A multi-population co-evolutionary algorithm for solving energy-efficient hybrid flow shop scheduling problem

With the worsening global climate, energy-efficient hybrid flow shop scheduling, which simultaneously considers both makespan and total energy consumption (TEC), has gained significant research attention in recent years. However, existing algorithmic frameworks often face challenges in effectively balancing these two conflicting objectives. To address this, this paper introduces a multi-objective multi-population co-evolutionary algorithm (MOMPCEA) based on the interaction between these objectives. Multiple sub-populations are established, each with makespan, TEC, or their weighted sum as its optimization objective. During the self-evolution phase of each sub-population, job-based crossover operators are employed to enhance the algorithm’s global search capability, while distinct neighborhood structures and a self-adaptive mechanism are applied to the weighted sub-population to improve local search performance. Three distinct information-sharing strategies are developed to facilitate inter-population interaction during the iterative process. Furthermore, a dynamic variable neighborhood search strategy, incorporating four types of neighborhood operators, is proposed to further enhance the quality of the non-dominated solution set. The proposed MOMPCEA is benchmarked against three state-of-the-art multi-objective algorithms using C , IGD , and HV indicators. Experimental results demonstrate that MOMPCEA can achieve non-dominated solution sets with superior convergence and diversity.