Scheduling flowshops with condition-based maintenance constraint to minimize expected makespan

Flexible job-shop scheduling problem (FJSP) is an extended traditional job-shop scheduling problem, which more approximates to practical scheduling problems. This paper presents a multi-objective genetic algorithm (MOGA) based on immune and entropy principle to solve the multi-objective FJSP. In this improved MOGA, the fitness scheme based on Pareto-optimality is applied, and the immune and entropy principle is used to keep the diversity of individuals and overcome the problem of premature convergence. Efficient crossover and mutation operators are proposed to adapt to the special chromosome structure. The proposed algorithm is evaluated on some representative instances, and the comparison with other approaches in the latest papers validates the effectiveness of the proposed algorithm.