The issue of controlling values of various parameters of an evolutionary algorithm is one of the most important and promising areas of research in evolutionary computation: it has a potential of adjusting the algorithm to the problem while solving the problem. In the paper we: 1) revise the terminology, which is unclear and confusing, thereby providing a classification of such control mechanisms, and 2) survey various forms of control which have been studied by the evolutionary computation community in recent years. Our classification covers the major forms of parameter control in evolutionary computation and suggests some directions for further research.

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Parameter control in evolutionary algorithms

The issue of setting the values of various parameters of an evolutionary algorithm is crucial for good performance. In this paper we discuss how to do this, beginning with the issue of whether these values are best set in advance or are best changed during evolution. We provide a classification of different approaches based on a number of complementary features, and pay special attention to setting parameters on-the-fly. This has the potential of adjusting the algorithm to the problem while solving the problem. This paper is intended to present a survey rather than a set of prescriptive details for implementing an EA for a particular type of problem. For this reason we have chosen to interleave a number of examples throughout the text. Thus we hope to both clarify the points we wish to raise as we present them, and also to give the reader a feel for some of the many possibilities available for controlling different parameters. © Springer-Verlag Berlin Heidelberg 2007.

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Parameter Control in Evolutionary Algorithms

Particle swarm optimization (PSO) is predominately used to find solutions for continuous optimization problems. As the operators of PSO are originally designed in an n-dimensional continuous space, the advancement of using PSO to find solutions in a discrete space is at a slow pace. In this paper, a novel set-based PSO (S-PSO) method for the solutions of some combinatorial optimization problems (COPs) in discrete space is presented. The proposed S-PSO features the following characteristics. First, it is based on using a set-based representation scheme that enables S-PSO to characterize the discrete search space of COPs. Second, the candidate solution and velocity are defined as a crisp set, and a set with possibilities, respectively. All arithmetic operators in the velocity and position updating rules used in the original PSO are replaced by the operators and procedures defined on crisp sets, and sets with possibilities in S-PSO. The S-PSO method can thus follow a similar structure to the original PSO for searching in a discrete space. Based on the proposed S-PSO method, most of the existing PSO variants, such as the global version PSO, the local version PSO with different topologies, and the comprehensive learning PSO (CLPSO), can be extended to their corresponding discrete versions. These discrete PSO versions based on S-PSO are tested on two famous COPs: the traveling salesman problem and the multidimensional knapsack problem. Experimental results show that the discrete version of the CLPSO algorithm based on S-PSO is promising.

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A Novel Set-Based Particle Swarm Optimization Method for Discrete Optimization Problems

We propose a novel variation to biogeography-based optimization (BBO), which is an evolutionary algorithm (EA) developed for global optimization. The new algorithm employs opposition-based learning (OBL) alongside BBO's migration rates to create oppositional BBO (OB O). Additionally, a new opposition method named quasi-reflection is introduced. Quasi-reflection is based on opposite numbers theory and we mathematically prove that it has the highest expected probability of being closer to the problem solution among all OBL methods. The oppositional algorithm is further revised by the addition of dynamic domain scaling and weighted reflection. Simulations have been performed to validate the performance of quasi-opposition as well as a mathematical analysis for a single-dimensional problem. Empirical results demonstrate that with the assistance of quasi-reflection, OB O significantly outperforms BBO in terms of success rate and the number of fitness function evaluations required to find an optimal solution.

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Oppositional biogeography-based optimization

The combination of genetic and local search heuristics has been shown to be an effective approach to solving the traveling salesman problem (TSP). This paper describes a new hybrid algorithm that exploits a compact genetic algorithm in order to generate high-quality tours, which are then refined by means of the Lin-Kernighan (LK) local search. The local optima found by the LK local search are in turn exploited by the evolutionary part of the algorithm in order to improve the quality of its simulated population. The results of several experiments conducted on different TSP instances with up to 13,509 cities show the efficacy of the symbiosis between the two heuristics.

A hybrid heuristic for the traveling salesman problem

In this paper we investigate the usefulness of a new operator, inver-over, for an evolutionary algorithm for the TSP. Inver-over is based on simple inversion, however, knowledge taken from other individuals in the population influences its action. Thus, on one hand, the proposed operator is unary, since the inversion is applied to a segment of a single individual, however, the selection of a segment to be inverted is population driven, thus the operator displays some characterictics of recombination.

Inver-over Operator for the TSP

Evolutionary algorithms (EAs), which are based on a powerful principle of evolution: survival of the fittest, and which model some natural phenomena: genetic inheritance and Darwinian strife for survival, constitute an interesting category of modern heuristic search. During the last two decades there has been a growing interest in these algorithms; today, many complex software systems include at least some evolutionary component. However, the process of building an evolutionary program is still art rather than science; often it is based on the intuition and experience of the designer. In this introductory article we present some important ideas behind the construction of evolutionary algorithms. These ideas are illustrated by three test cases: the transportation problem, a particular nonlinear parameter optimization problem, and the traveling salesman problem. We conclude the paper with a brief discussion on how an evolutionary algorithm can be tuned to the problem while solving it, which may increase further efficiency of the algorithm in a significant way.

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Guo Tao

Papers

Inver-over Operator for the TSP

The Spirit of Evolutionary Algorithms