Capacitated lot sizing by using multi-chromosome crossover strategy

The capacitated lot sizing problem (CLSP) arises when, under capacity constraints, the decision maker has to determine the production schedule and lot sizes that will minimize the total costs involved. The costs considered in this article are order, inventory carrying, and labor costs. The fitness function for the chromosome is computed using these cost elements. Next, the chromosomes are partitioned into good and poor segments based on the individual product chromosomes. This information is later used during crossover operation and results in crossover among multiple chromosomes. Product chromosomes are grouped into three groups, group 1 (top X%), group 2 (next Y%), and group 3 (last Z%). Product chromosomes from Groups 1, 2 and 3 can only form pairs with chromosomes from group 1. Besides, different crossover and mutation probabilities are applied for each group. The results of the experimentation showed that the different strategies of the proposed approach produced much better results than the classical genetic algorithm.