Genetic Algorithm Based on Schemata Theory

Abstract

In actual complicated optimization problems, it is often difficult to find a global optimum solution in admissible computing time. Therefore, in industrial problems, we should find quasi-optimum solution in admissible computing time. In that case, evolutionary computations (ECs) are very attractive. There are several algorithms in the EC family; genetic algorithm (GA), evolutionary strategy (ES), genetic programming (GP), and so on(4; 5; 10). Genetic algorithm (GA) has been firstly presented by J.Holland in 1975(5). The GA, which is the algorithm to mimic the natural evolution, is widely applied to optimization, adaptation and learning problems. The basic algorithm of the GA is often called as simple genetic algorithm (SGA)(4). Many improved algorithms are derived from the SGA. The search performance of the SGA can be discussed from the viewpoints of the early convergence and the evolutionary stagnation(2; 10). The early convergence means that all individuals are rapidly attracted to a local optimum solution and therefore, the global optimum solution cannot be found. The evolutionary stagnation means that the convergence speed becomes slower as the iterative process goes. Once a quasi-optimal solution is found, it is generally difficult for the SGA to find better ones. For overcoming these difficulties, Sato et.al. has presented Minimal Generation Gap (MGG)(8). The application of GA with MGG to several actual problems reveals that the GA with MGG is very effective for actual optimization problems(6). Stochastic Schemata Exploiter (SSE) is also classified into the ECs(1). Although the basic concept of SSE comes from the GA, its algorithm is very different from GA. In GA, the individuals are generated randomly in order to construct a population. After estimating the fitness of individuals, parents are selected from the population according to the fitness value. Offspring are generated from the parents by using genetic operators such as the mutation, the crossover, and so on. SSE algorithm also starts from the population of randomly generated individuals. After estimating the fitness of individuals, sub-populations are generated from the whole population according to semi-order relationship of the sub-populations. Common schemata are extracted from the sub-populations and offspring are generated from the common schemata. The SSE has two attractive features. Firstly, the SSE convergence speed is faster than the SGA because SSE can spread better schemata over the whole population faster than the GA. Secondly, there are very small number of control parameters which has to be defined by users in advance. Since the selection and crossover operators are not necessary in SSE, the control parameters are only population size and mutation rate. However, SSE sometimes converges to not global optimum solution but local one. Genetic Algorithm Based on Schemata Theory