Parameterized runtime analysis seeks to understand the influence of problem structure on algorithmic runtime. In this paper, we contribute to the theoretical understanding of evolutionary algorithms and carry out a pa...
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Parameterized runtime analysis seeks to understand the influence of problem structure on algorithmic runtime. In this paper, we contribute to the theoretical understanding of evolutionary algorithms and carry out a parameterized analysis of evolutionary algorithms for the Euclidean traveling salesperson problem (Euclidean TSP). We investigate the structural properties in TSP instances that influence the optimization process of evolutionary algorithms and use this information to bound their runtime. We analyze the runtime in dependence of the number of inner points k. In the first part of the paper, we study a (mu + lambda) EA in a strictly black box setting and show that it can solve the Euclidean TSP in expected time O (n . A(epsilon) . max ((mu/lambda) . n(2), 1) + (mu/lambda) . n(4k)(2k - 1)!) where A is a function of the minimum angle epsilon between any three points. Based on insights provided by the analysis, we improve this upper bound by introducing a mixed mutation strategy that incorporates both 2-opt moves and permutation jumps. This strategy improves the upper bound to O(n . A(epsilon) . max {(mu/lambda) . n(2), 1} + (mu/lambda) . n(2k)(k - 1)!). In the second part of the paper, we use the information gained in the analysis to incorporate domain knowledge to design two fixed-parameter tractable (FPT) evolutionary algorithms for the planar Euclidean TSP. We first develop a (mu + lambda) EA based on an analysis by M. Theile, 2009, "Exact solutions to the traveling salesperson problem by a population-based evolutionary algorithm," Lecture notes in computer science, Vol. 5482 (pp. 145-155), that solves the TSP with k inner points in O(max{2(k)k(2)n(2)lambda(-1), n}) generations with probability 1 - e(-Omega(n)). We then design a (mu + lambda) EAthat incorporates a dynamic programming step into the fitness evaluation. We prove that a variant of this evolutionary algorithm using 2-opt mutation solves the problem after O(max{(k - 2)!k(2k-2)lambda(-1), 1}) steps
In spite of many applications of evolutionary algorithms in optimisation, theoretical results on the computation time and time complexity of evolutionary algorithms on different optimisation problems are relatively fe...
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In spite of many applications of evolutionary algorithms in optimisation, theoretical results on the computation time and time complexity of evolutionary algorithms on different optimisation problems are relatively few. It is still unclear when an evolutionary algorithm is expected to solve an optimisation problem efficiently or otherwise. This paper gives a general analytic framework for analysing first hitting times of evolutionary algorithms. The framework is built on the absorbing Markov chain model of evolutionary algorithms. The first step towards a systematic comparative study among different EAs and their first hitting times has been made in the paper. (C) 2003 Published by Elsevier Science B.V.
In recent years, there has been a growing interest for the experimental analysis in the field of evolutionary algorithms. It is noticeable due to the existence of numerous papers which analyze and propose different ty...
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In recent years, there has been a growing interest for the experimental analysis in the field of evolutionary algorithms. It is noticeable due to the existence of numerous papers which analyze and propose different types of problems, such as the basis for experimental comparisons of algorithms, proposals of different methodologies in comparison or proposals of use of different statistical techniques in algorithms' comparison. In this paper, we focus our study on the use of statistical techniques in the analysis of evolutionary algorithms' behaviour over optimization problems. A study about the required conditions for statistical analysis of the results is presented by using some models of evolutionary algorithms for real-coding optimization. This study is conducted in two ways: single-problem analysis and multiple-problem analysis. The results obtained state that a parametric statistical analysis could not be appropriate specially when we deal with multiple-problem results. In multiple-problem analysis, we propose the use of non-parametric statistical tests given that they are less restrictive than parametric ones and they can be used over small size samples of results. As a case study, we analyze the published results for the algorithms presented in the CEC'2005 Special Session on Real Parameter Optimization by using non-parametric test procedures.
