Solving stochastic programming problems using new approach to Differential Evolution algorithm

Abstract

This paper presents a new approach to Differential Evolution algorithm for solving stochastic programming problems, named DESP. The proposed algorithm introduces a new triangular mutation rule based on the convex combination vector of the triangle and the difference vector between the best and the worst individuals among the three randomly selected vectors. The proposed novel approach to mutation operator is shown to enhance the global and local search capabilities and to increase the convergence speed of the new algorithm compared with conventional DE. DESP uses Deb’s constraint handling technique based on feasibility and the sum of constraint violations without any additional parameters. Besides, a new dynamic tolerance technique to handle equality constraints is also adopted. Two models of stochastic programming (SP) problems are considered: Linear Stochastic Fractional Programming Problems and Multi-objective Stochastic Linear Programming Problems. The comparison results between the DESP and basic DE, basic particle swarm optimization (PSO), Genetic Algorithm (GA) and the available results from where it is indicated that the proposed DESP algorithm is competitive with, and in some cases superior to, other algorithms in terms of final solution quality, efficiency and robustness of the considered problems in comparison with the quoted results in the literature.