Non-population Metaheuristics with a New Fitness Evaluation to Minimise Total Penalty Costs for a Hybrid Flow Shop with Assembly Operations Scheduling Problem

This paper proposes a new fitness evaluation heuristic called NF. It was used to increase the search ability for two non-population metaheuristics—tabu search (TS) and variable neighborhood search (VNS)—for a hybrid flow shop with assembly operations and unrelated parallel machines. The objective was to minimise the total penalty costs defined as the sum of tardiness, earliness, and flow time costs. The NF heuristic is an adaptation of the backward and forward scheduling heuristics with a new trade-off process among the components of the total penalty costs. It was applied to all operations of a given sequence with simultaneously considering the precedence constraints. The effectiveness of the NF heuristic was compared to the existing fitness evaluation heuristic (EF) by applying all of them to TS and VNS to solve five industrial case studies. The results showed that the NF heuristic dramatically outperformed the EF heuristic for both TS and VNS in terms of solution quality with the relative percentage improvement (%RPI) of 90% approximately. It was also observed that TS obtained a better solution than VNS for a given fitness evaluation with the %RPI in a narrow range of 2-3%. In addition, all proposed solution methods required a time converging to the stable solutions within a practical limit of the planner.