Hideaki Suzuki Page 1 of 10 Yoh Iwasa Dep. of Biology, Kyushu Univ. Fukuoka 812-81, JPN yiwasscb@mbox.nc.kyushu-u.ac.jp Hideaki Suzuki Honda R&D Co., Ltd. Wako Res. Cen. 1-4-1 Chuo, Wako, Saitama 351-01 JPN h_suzuki@fun.f.rd.honda.co.jp GA Performance in a Babel-like Fitness Landscape Abstract The performance of genetic algorithms (GAs) is studied under a babel-like fitness landscape, in which only a one bit sequence is significantly advantageous over the others. Under this landscape, the most dominant process to determine the GA performance is creation of the advantageous sequence, and crossover facilitates the creation, thereby improves the GA performance. We first conduct a computer simulation using the simple GA, and examine the waiting time until domination of the advantageous sequence ( ). It is shown that crossover with mildly high rate reduces significantly and that the magnitude of this reduction ( ) is the largest when the mutation rate is an intermediate value. Second, we mathematically analyze the model and estimate the value of . From these observations, we determine implementation criteria for GAs, which are useful when we apply GAs to engineering problems such as having a conspicuously discontinuous fitness landscape. 1: Introduction Recently in the engineering field, genetic algo- rithms (GAs) have attracted a great deal of attention as optimization methods [9, 8, 15, 7, 6, 17, 14]. In GAs, each design of an object is typically coded in a gene-like bit sequence and a population of those sequences is prepared. An optimal (or a close to optimal) design is searched for by evolutionary opera- tions including reproduction, natural selection, mutation, and genetic recombination. Among these operations, the most characteristic one is the genetic recombination, or crossover operation. Since GAs without crossover are nothing more than a parallel hill-climbing method, crossover is a key operation to achieve the optimal design in the shortest number of trials. In previous studies, however, crossover’s effec- T d T d A cross A cross tiveness in GAs has met with varying degrees of success, depending upon the problem domain and its fitness landscape. We are still far from achieving a complete understanding of GAs, which is important from not only an engineering but also a biological point of view. Recently, Suzuki [18, 19] proposed an evolu- tionary programming methodology, MUNCs, in which multiple von Neumann computers with machine language architecture evolve towards the creation of a program that solves a problem prepared in an environ- mental database. He used GAs for the evolution of MUNCs and found that crossover contributed to the acceleration. Fig. 1 shows the basic evolutionary picture of this system. A sequence of binary bits, which is represented in a row of a binary matrix, codes a program which determines the function of the computer. A part of this bit sequence can constitute an advantageous “schema” which corresponds to a set of machine instructions with an advantageous function, and through the processes shown in Fig. 1(b), those functional schemas appear and dominate the popula- tion. Because in MUNCs typical orders of those advantageous schemas are rather large, evolution proceeds with a discontinuous picture; long neutral evolutionary periods [10] are punctuated by intermit- tent short adaptive evolutionary phases during which advantageous schemas spread through the population. In this paper, we use a simpler model and study the acceleration effect by the crossover in MUNCs. We focus on a single advantageous schema and conduct a computer simulation examining the time until an advantageous schema comes to predominate. Taking after MUNCs, the fitness landscape is a babel-like one: an individual enjoys a very high selective advantage if the advantageous schema is present in that individual, and all other sequences without the schema are assumed to be neutral. This very epistatic fitness function makes ‘creation’ the most dominant process in evolution, and makes crossover a beneficial process