Avoiding premature convergence in a mixed-discrete Particle Swarm Optimization (MDPSO) algorithm

Over the past decade or so, Particle Swarm Optimization (PSO) has emerged to be one of most useful methodologies to address complex high dimensional optimization problems - it's popularity can be attributed to its ease of implementation, and fast convergence property (compared to other population based algorithms). However, a premature stagnation of candidate solutions has been long standing in the way of its wider application, particularly to constrained single-objective problems. This issue becomes all the more pronounced in the case of optimization problems that involve a mixture of continuous and discrete design variables. In this paper, a modification of the standard Particle Swarm Optimization (PSO) algorithm is presented, which can adequately address system constraints and deal with mixed-discrete variables. Continuous optimization, as in conventional PSO, is implemented as the primary search strategy; subsequently, the discrete variables are updated using a deterministic nearest vertex approximation criterion. This approach is expected to avoid the undesirable discrepancy in the rate of evolution of discrete and continuous variables. To address the issue of premature convergence, 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 towards the globally best 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 successfully 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.