Search Space Reduction Model with Trigonometric Function for Linear Equality Constraint-handling: The Case of Portfolio Replication Problem

In the constrained optimization problem, it is difficult that the evolutionary algorithm finds the optimal solution on the whole solution space. The algorithm needs a constraint-handling technique for obtaining the solutions only in the feasible region. In this paper, for the portfolio replication problem which is the linear equality constrained optimization problem, we propose the search space reduction model with larger dimensionality using trigonometric functions as a new constraint-handling technique. The proposed model is employed in an estimation of distribution algorithm and it is applied to the portfolio replication problem. In the numerical experiments, we show the usefulness of the proposed model as compared with a standard constraint-handling technique.