A Filter-Genetic Algorithm For Solving Constrained Optimization Problems And Lot Sizing Problems

In this paper we propose two new methods for solving constrained optimization problems by combining the genetic algorithms and filter methods. The new algorithm was applied to solve one kind of Lot-Sizing problems.Using Filter methods’ filterability instead of fitness function to determine the merits of individuals in the first Filter-Genetic algorithm of the paper, it not only ensures the optimization of the offspring, but also avoids selecting the penalty parameter of the penalty function which is used as a fitness function. Finally, the algorithm is proved to be convergence in theory and the numerical results show the algorithm is effective.The filterability of the Filter would be strengthened in the second Improved Filter-Genetic algorithm introduced of the paper. The selection of the offspring would be focused on the Filter Set when the Filter Set reached a certain size during the iterative process. The evolution would be accelerated by the Filter’s filterability. The convergence of the algorithm is discussed and the numerical results show the algorithm is effective, too.At the last of the paper, an Economic Lot Sizing model with three suppliers was proposed. The property of the model had been proved and the Filter-Genetic algorithm was applied to solve one kind of Lot Sizing problem. A numerical simulation had been done for further research.