Metamodel Assisted Mixed-Integer Evolution Strategies Based on Kendall Rank Correlation Coefficient

Although mixed-integer evolution strategies (MIES) have been successfully applied to optimization of mixed-integer problems, they may encounter challenges when fitness evaluations are time consuming. In this paper, we propose to use a radial-basis-function network (RBFN) trained based on the rank correlation coefficient distance metric to assist MIES. For the distance metric of the RBFN, we modified a heterogeneous metric (HEOM) by multiplying the weight for each dimension. Whilst the standard RBFN aims to approximate the fitness accurately, the proposed RBFN tries to rank the individuals (according to their fitness) correctly. Kendall rank correlation Coefficient (RCC) is adopted to measure the degree of rank correlation between the fitness and each variable. The higher the rank similarity with fitness, the greater the weight one variable will be given. Experimental results show the efficacy of the MIES assisted by the RBFN trained by maximizing the RCC performs.