Improved nondominated sorting genetic algorithm-II for bi-objective flexible job-shop scheduling problem

In modern manufacturing industry, not only production efficiency, but also fairness in wages should be emphasized so as to motivate the staff. To this end, this paper addresses the multi-objective flexible job shop scheduling problem (MOFJSP) aiming at minimizing the makespan and maximum wage gap among workers simultaneously. An improved nondominated sorting genetic algorithm-II (INSGAII) is developed. The novelties are mainly presented as follows. First, a probability-based extended precedence preservative crossover operator (PEPPX) is designed for accelerating the convergence rate. Second, in order to solve the multi-modal problem, a “pruning-regenerating” mechanism (PRM) is developed to remove the redundant solutions in objective space and reinsert new solutions. Specifically, a novel metric called “encoding distance” is proposed to measure the diversity of solutions with exactly the same objective function values in chromosome encoding. Meanwhile, a critical path based variable neighborhood search (VNS) is designed to regenerate new solutions replacing the removed ones. Numerical experiments on a wide set of well-known benchmarks have confirmed the effectiveness and efficiency of the proposed INSGA-II.