This paper proposes a four corners' heuristic for application in evolutionary algorithms (EAs) applied to two-dimensional packing problems. The four corners' (FQ heuristic is specifically designed to increase ...
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This paper proposes a four corners' heuristic for application in evolutionary algorithms (EAs) applied to two-dimensional packing problems. The four corners' (FQ heuristic is specifically designed to increase the search efficiency of EAs. Experiments with the FC heuristic are conducted on 31 problems from the literature both with rotations permitted and without rotations permitted, using two different EA algorithms: a self-adaptive parallel recombinative simulated annealing (PRSA) algorithm, and a self-adaptive genetic algorithm (GA). Results on bin packing problems yield the smallest trim losses we have seen in the published literature;with the FC heuristic, zero trim loss was achieved on problems of up to 97 rectangles. A comparison of the self-adaptive GA to fixed-parameter GAs is presented and the benefits of self-adaption are highlighted. (C) 2006 Elsevier B.V. All rights reserved.
A general review of game-theory based evolutionary algorithms (EAs) is presented in this study. Nash equilibrium, Stackelberg game and Pareto optimality are considered, as game-theoretical basis of the evolutionary al...
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A general review of game-theory based evolutionary algorithms (EAs) is presented in this study. Nash equilibrium, Stackelberg game and Pareto optimality are considered, as game-theoretical basis of the evolutionary algorithm design, and also, as problems solved by evolutionary computation. Applications of game-theory based EAs in computational engineering are listed, with special emphasis in structural optimization and, particularly, in skeletal structures. Additionally, a set of three problems are solved: reconstruction inverse problem, fully stressed design problem and minimum constrained weight, for discrete sizing of frame skeletal structures. We compare panmictic EAs, Nash EAs using 4 different static domain decompositions, including also a new dynamic domain decomposition. Two frame structural test cases of 55 member size and 105 member size are evaluated with the linear stiffness matrix method. Numerical experiments show the efficiency of the Nash EAs approach, confirmed with statistical significance analysis of results, and enhanced with the dynamic domain decomposition.
With the increasing uptake of electric vehicles (EVs), the need for efficient scheduling of EV charging is becoming increasingly important. A charging station operator needs to identify charging/discharging power of t...
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With the increasing uptake of electric vehicles (EVs), the need for efficient scheduling of EV charging is becoming increasingly important. A charging station operator needs to identify charging/discharging power of the client EVs over a time horizon while considering multiple objectives, such as operating costs and the peak power drawn from the grid. evolutionary algorithms (EAs) are a popular choice when faced with problems involving multiple objectives. However, since the objectives and constraints of this problem can be expressed using linear functions, it is also possible to come up with improvised multi-objective formulations which can be solved with exact techniques such as mixed-integer linear programming (MILP). With both approaches having their potential strengths and pitfalls, it is worth investigating their use to inform the algorithmic choices, which this study aims to address. In doing so, it makes a number of contributions to the topic, including extension of an existing EV charging problem to a multi-objective form;observing some interesting properties of the problem to improve both the MILP and EA solution approaches;and comparing the performance of MILP and EA. The study provides some useful insights into the problem, initial results and quantitative basis for selecting solution approaches, and highlights some areas of further development.
Structural damage identification based on finite element (FE) model updating has been a research direction of increasing interest over the last decade in the mechanical, civil, aerospace, etc., engineering fields. Var...
