A hybrid evolutionary algorithm with importance sampling for multi-dimensional optimization

A hybrid evolutionary algorithm with importance sampling method is proposed for multi-dimensional optimization problems in this paper. In order to make use of the information provided in the search process, a set of visited solutions is selected to give scores for intervals in each dimension, and they are updated as algorithm proceeds. Those intervals with higher scores are regarded as good intervals, which are used to estimate the joint distribution of optimal solutions through an interaction between the pool of good genetics, which are the individuals with smaller fitness values. And the sampling probabilities for good genetics are determined through an interaction between those estimated good intervals. It is a cross validation mechanism which determines the sampling probabilities for good intervals and genetics, and the resulted probabilities are used to design crossover, mutation and other stochastic operators with importance sampling method. As the selection of genetics and intervals is not directly dependent on the values of fitness, the resulted offsprings may avoid the trap of local optima. And a purely random EA is also combined into the proposed algorithm to maintain the diversity of population. 30 benchmark test functions are used to evaluate the performance of the proposed algorithm, and it is found that the proposed hybrid algorithm is an efficient algorithm for multi-dimensional optimization problems considered in this paper.