Bayesian learning based elitist nondominated sorting algorithm for a kind of multi-objective integrated production scheduling and transportation problem

This paper focuses on a kind of multi-objective integrated production scheduling and transportation problem (MIPSTP), which is encountered in many real-life industrial processes. MIPSTP contains a production stage for processing products and a transportation stage for transporting products. In MIPSTP, we consider a dedicated integration of distributed scheduling and transportation regarding the two stages, arising from a practical project for a cooperative iron and steel company. The objective of MIPSTP is to minimize the total completion time of each factory and total transportation cost. To solve the problem, a Bayesian learning-based elitist nondominated sorting algorithm (BLENSA) is proposed. The primary highlights of this work are two-fold: 1) new solution structures of MIPSTP and 2) novel search model of BLENSA. For the solution structures, we propose for the first time the mathematical description of MIPSTP, accounting for several features in applications and so is different from conventional scheduling problems. For the search model of BLENSA, we propose a Bayesian learning-based probability model to learn valuable knowledge about nondominated solutions. Thereby, BLENSA combines the Bayesian learning-based probability model to produce a candidate population (CP) and the nondominated sorting method to generate a main population (MP). Next, we propose a greedy competition strategy to construct MP from CP and MP for the next generation. Results of experiments on 57 test instances and a real-life case study demonstrate the effectiveness and practical values of BLENSA.