Title: Reference-point-based GWO algorithm for cutting parallel scheduling problems with bi-criteria objective

Authors: Ronghua Meng; Yunqing Rao; Zhengjia Wu; Xiaofei Xu

Addresses: The Hubei Key Laboratory of Hydroelectric Machinery Design and Maintenance, China Three Gorges University, Yichang, 443002, China ' The State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China ' The Hubei Key Laboratory of Hydroelectric Machinery Design and Maintenance, China Three Gorges University, Yichang, 443002, China ' The State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China

Abstract: This study investigates an unrelated parallel machine scheduling problem (UPMSP) with machine eligibility, setup times, and collecting times, which is inspired from a realistic scheduling problem in the cutting workshop. A new mixed-integer programming model that minimises total cost and makespan is proposed to address this problem. The main characteristic of UPMSP is the available machine constraint. An improved grey wolf optimiser (GWO) with non-dominated sorting and reference-point-based selection strategy balance the distribution of the Pareto solutions. The improved encircling and attacking strategies help to avoid the local optima or adjust the evolutionary direction. The proposed algorithm is compared with four other algorithms in our paper. Experimental results demonstrate that the proposed algorithm outperforms the other algorithms, especially in terms of the number and distribution of Pareto solutions. [Submitted: 26 July 2019; Accepted: 24 March 2021]

Keywords: parallel machine scheduling problem; mixed-integer programming model; grey wolf optimiser; GWO; total costing and total makespan.

DOI: 10.1504/EJIE.2026.155562

European Journal of Industrial Engineering, 2026 Vol.22 No.1, pp.1 - 21

Accepted: 24 Mar 2021
Published online: 05 Aug 2026 *

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