemble of many different genetic algorithms. The proposed approach combines concepts of the island model and cooperative and competitive coevolutions. The general method and some particular applications are discussed. The experimental results for a wide range of optimization problems are presented. The experiments show that the proposed approach outperforms its component metaheuristics on average. It also outperforms some state-of-the-art techniques. The main advantage of the approach is that it does not require the participation of the human-expert, because it operates in an automated, self-configuring way.

Bayesian network as an adaptive parameter setting approach for genetic algorithms

Parameter setting currently ranks among the most actively researched topics in the evolutionary algorithm (EA) community. This can be explained by the major impact EA parameters have on search performance. However, parameter setting has been shown to be both problem dependent and evolution dependent. Moreover, because parameters interact in complex ways, developing an efficient and beneficial parameter setting approach is not an easy feat, and no broadly recognized solution has emerged to date. In this paper, we borrow the notion of parameter adaptation with the objective of addressing the parameter setting dependencies mentioned above, using a strategy based on a Bayesian network. The adaptive framework is elaborated for a steady-state genetic algorithm (SSGA) to control nine parameters. To judge parameter state productivities, we consider the population’s fitness improvement, as well as exploration/exploitation balance management. The performance of this proposal, a Bayesian network for genetic algorithm parameter adaptation (BNGA), is assessed based on the CEC’05 benchmark. BNGA is compared to a static parameter setting, a naive approach, three common adaptive systems (PM, AP, and FAUC–RMAB), and two state-of-the-art EAs (CMA-ES and G-CMA-ES). Our results statistically demonstrate that the performance of BNGA is equivalent to that of FAUC–RMAB, CMA-ES, and G-CMA-ES, and overall is superior to that of all the other SSGA parameter setting approaches. However, these results also reveal that all the approaches considered have great difficulty finding global optima in a multimodal problem set. This suggests a lack of complementarity and/or synergy among parameter states.

A guideline for parameter setting of an evolutionary algorithm using optimal latin hypercube design and statistical analysis

It is well known that the performance of an evolutionary algorithm (EA) is highly dependent on the setting of EA parameters. There have been many studies on EA parameter setting, but no single method outperformed all other methods on all classes of problems as declared by the no free lunch theorem. In order to overcome the heavy computational burden usually required for parameter tuning, we propose an EA parameter tuning procedure applicable to any set of test problems. First, we employ an optimal Latin hypercube design (OLHD) in which parameters of an EA algorithm are set as factors. Next, using parameter settings sampled by OLHD, we run EAs to solve the test problems. Then, we statistically recommend parameter settings suitable for the test problems. Statistical evaluation of this application results suggests the best recombination method, and the recommended parameter ranges of population size, selection rate, and mutation rate are reduced by 93%, 80%, and 84%, respectively, compared to those usually used in parameter ranges. Finally, the recommended parameter setting is applied to the optimization problem of a high-speed spindle motor for a hard disk drive, and shows the effectiveness of the proposed procedure for a practical design optimization application.

Comparison of Metaheuristic Algorithms for Evolving a Neural Controller for an Autonomous Robot

Evolutionary algorithms are a possible way to automatically design the behavior of autonomous robots. In this paper we compare different evolutionary algorithms (EA), namely simple EA, two dimensional cellular EA, and random search, according to their performance in a simple simulation, where a phototaxis robot with two sensors of limited range has to find a light source in a closed area. In our experiments we studied the effects on performance of EA parameters, such as population size and number of generation. The results explain how the choice of the neural network (three-layered or fully-connected) may influence the quality of a final solution. Our findings indicate that acceptable results can be achieved using all EAs but not with random search. The utilization of a fully-connected neural network allows achieving better results for all EAs as compared to a three-layered neural network. Two dimensional cellular EA and simple EA evolve the best strategies for a robot’s behavior which allow the robot to reach the light source in almost all cases.

