A mixed-discrete Particle Swarm Optimization algorithm with explicit diversity-preservation

Abstract

Engineering design problems often involve non-linear criterion functions, including inequality and equality constraints, and a mixture of discrete and continuous design variables. Optimization approaches entail substantial challenges when solving such an all-inclusive design problem. In this paper, a modification of the Particle Swarm Optimization (PSO) algorithm is presented, which can adequately address system constraints while dealing with mixed-discrete variables. Continuous search (particle motion), as in conventional PSO, is implemented as the primary search strategy; subsequently, the discrete variables are updated using a deterministic nearest-feasible-vertex criterion. This approach is expected to alleviate the undesirable difference in the rates of evolution of discrete and continuous variables. The premature stagnation of candidate solutions (particles) due to loss of diversity is known to be one of the primary drawbacks of the basic PSO dynamics. To address this issue in high dimensional design problems, a new adaptive diversity-preservation technique is developed. This technique characterizes the population diversity at each iteration. The estimated diversity measure is then used to apply (i) a dynamic repulsion away from the best global solution in the case of continuous variables, and (ii) a stochastic update of the discrete variables. For performance validation, the Mixed-Discrete PSO algorithm is applied to a wide variety of standard test problems: (i) a set of 9 unconstrained problems, and (ii) a comprehensive set of 98 Mixed-Integer Nonlinear Programming (MINLP) problems. We also explore the applicability of this algorithm to a large scale engineering design problem—-wind farm layout optimization.