A Genetic Algorithm with randomly shifted Gray codes and local optimizations based on quadratic approximations of the fitness

We present a Genetic Algorithm that we developed in order to address computationally expensive optimization problems. In order to accelerate this algorithm, we establish, generation after generation, quadratic approximations of the fitness in the close neighborhood of the best-so-far individual. We then inject in the population an individual that corresponds to the optimum of this approximation. We also introduce a modified mutation operator that acts on randomly-shifted Gray codes. We show that these techniques lead to the global optimum of typical benchmark problems in 5, 10 and 20 dimensions with a probability of success in one run of the order
of 95-97% and an average number of fitness evaluations of the order of 400−750×n, where n refers to the dimension of the problem.