Efficient multi-objective meta-heuristic algorithms for energy-aware non-permutation flow-shop scheduling problem

• Addressing the energy awareness in a flexible flow-shop scheduling problem. • Proposing multi-objective algorithms for the proposed problem. • Utilizing recent multi-objective and hybrid algorithms in this research area. • Evaluating the performance of the proposed algorithms in extensive cases. This study investigates the optimization of non-permutation flow-shop scheduling problems and lot-sizing simultaneously. Contrary to previous works, we first study the energy awareness of non-permutation flow-shop scheduling and lot-sizing using modified novel meta-heuristic algorithms. In this regard, first, a mixed-integer linear mathematical model is proposed. This model aimed to determine the size of each sub-category and determine each machine's speed within each sub-category to minimize makespan and total consumed energy simultaneously. In order to optimize this model, Multi-objective Ant Lion Optimizer (MOALO), Multi-objective Keshtel Algorithm (MOKA), and Multi-objective Keshtel and Social Engineering Optimizer (MOKSEA) are proposed. First, the validation of the mathematical model is evaluated by implementing it in a real case of the food industry using GAMS software. Next, the Taguchi design of the experiment is applied to adjust the meta-heuristic algorithms' parameters. Then the efficiency of these meta-heuristic algorithms is evaluated by comparing with Epsilon-constraint (EPC), Non-dominated Sorting Genetic Algorithm II (NSGA-II) and Multi-objective Particle Swarm Optimization (MOPSO) using several test problems. The results demonstrated that the MOALO, MOKA, and MOKSEO algorithms could find optimal solutions that can be viewed as a set of Pareto solutions, which means the used algorithm has the necessary validity. Moreover, the proposed hybrid algorithm can provide Pareto solutions in a shorter time than EPC and higher quality than NSGA-II and MOPSO. Finally, the model's key parameters were the subject of sensitivity analysis; the results showed a linear relationship between the processing time and the first and second objective functions.