To solve constrained optimization problems (COPs) with genetic algorithms, different methods have been proposed to handle constraints, but none of them are specifically designed for model-building genetic algorithms (MBGAs). This paper presents a three-population scheme, abbreviated as B-3Pop, which features three populations: a feasible one, an infeasible one, and a third one to explore the boundary between the feasible and infeasible spaces with MBGAs. The core idea is to learn how to combine feasible and infeasible solutions to evolve optimal solutions near the boundary. Empirically, B-3Pop outperforms five widely used constraint-handling methods—elimination, dominance concept, penalization, adaptive segregational constraint-handling methods, and the feasible-infeasible two-population scheme—in terms of the number of function evaluations on all six tested COPs: dimensional knapsack, uncapacitated warehouse location, Steiner tree, capacitated minimum spanning tree, capacitated p-median, and weighted maximum-2-satisfiability problems.

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A Constraint-Handling Method for Model-Building Genetic Algorithm: Three-Population Scheme

  • Yu-Hao Kao,
  • Chi-Hsien Chang,
  • Tian-Li Yu

摘要

To solve constrained optimization problems (COPs) with genetic algorithms, different methods have been proposed to handle constraints, but none of them are specifically designed for model-building genetic algorithms (MBGAs). This paper presents a three-population scheme, abbreviated as B-3Pop, which features three populations: a feasible one, an infeasible one, and a third one to explore the boundary between the feasible and infeasible spaces with MBGAs. The core idea is to learn how to combine feasible and infeasible solutions to evolve optimal solutions near the boundary. Empirically, B-3Pop outperforms five widely used constraint-handling methods—elimination, dominance concept, penalization, adaptive segregational constraint-handling methods, and the feasible-infeasible two-population scheme—in terms of the number of function evaluations on all six tested COPs: dimensional knapsack, uncapacitated warehouse location, Steiner tree, capacitated minimum spanning tree, capacitated p-median, and weighted maximum-2-satisfiability problems.