Implicit memory-based technique in solving dynamic scheduling problems through Response Surface Methodology – Part I

Purpose – This is the first part of a two-part paper. The purpose of this paper is to report on methods that use the Response Surface Methodology (RSM) to investigate an Evolutionary Algorithm (EA) and memory-based approach referred to as McBAR – the Mapping of Task IDs for Centroid-Based Adaptation with Random Immigrants. Some of the methods are useful for investigating the performance (solution-search abilities) of techniques (comprised of McBAR and other selected EA-based techniques) for solving some multi-objective dynamic resource-constrained project scheduling problems with time-varying number of tasks. Design/methodology/approach – The RSM is applied to: determine some EA parameters of the techniques, develop models of the performance of each technique, legitimize some algorithmic components of McBAR, manifest the relative performance of McBAR over the other techniques and determine the resiliency of McBAR against changes in the environment. Findings – The results of applying the methods are explored in the second part of this work. Originality/value – The models are composite and characterize an EA memory-based technique. Further, the resiliency of techniques is determined by applying Lagrange optimization that involves the models.

Global Robot Localization Under Noise Stress Utilizing EA Methods and Semisemantic Classification of a Known Environment

Global localization algorithms belong to the key research areas in the field of autonomous mobile robotics. The ability to correctly estimate the initial position after activation or to recover the global position if orientation is lost is required from all modern autonomous systems. This article presents an algorithm for unmanned global navigation in a known environment containing noise and moving objects. Evolutionary algorithms (EA) form an important part of the discussed method. We also present a novel method of semisemantic classification of the environment in which a robot moves. This semisemantic description of the environment allows for a significantly better setup of the working parameters of individual EAs. It also enables to better connect EAs with the basic navigation methodology based on algebraic criteria, in other words, on the minimization of L1-norm. An extensive set of experimental results confirms that the connection of the semantic environment description and the navigation methods creates an important advantage.

Choosing the Appropriate Forecasting Model for Predictive Parameter Control

All commonly used stochastic optimisation algorithms have to be parameterised to perform effectively. Adaptive parameter control (APC) is an effective method used for this purpose. APC repeatedly adjusts parameter values during the optimisation process for optimal algorithm performance. The assignment of parameter values for a given iteration is based on previously measured performance. In recent research, time series prediction has been proposed as a method of projecting the probabilities to use for parameter value selection. In this work, we examine the suitability of a variety of prediction methods for the projection of future parameter performance based on previous data. All considered prediction methods have assumptions the time series data has to conform to for the prediction method to provide accurate projections. Looking specifically at parameters of evolutionary algorithms (EAs), we find that all standard EA parameters with the exception of population size conform largely to the assumptions made by the considered prediction methods. Evaluating the performance of these prediction methods, we find that linear regression provides the best results by a very small and statistically insignificant margin. Regardless of the prediction method, predictive parameter control outperforms state of the art parameter control methods when the performance data adheres to the assumptions made by the prediction method. When a parameter's performance data does not adhere to the assumptions made by the forecasting method, the use of prediction does not have a notable adverse impact on the algorithm's performance.

Crossover can be constructive when computing unique input–output sequences

Unique input–output (UIO) sequences have important applications in conformance testing of finite state machines (FSMs). Previous experimental and theoretical research has shown that evolutionary algorithms (EAs) can compute UIOs efficiently on many FSM instance classes, but fail on others. However, it has been unclear how and to what degree EA parameter settings influence the runtime on the UIO problem. This paper investigates the choice of acceptance criterion in the (1 + 1) EA and the use of crossover in the $$(\mu+1)$$ Steady State Genetic Algorithm. It is rigorously proved that changing these parameters can reduce the runtime from exponential to polynomial for some instance classes of the UIO problem.

