Multi-Objective Flexible Job Shop Scheduling Minimizing Makespan, Machine Workload, and Energy Consumption

This study establishes a tri-objective model for the flexible job shop scheduling problem to minimize makespan, total machine workload, and energy consumption. A multi-objective hiking optimization algorithm (MOHOA) is developed by combining good-point-set initialization, Cauchy mutation, and reference-point-based environmental selection. Its performance is evaluated on twelve benchmark functions and MK01–MK10 against six general multi-objective algorithms; a scheduling-specific HSGA adaptation is additionally evaluated on the MK instances. Statistical tests, ablation experiments, and mutation-probability sensitivity analysis are conducted to assess its performance. MOHOA achieves the best mean IGD and HV on ZDT1, ZDT2, and ZDT6 and ranks second overall on the benchmark functions. On the MK instances, it ranks second overall for both indicators and obtains the second-best mean IGD on five cases. Retaining the hiking update significantly improves IGD over Cauchy-only search on eight MK instances, supporting the contribution of the combined search mechanisms.