### Mixed-discrete Structural Optimization Using a Rank-niche Evolution Strategy

Abstract

In this study, the evolution strategy, which is one of the evolutionary algorithms, is modified to solve mixed-discrete optimization problems. Three approaches are proposed for handling discrete variables. The first approach is to treat discrete variables as continuous variables and replace the latter with discrete variables that are closest to the continuous variables. The second approach is to compress the difference between discrete variables so that discrete variables far away from the current value will have a higher probability of being selected. The third approach is to represent the discrete variables as integers. As a result, the difference between neighbouring discrete variables becomes equal. This also increases the probability of selection of discrete variables far away from the current value through the mutation operation. Five examples are tested representing single objective, multi-objective, unconstrained, constrained, pure discrete and mixed-discrete variable problems. From the results obtained from the test problems it is evident that the enhanced rank-niche evolution strategy algorithm yields better solutions than other methods for most of the test problems.