Guest Editorial: special issue on evolutionary optimisation and learning

Problem-solving techniques based on simulated evolution, particularly those inspired by the Darwinian theory of natural selection and biological evolution, have attracted great attention. These evolutionary optimisation and learning algorithms differ from the traditional optimisation and learning methods in that they involve a search from a population of solutions. Over the past decades, evolutionary optimisation and learning algorithms have been successfully applied to a wide variety of real-world problems. This special issue brings together some recent works from a wide range of topics concerning evolutionary optimisation and learning, including Differential Evolution, Cellular Genetic Algorithms, Particle Swarm Optimisation, Artificial Immune System, Coevolution, Crossover Analysis, Dynamic Combinatorial Optimisation, and Multimodal Optimisation. The eight papers included in this special issue originated from SEAL’08 (7th International Conference on Simulated Evolution and Learning), but have been substantially extended and revised from the conference version. These further extended papers were again rigorously reviewed in two rounds by at least three anonymous reviewers. The paper by Lehre and Yao investigates the impact of the parameter settings particularly the acceptance criterion in evolutionary algorithms (EAs) and the crossover operator SSGA when computing unique input output sequences (UIOs) from finite state machines. The objective is to identify simple, archetypical cases where these EA parameter settings have a particularly strong effect on the runtime of the algorithm. This result shows that minor modification in evolutionary algorithms can have an exponentially large runtime impact for computing UIOs and that when computing UIOs, the crossover operator can be essential, and simple EAs can be inefficient. The paper by Ronkknen et al. describes a software framework for generating multimodal test functions. The framework provides an easy way to construct parameterisable functions and offers an environment for testing multimodal optimisation algorithms. A number of function families with different characteristics are included. The framework implements new parameterisable function families for generating desired landscapes. In addition, the framework implements a selection of well-known test functions from the literature, which can be rotated and stretched. The software module can be easily imported into any optimisation algorithm implementation compatible with the C-programming language. As an example, eight optimisation approaches are compared by their ability to locate several global optima over a set of 16 functions with different properties generated by the proposed module. The paper by Dick and Whigham introduces two modifications to the local sharing method for multimodal optimisation. The first alters local sharing so that parent selection and fitness sharing operate at two different spatial levels: parent selection is performed within small demes, M. Zhang (&) School of Engineering and Computer Science, Victoria University of Wellington, PO Box 600, Wellington, New Zealand e-mail: mengjie.zhang@ecs.vuw.ac.nz

Self-adaptation of parameters in a learning classifier system ensemble machine

Self-adaptation of parameters in a learning classifier system ensemble machineSelf-adaptation is a key feature of evolutionary algorithms (EAs). Although EAs have been used successfully to solve a wide variety of problems, the performance of this technique depends heavily on the selection of the EA parameters. Moreover, the process of setting such parameters is considered a time-consuming task. Several research works have tried to deal with this problem; however, the construction of algorithms letting the parameters adapt themselves to the problem is a critical and open problem of EAs. This work proposes a novel ensemble machine learning method that is able to learn rules, solve problems in a parallel way and adapt parameters used by its components. A self-adaptive ensemble machine consists of simultaneously working extended classifier systems (XCSs). The proposed ensemble machine may be treated as a meta classifier system. A new self-adaptive XCS-based ensemble machine was compared with two other XCS-based ensembles in relation to one-step binary problems: Multiplexer, One Counts, Hidden Parity, and randomly generated Boolean functions, in a noisy version as well. Results of the experiments have shown the ability of the model to adapt the mutation rate and the tournament size. The results are analyzed in detail.

Robust Evolutionary Algorithm Design for Socio-Economic Simulation: Some Comments

In the original papers by Alkemade et al. (2006, 2007), their evolutionary algorithms (EAs) exhibited an extreme degree of premature convergence when they were run according to approach I. This seemed a quite curious result. We are happy that the correction (Alkemade et al. 2008) makes clear that the degree of premature convergence is much lower than originally reported. There are three further comments that we would like to make on the work of Alkemade et al. First, Alkemade et al. state that “convergence behavior differs for different values of the EA parameters such as initial density and chromosome length”. We would like to emphasize that the behavior of an EA depends on the initial density parameter only in the short run. In the long run, the initial density parameter has no effect on the behavior of an EA. This is because from amathematical point of view an EA (or, more precisely, a genetic algorithm) is an ergodic Markov chain (e.g., Nix and Vose 1992; Dawid 1996). In the long run, the state of such a Markov chain no longer depends on the initial state. We agree with Alkemade et al. that the behavior of an EA depends on the chromosome length. This is the case not only in the short run but also in the long run. Since the chromosome length is a technical parameter that usually does not have a clear economic interpretation, we regard the dependence of EA behavior on the chromosome length as a disadvantage of the use of EAs for economic modeling. Second, Alkemade et al. point out that two popular approaches to the use of EAs for economic modeling can yield quite different results. This is a very interesting observation, especially since earlier studies usually simply took one of the two approaches

Two aspects of evolutionary algorithms

In this paper we discuss the paradigm of evolutionary algorithms (EAs). We argue about the need for new heuristics in real-world problem solving, discussing reasons why some problems are difficult to solve. After introducing the main concepts of evolutionary algorithms, we concentrate on two issues: (1) self-adaptation of the parameters of EA, and (2) handling constraints.