A self-guided differential evolution with neighborhood search for permutation flow shop scheduling

• Constructive heuristics and discrete harmony search are used to initialize.
• A guided agent based on the probabilistic model is proposed.
• Multiple mutation and crossover based on the guided agent are proposed.
• Neighborhood search based on the variable neighborhood search is designed.
• The convergence of the proposed algorithm is analyzed with Markov chain.

The permutation flow shop scheduling problem (PFSSP) is one of the most widely studied production scheduling problems and a typical NP-hard combinatorial optimization problems as well. In this paper, a self-guided differential evolution with neighborhood search (NS-SGDE) is presented for the PFSSP with the objectives of minimizing the maximum completion time. Firstly, some constructive heuristics are incorporated into the discrete harmony search (DHS) algorithm to initialize the population. Secondly, a guided agent based on the probabilistic model is proposed to guide the DE-based exploration phase to generate the offspring. Thirdly, multiple mutation and crossover operations based on the guided agent are employed to explore more effective solutions. Fourthly, the neighborhood search based on the variable neighborhood search (VNS) is designed to further improve the search ability. Moreover, the convergence of NS-SGDE for PFSSP is analyzed according to the theory of Markov chain. Computational simulations and comparisons with some existing algorithms based on some widely used benchmark instances of the PFSSP are carried out, which demonstrate the effectiveness of the proposed NS-SGDE in solving the PFSSP.