Species Based Evolutionary Algorithms for Multimodal Optimization: a Brief Review
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WCCI 2010 IEEE World Congress on Computational Intelligence July, 18-23, 2010 - CCIB, Barcelona, Spain CEC IEEE Species Based Evolutionary Algorithms for Multimodal Optimization: A Brief Review Jian-Ping Li, Xiao-Dong Li and Alastair Wood Abstract—The species conservation technique is a relatively problem by dividing a population into sub-populations new approach to finding multiple solutions of a multimodal that evolve in parallel, such as Multiple-National GA optimization problem. When adopting such a technique, a [4], Island Gas [5], the Adaptive Isolation Model [6], species is defined as a group of individuals in a population that and Particle Swarm Optimization [7]. Without have similar characteristics and are dominated by the best communications among the populations, these methods individual, called the species seed. Species conservation techniques are used to identify species within a population and are similar to iterative methods; to conserve the identified species in the current generation. A z implicit parallel sub-population methods attempt to ‘species-based evolutionary algorithm’ (SEA) is the produce multiple solutions by introducing combination of a species conservation technique with an niche/speciation techniques so that a population evolutionary algorithm, such as genetic algorithms, particle diversity is maintained and many niches survive in a swarm optimization, or differential evolution. These SEAs have single population, such as crowding ([8], [9]), fitness been demonstrated to be effective in searching multiple solutions of a multimodal optimization problem. This paper will sharing ([10]-[11]), restricted tournament selection [12] briefly review its principles and its variants developed to date. and species conservation techniques [13], Genetic These methods had been used to solve engineering optimization Sampler [14]. The crowding and fitness sharing are problems and found some new solutions. well-known methods but cannot guarantee that all Keywords - Species conservation technique, species niches survive in a new population. optimization, evolutionary computation, genetic Species conservation is a relatively new technique for algorithm. solving multimodal optimization problems [13] and has been proved to be effective to obtain multiple solutions of tested I. INTRODUCTION multimodal problems. In a recent work by Stoean et al. [15] it any real-world optimization problems are multimodal was shown that the species conservation algorithm can M by nature, where many equally good solutions exist. efficiently keep track of several good search space regions at Finding multiple solutions can help designers to understand once. the design space more thoroughly and to create alternative The aim of this paper is to introduce the basic principles of designs to satisfy design requirements. species conservation techniques and briefly review the Nature has inspired the development of many computational progress of research in this area. This paper is constructed as models, amongst which Evolutionary Computation (EC) is a follows: Section 2 defines the concept of species. Section 3 good example. Even though the majority of EC algorithms and 4 present some species-based evolutionary algorithms. are specifically designed for locating a single global Section 5 summarizes the performance of species optimum, there are many techniques that have been conservation techniques. Finally, some conclusions are developed to solve multimodal optimization problems: presented in Section 6. z iterative methods address the problem of locating multiple optima of a multimodal function by repeatedly II. SPECIES CONCEPT applying the same optimization algorithm. Several techniques have been used to avoid iterations towards A. Species with Fixed Species Distance local minima, such as the tabu technique [1], the Species conservation techniques are based on the species Sequential Niche technique [2] and jump techniques [3]; concept. A species is defined as a group of individuals in a z explicit parallel sub-population methods attempt to population that have similar characteristics and are dominated produce multiple solutions to a multimodal optimization by the best individual, called the species seed. A species will depend on a parameter, called the species distance and σ Manuscript received January 31, 2010. denoted by s J.-P. Li is with School of Engineering, Design and Technology, The distance between two individuals x = xxx ],,,[ University of Bradford, United Kingdom (corresponding author; tel.: iii 21 in = +44-1274234539; e-mail: [email protected]). and x jjj 21 xxx jn ],,,[ can be defined by the Euclidean X.-D. Li is with School of Computer Science and Information Technology, RMIT University, Australia (e-mail: distance: [email protected]). A.S. Wood is with School of Engineering, Design and Technology, University of Bradford, United Kingdom(e-mail:[email protected] ). 