Avoiding Premature Convergence in a Mixed-Discrete Particle Swarm Optimization (MDPSO) Algorithm

Abstract

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 problemsit'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.

Particle Swarm Optimization: A Survey of Historical and Recent Developments with Hybridization Perspectives

“…Sun et al [191] introduced a constraint preserving mechanism in PSO (CPMPSO) to solve mixed-variable optimization problems and reported competitive results when tested on two real-world mixed-variable optimization problems. Chowdhury et al [192] considered the issue of premature stagnation of candidate solutions especially in single objective, constrained problems when using PSO and noted its pronounced effect in objective functions that make use of a mixture of continuous and discrete design variables. In order to address this issue, the authors proposed a modification in PSO which made use of continuous optimization as its primary strategy and subsequently a nearest vertex approximation criterion for updating of discrete variables.…”

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