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Structural damage identification based on finite element (FE) model updating has been a research direction of increasing interest over the last decade in the mechanical, civil, aerospace, etc., engineering fields. Various studies have addressed direct, sensitivity-based, probabilistic, statistical, and iterative methods for updating FE models for structural damage identification. In contrast, evolutionary algorithms (EAs) are a type of modern method for FE model updating. Structural damage identification using FE model updating by evolutionary algorithms is an active research focus in progress but lacking a comprehensive survey. In this situation, this study aims to present a review of critical aspects of structural damage identification using evolutionary algorithm-based FE model updating. First, a theoretical background including the structural damage detection problem and the various types of FE model updating approaches is illustrated. Second, the various residuals between dynamic characteristics from FE model and the corresponding physical model, used for constructing the objective function for tracking damage, are summarized. Third, concerns regarding the selection of parameters for FE model updating are investigated. Fourth, the use of evolutionary algorithms to update FE models for damage detection is examined. Fifth, a case study comparing the applications of two single-objective EAs and one multi-objective EA for FE model updating-based damage detection is presented. Finally, possible research directions for utilizing evolutionary algorithm-based FE model updating to solve damage detection problems are recommended. This study should help researchers find crucial points for further exploring theories, methods, and technologies of evolutionary algorithm-based FE model updating for structural damage detection.
This work presents sequential and parallel evolutionary algorithms (EAs) applied to the scheduling problem in heterogeneous computing environments, a NP-hard problem with capital relevance in distributed computing. Th...
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This work presents sequential and parallel evolutionary algorithms (EAs) applied to the scheduling problem in heterogeneous computing environments, a NP-hard problem with capital relevance in distributed computing. These methods have been specifically designed to provide accurate and efficient solutions by using simple operators that allow them to be later extended for solving realistic problem instances arising in distributed heterogeneous computing (HC) and grid systems. The EAs were codified over MALLBA, a general-purpose library for combinatorial optimization. Efficient numerical results are reported in the experimental analysis performed on well-known problem instances. The comparative study of scheduling methods shows that the parallel versions of the implemented evolutionary algorithms are able to achieve high problem solving efficacy, outperforming traditional scheduling heuristics and also improving over previous results already reported in the related literature.
evolutionary algorithms (EAs) are a kind of nature-inspired general-purpose optimization algorithm, and have shown empirically good performance in solving various real-word optimization problems. During the past two d...
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evolutionary algorithms (EAs) are a kind of nature-inspired general-purpose optimization algorithm, and have shown empirically good performance in solving various real-word optimization problems. During the past two decades, promising results on the running time analysis (one essential theoretical aspect) of EAs have been obtained, while most of them focused on isolated combinatorial optimization problems, which do not reflect the general-purpose nature of EAs. To provide a general theoretical explanation of the behavior of EAs, it is desirable to study their performance on general classes of combinatorial optimization problems. To the best of our knowledge, the only result towards this direction is the provably good approximation guarantees of EAs for the problem class of maximizing monotone submodular functions with matroid constraints. The aim of this work is to contribute to this line of research. Considering that many combinatorial optimization problems involve non-monotone or non-submodular objective functions, we study the general problem classes, maximizing submodular functions with/without a size constraint and maximizing monotone approximately submodular functions with a size constraint. We prove that a simple multi-objective EA called GSEMO-C can generally achieve good approximation guarantees in polynomial expected running time. (C) 2019 Elsevier B.V. All rights reserved.
This paper proposes the use of the q-Gaussian mutation with self-adaptation of the shape of the mutation distribution in evolutionary algorithms. The shape of the q-Gaussian mutation distribution is controlled by a re...
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This paper proposes the use of the q-Gaussian mutation with self-adaptation of the shape of the mutation distribution in evolutionary algorithms. The shape of the q-Gaussian mutation distribution is controlled by a real parameter q. In the proposed method, the real parameter q of the q-Gaussian mutation is encoded in the chromosome of individuals and hence is allowed to evolve during the evolutionary process. In order to test the new mutation operator, evolution strategy and evolutionary programming algorithms with self-adapted q-Gaussian mutation generated from anisotropic and isotropic distributions are presented. The theoretical analysis of the q-Gaussian mutation is also provided. In the experimental study, the q-Gaussian mutation is compared to Gaussian and Cauchy mutations in the optimization of a set of test functions. Experimental results show the efficiency of the proposed method of self-adapting the mutation distribution in evolutionary algorithms.
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