Gaussian Linear Regression Crossover for Genetic Algorithms

In the simulated binary crossover, offspring are generated from parents with a coefficient of variation and uses a probability distribution function for the coefficient and there is a linear relationship between parents and offspring. Most existing methods of crossover operators generate offspring on the solution on the decision space during the search and so far, no suggestion has been proposed on making a regression model for generating the offspring on the objective space. In this paper, a Gaussian linear regression crossover has been proposed. The idea is to apply linear regression to model a relationship between parents and offspring in crossover operations through the Gaussian process. The reason for using this process is that the probability distribution of the simulated binary operator is based on the parent in the mating pool on decision space, while the probability distribution of the proposed method is on objective space in the mating pool. To optimize problems on the combinatorial sets, the proposed method is applied. The performance of the proposed algorithm was tested on Computational Expensive Optimization benchmark tests and indicates that the proposed operator is a competitive and promising approach.

Keywords:

Genetic Algorithm , Crossover , Simulated Binary Crossover (SBX) , Gaussian Process , Bayesian Linear Regression