Advanced Metaheuristics for Bi-criteria Optimization in a Distributed Blocking Flow Shop Problem with Setup Times

Achraf Sayah (), Said Aqil () and Mohamed Lahby ()
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Achraf Sayah: Hassan II University of Casablanca
Said Aqil: Hassan II University of Casablanca
Mohamed Lahby: Hassan II University of Casablanca

SN Operations Research Forum, 2025, vol. 6, issue 4, 1-63

Abstract: Abstract In this paper, a bi-criteria Distributed Blocking Flow Shop Scheduling Problem with Sequence-Independent Setup Times (DBFSSP-SIST) is considered. The primary objective is to minimize the maximum completion time (makespan) ( $$\mathcal {C}_{\max }$$ C max ) and the maximum tardiness ( $$\mathcal {T}_{max}$$ T max ). These criteria are combined into a single weighted objective function ( $$\mathcal {K}$$ K ) using linear weights to balance their importance. To address this problem, we propose a Mixed Integer Linear Programming (MILP) model as an exact solution method, alongside a set of advanced metaheuristics. Specifically, three metaheuristics are developed: the Oriented Self-Crossover Genetic Algorithm (OSCGA), the Exchanged Multi-Population Migratory Bird Optimization (EMPMBO), and the Multi-Strategy Iterated Greedy (MSIG) algorithm. Each algorithm is implemented with two initialization strategies: the Nawaz-Enscore-Ham (NEH) and the Greedy Randomized Adaptive Search Procedure (GRASP), resulting in six variations. Computational experiments were conducted on a range of test instances. The results demonstrate that the MSIG algorithm consistently outperforms the other methods, with MSIG using NEH initialization (MSIG $$_{1}$$ 1 ) delivering the best performance, even surpassing its GRASP-initialized counterpart (MSIG $$_2$$ 2 ).

Keywords: Bi-criteria scheduling; Distributed permutation flow shop; Metaheuristics; Makespan and maximum tardiness; Blocking constraint (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s43069-025-00559-1

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