Crossover

About: Crossover is a research topic. Over the lifetime, 15599 publications have been published within this topic receiving 283676 citations.

Genetic Algorithms for Real Parameter Optimization

Abstract: This paper is concerned with the application of genetic algorithms to optimization problems over several real parameters. It is shown that k-point crossover (for k small relative to the number of parameter) can be viewed as a crossover operation on the vector of parameters plus perturbations of some of the parameters. Mutation can also be considered as a perturbation of some of the parameters. This suggests a genetic algorithm that uses real parameter vectors as chromosomes, real parameters as genes, and real numbers as alleles. Such an algorithm is proposed with two possible crossover methods. Schemata are defined for this algorithm, and it is shown that Holland's Schema theorem holds for one of these crossover methods. Experimental results are given that indicate that this algorithm with a mixture of the two crossover methods outperformed the binary-coded genetic algorithm on 7 of 9 test problems.

A study of permutation crossover operators on the traveling salesman problem

Abstract: The application of Genetic Algorithms to problems which are not amenable to bit string representation and traditional crossover has been a growing area of interest. One approach has been to represent solutions by permutations of a list, and "permutation crossover" operators have been introduced to preserve legality of offspring. Three permutation crossovers are analyzed to characterize how they sample the o-schema space, and hence what type of problems they may be applicable to. Experiments performed on the Traveling Salesman Problem go some way to support the theoretical analysis.

Niching methods for genetic algorithms

Abstract: Niching methods extend genetic algorithms to domains that require the location and maintenance of multiple solutions. Such domains include classification and machine learning, multimodal function optimization, multiobjective function optimization, and simulation of complex and adaptive systems. This study presents a comprehensive treatment of niching methods and the related topic of population diversity. Its purpose is to analyze existing niching methods and to design improved niching methods. To achieve this purpose, it first develops a general framework for the modelling of niching methods, and then applies this framework to construct models of individual niching methods, specifically crowding and sharing methods. Using a constructed model of crowding, this study determines why crowding methods over the last two decades have not made effective niching methods. A series of tests and design modifications results in the development of a highly effective form of crowding, called deterministic crowding. Further analysis of deterministic crowding focuses upon the distribution of population elements among niches, that arises from the combination of crossover and replacement selection. Interactions among niches are isolated and explained. The concept of crossover hillclimbing is introduced. Using constructed models of fitness sharing, this study derives lower bounds on the population size required to maintain, with probability $\gamma$, a fixed number of desired niches. It also derives expressions for the expected time to disappearance of a desired niche, and relates disappearance time to population size. Models are presented of sharing under selection, and sharing under both selection and crossover. Some models assume that all niches are equivalent with respect to fitness. Others allow niches to differ with respect to fitness. Focusing on the differences between parallel and sequential niching methods, this study compares and further examines four niching methods--crowding, sharing, sequential niching, and parallel hillclimbing. The four niching methods undergo rigorous testing on optimization and classification problems of increasing difficulty; a new niching-based technique is introduced that extends genetic algorithms to classification problems.

A multi-objective genetic local search algorithm and its application to flowshop scheduling

Abstract: We propose a hybrid algorithm for finding a set of nondominated solutions of a multi objective optimization problem. In the proposed algorithm, a local search procedure is applied to each solution (i.e., each individual) generated by genetic operations. Our algorithm uses a weighted sum of multiple objectives as a fitness function. The fitness function is utilized when a pair of parent solutions are selected for generating a new solution by crossover and mutation operations. A local search procedure is applied to the new solution to maximize its fitness value. One characteristic feature of our algorithm is to randomly specify weight values whenever a pair of parent solutions are selected. That is, each selection (i.e., the selection of two parent solutions) is performed by a different weight vector. Another characteristic feature of our algorithm is not to examine all neighborhood solutions of a current solution in the local search procedure. Only a small number of neighborhood solutions are examined to prevent the local search procedure from spending almost all available computation time in our algorithm. High performance of our algorithm is demonstrated by applying it to multi objective flowshop scheduling problems.