Estimation of distribution algorithm for permutation flow shops with total flowtime minimization

In this paper, an Estimation of Distribution Algorithm (EDA) is proposed for permutation flow shops to minimize total flowtime. Longest Common Subsequence (LCS) is incorporated into the probability distribution model to mine good ‘‘genes’’. Different from common EDAs, each offspring individual is produced from a seed, which is selected from the population by the roulette method. The LCS between the seed individual and the best solution found so far is regarded as good ‘‘genes’’, which are inherited by offspring with a probability less than 100% to guarantee the population diversity. An effective Variable Neighborhood Search (VNS) is integrated into the proposed EDA to further improve the performance. Experimental results show that the inheritance of good ‘‘genes’’ obtained by LCS can improve the performance of the proposed EDA. The proposed hybrid EDA outperforms other existing algorithms for the considered problem in the literature. Furthermore, the proposed hybrid EDA improved 42 out of 90 current best solutions for Taillard benchmark instances.