Theory of Genetic Algorithms II: models for genetic operators over the string-tensor representation of populations and convergence to global optima for arbitrary fitness function under scaling

AbstractWe present a theoretical framework for an asymptotically converging, scaled genetic algorithm which uses an arbitrary-size alphabet and common scaled genetic operators. The alphabet can be interpreted as a set of equidistant real numbers and multiple-spot mutation performs a scalable compromise between pure random search and neighborhood-based change on the alphabet level. We discuss several versions of the crossover operator and their interplay with mutation. In particular, we consider uniform crossover and gene-lottery crossover which does not commute with mutation. The Vose–Liepins version of mutation-crossover is also integrated in our approach. In order to achieve convergence to global optima, the mutation rate and the crossover rate have to be annealed to zero in proper fashion, and unbounded, power-law scaled proportional fitness selection is used with logarithmic growth in the exponent. Our analysis shows that using certain types of crossover operators and large population size allows for particularly slow annealing schedules for the crossover rate. In our discussion, we focus on the following three major aspects based upon contraction properties of the mutation and fitness selection operators: (i) the drive towards uniform populations in a genetic algorithm using standard operations, (ii) weak ergodicity of the inhomogeneous Markov chain describing the probabilistic model for the scaled algorithm, (iii) convergence to globally optimal solutions. In particular, we remove two restrictions imposed in Theorem 8.6 and Remark 8.7 of (Theoret. Comput. Sci. 259 (2001) 1) where a similar type of algorithm is considered as described here: mutation need not commute with crossover and the fitness function (which may come from a coevolutionary single species setting) need not have a single maximum

Performance evaluation of WMN-GA for different mutation and crossover rates considering number of covered users parameter

Node placement problems have been long investigated in the optimization field due to numerous applications in location science and classification. Facility location problems are showing their usefulness to communication networks, and more especially from Wireless Mesh Networks (WMNs) field. Recently, such problems are showing their usefulness to communication networks, where facilities could be servers or routers offering connectivity services to clients. In this paper, we deal with the effect of mutation and crossover operators in GA for node placement problem. We evaluate the performance of the proposed system using different selection operators and different distributions of router nodes considering number of covered users parameter. The simulation results show that for Linear and Exponential ranking methods, the system has a good performance for all rates of crossover and mutation.Peer ReviewedPostprint (published version

Recombination and Self-Adaptation in Multi-objective Genetic Algorithms

This paper investigates the influence of recombination and self-adaptation in real-encoded Multi-Objective Genetic Algorithms (MOGAs). NSGA-II and SPEA2 are used as example to characterize the efficiency of MOGAs in relation to various recombination operators. The blend crossover, the simulated binary crossover and the breeder genetic crossover are compared for both MOGAs on multi-objective problems of the literature. Finally, a self-adaptive recombination scheme is proposed to improve the robustness of MOGAs

Multi-population methods with adaptive mutation for multi-modal optimization problems

open access journalThis paper presents an efficient scheme to locate multiple peaks on multi-modal optimization problems by using genetic algorithms (GAs). The premature convergence problem shows due to the loss of diversity, the multi-population technique can be applied to maintain the diversity in the population and the convergence capacity of GAs. The proposed scheme is the combination of multi-population with adaptive mutation operator, which determines two different mutation probabilities for different sites of the solutions. The probabilities are updated by the fitness and distribution of solutions in the search space during the evolution process. The experimental results demonstrate the performance of the proposed algorithm based on a set of benchmark problems in comparison with relevant algorithms

Self-adaptation of Genetic Operators Through Genetic Programming Techniques

Here we propose an evolutionary algorithm that self modifies its operators at the same time that candidate solutions are evolved. This tackles convergence and lack of diversity issues, leading to better solutions. Operators are represented as trees and are evolved using genetic programming (GP) techniques. The proposed approach is tested with real benchmark functions and an analysis of operator evolution is provided.Comment: Presented in GECCO 201