978-1-4244-8126-2/10/$26.00 c 2010 IEEE 4156 n points, in which there are three clustering actions: migration, = − 2 splitting, and merging. Hua et al. [22] proposed a Detecting d(xi ,x j ) ∑(xik x jk ) = Peak's Number (DPN) technique to explore new possible k 1 (1) species by using heuristic methods to check each orthogonal This is not the only way in which the distance between two direction from an individual. individuals represented by vectors of real numbers can be defined. Sometimes, the distance term can be defined Li and Wood ([23] and [24]) developed an adaptive species according to specific domain knowledge ([17]-[18]). concept, which we will describe as follows. Intuitively the similarity threshold specifies the upper bound b Adaptive species, denoted bys(x, rx , fx ) , was defined with: on the distance between two individuals for which they are r considered to be similar. In the approach the similarity species seed ( x ), species radius ( x ) and species boundary b threshold will also be used to determine which individuals are fitness ( f x ). Again, a species is dominated by its species worth preserving from one generation to the next. seed and is centered upon the species seed x . For any points ∈ b ∈ b A species is defined with respect to a finite population y s(x, rx , f x ) and z s(x, rx , fx ) , we have P = {}x , x ,…, x and the best individual in the species is N 1 2 N called its species seed, which dominates all the individuals in f (y) + f (z) ⎛ y + z ⎞ the species. Briefly, a species Si is centered upon its < f ⎜ ⎟ 2 ⎝ 2 ⎠ dominating individual (the species seed) x* if, for every ∈ f (y) ≤ f (x) individual y Si , d(x,y) ≤ r (4) x ≥ b * < σ f (y) f x d(x ,y) s / 2 (2) and f (y) ≤ f (x* ) (3) In this definition of species, there is one more parameter. However, the new species definition aims to develop some x2 algorithms to automatically adjust those parameters. It is assumed that the fitness (objective) function is symmetric to the species seed within the species domain. A typical species in one-dimensional space is shown in Fig. 2 n d x represents the distance between the species seed and the nearest neighbor species seed. f n x 0 1 dx Species seed Species Non-dominating individuals Fig. 1 A sample distribution of species in a two-dimensional domain. Fig. 1 illustrates a sample distribution of species in a r r two-dimensional domain. A species is formed of actual x x individuals and occupies a region of the feasibility domain. b f x B. Adaptive Species 0 x z x Without prior knowledge of a problem, it is impossible to 1 choose a single value of niche radius/species distance for all Fig. 2 Distributions of species in one-dimensional space. species [2], since species in a problem will not, in general, be the same size. To overcome the dilemma of selecting a From the optimization point of view, a species is an area suitable species distance, some researchers are studying occupied by a local optimal solution. Its species seed is the adaptive techniques. Bird and Li [19] used the average local optimal solution and so there is only one peak in a distance among members in a population as its ‘species’ species. The maximum number of species is equal to the radius so that no species radius parameter needs to be number of local (including global) solutions of the problem, specified by users. Parmee [20] proposed a Cluster Oriented while in the definition of adaptive species there may be more Genetic Algorithms (COGA) to identify high-performance than one peak in a species, defined by using a fixed species σ regions of complex designs rather than to explore all distance ( s ). solutions. Yao et al. [21] developed a Recursive Middling Algorithm to detect if there is a valley between two given 4157 From the genetic algorithm point of view, an adaptive The only significant differences between the SCGA and the species is a group of individuals that have similar SGA are (i) that, within the generation loop, first the species characteristics. Let s1 ,s 2 ,..., s k be a partitioning of a feasible seeds are determined, and (ii) that, after the genetic operators region into species. Each species has its own parameters. To (selection, crossover, mutation) have been applied and the illustrate this, Fig. 3 shows a possible distribution of species population evaluated, the species conservation process is in a two-dimensional domain. There are some intersections performed. In the above algorithm X s denotes the set of and spaces among species, because a species is defined by a species seeds found in the current generation, G(t) . radius. Therefore, the union of all species sets is part of the feasible region of a problem. There are three special procedures in SCGA: s ∈ R z Determine species seeds: This procedure is developed to ∪ i (5) determine species seeds from a current population. z Conserve species seeds: The new generation is x2 constructed by applying the usual genetic operations: selection, crossover and mutation and by “copying” the found species into the population to keep its diversity.