Equality constraint-handling technique with various mapping points: The case of portfolio replication problem

For solving an equality constrained optimization problem, it is difficult to find an optimal solution by using any evolutionary algorithms. We propose a new technique that handles an equality constraint in this paper. The technique transforms variables of solution on equality constrained search space to them on unconstrained search space through trigonometrical functions. Thus, this paper presents the contribution that an evolutionary algorithm effectively finds good feasible solutions without evolutionary stagnation because an unconstrained space consists only of feasible solutions. However, our technique searches mapping points only on the part of constrained space because it cannot transform the constrained space to fully unconstrained space. Therefore, we expand such a space consisting of various mapping points by exchanging trigonometrical functions on EDA (Estimation of Distribution Algorithm). In numerical experiments, for portfolio replication problems, we demonstrate the effectiveness of our technique.