A hybrid particle swarm optimization with a feasibility-based rule for constrained optimization

Qie He, Ling Wang

Research output: Contribution to journalArticlepeer-review

348 Scopus citations


During the past decade, hybrid algorithms combining evolutionary computation and constraint-handling techniques have shown to be effective to solve constrained optimization problems. For constrained optimization, the penalty function method has been regarded as one of the most popular constraint-handling technique so far, whereas its drawback lies in the determination of suitable penalty factors, which greatly weakens the efficiency of the method. As a novel population-based algorithm, particle swarm optimization (PSO) has gained wide applications in a variety of fields, especially for unconstrained optimization problems. In this paper, a hybrid PSO (HPSO) with a feasibility-based rule is proposed to solve constrained optimization problems. In contrast to the penalty function method, the rule requires no additional parameters and can guide the swarm to the feasible region quickly. In addition, to avoid the premature convergence, simulated annealing (SA) is applied to the best solution of the swarm to help the algorithm escape from local optima. Simulation and comparisons based on several well-studied benchmarks demonstrate the effectiveness, efficiency and robustness of the proposed HPSO. Moreover, the effects of several crucial parameters on the performance of the HPSO are studied as well.

Original languageEnglish (US)
Pages (from-to)1407-1422
Number of pages16
JournalApplied Mathematics and Computation
Issue number2
StatePublished - Mar 15 2007


  • Constrained optimization
  • Feasibility-based rule
  • Particle swarm optimization
  • Simulated annealing


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