A Genetic Algorithm Using Infeasible Solutions for Constrained Optimization Problems

The use of genetic algorithms (GAs) to solve combinatorial optimization problems often produces a population of infeasible solutions because of optimization problem constraints. A solution pool with a large number of infeasible solutions results in poor search performance of a GA, or worse, the algorithm ceases to run. In such cases, the methods of penalty function and multi-objective optimization can help GAs run to some extent. However, these methods prevent infeasible solutions from surviving in the solutions pool. Infeasible solutions, particularly those that are produced after several generations, exhibit some achievements in evolutionary computation. They should serve as a positive function in the process of evolution instead of being abandoned from the solution pool. In this study, we extract excellent gene segment for infeasible solutions with a function operation to increase the search performance of GAs. Simulation results on zero-one knapsack problems demonstrate that applying infeasible solutions can improve the search capability of GAs.