A Real-coded Genetic Algorithm using the Unimodal Normal Distribution Crossover

Abstract

of Techn ology, 4259, Nagatsu ta , Mido ri-ku, Yokoh am a , 226-8502, J ap an E-ma il : kobayasi@dis.ti tech .ac.j p Summary. This chapter pr esent s a real-cod ed genetic algorit hm using th e Unimod al Nor mal Distribu t ion Crossover (UN DX) th at can efficiently optimize fun cti ons with epistasis among param eters. Most convent iona l crossover operators for fun ction optimization have been repor ted to have a serio us problem in t hat th eir performan ce deteriorates considera bly when th ey are a pplied to functions with epistasis among par am eters. We believe that t he reason for the poor performan ce of t he convent iona l crossover operators is that t hey cannot keep t he d ist ribut ion of ind ividu als un chan ged in t he process of repeti t ive crossover operations on functions with epistasis among par ameters. In conside ring t he a bove probl em , we introduce three guidelines , 'P reservat ion of Statistics' , 'Diversity of Offspring' , and 'Enhancement of Robu stness' , for design ing crossover ope rators t hat show good performan ce even on epistatic functions . We show t hat t he UNDX meets t he guidelines very well by a t heore tical ana lysis and t hat t he UNDX shows bet ter performan ce th an some convent iona l crossover operators by applying them to some benchm ark fun cti ons including mu ltimodal and epistatic ones . We also discuss some improvem ents of the UNDX und er the guidelines an d t he relati on between real-coded genetic algorit hms using the UNDX and evolut ion strateg ies (ESs) using th e correlated mu tation .

GA-Based Inference of Euler Angles for Single Particle Analysis

“…By including the best solution of the previous optimization as an initial individual, a more optimal initial population can be generated than for the case in which all parameters are initially random. Since the crossover method is UNDX [7], the best solution portion of the previous optimization of an individual can be changed, except by mutation. By this method, we believe that an incredibly large search space can be searched efficiently.…”

“…Thus, in recent years, the real-coded GA, which uses directly the actual number of vectors for coding, has been proposed. One example of the successful practical application of real-coded GA is the lens design system [7]. As the crossover method, Unimodal Normal Distribution Crossover (UNDX) is used in the current experiment.…”

An Improved Genetic Algorithm with Average-bound Crossover and Wavelet Mutation Operations

“…The crossover operation for comparison is the UNDXBXover, which consists of two published crossover operations: Unimodal normal distribution crossover (UNDX) [12,22] and Blend crossover (BLX-α) [7]. The details of these two crossovers are shown in Appendix B and Appendix C respectively.…”

Automatic Design for Pipe Arrangement using Multi-objective Genetic Algorithms

“…Recently, various real-coded genetic algorithms have been proposed in which the phase of the phenotype place is corresponds to the phase of the genotype place (Ono [4]). Unfortunately, it is difficult to apply the traditional representation and crossover to the current problem because it contains both numerical optimization and combinatorial optimization problems.…”