An Improved Estimation of Distribution Algorithm for Mixed-Integer Nonlinear Programming Problems: EDAIImv

Abstract

In a mixed-integer nonlinear programming problem, integer restrictions divide the feasible region into discontinuous feasible parts with different sizes. Meta-heuristic optimization algorithms quickly lose diversity in such scenarios and get trapped in local optima. In this work, we propose an Estimation of Distribution Algorithm (EDA) with two modifications from its previous version (EDAmv). The first modification consists in establishing the exploration and exploitation components for the histogram of discrete variables, aimed at improving the performance of the algorithm during the evolution. The second modification is a repulsion operator to overcome the population stagnation in discontinuous parts, so as continuing the search for possible solutions in other regions. From a comparative study on 16 test problems, the individual contribution of each modification was verified. According to statistical test results, the new proposal shows a significantly better performance than the other competitors tested.