Bi-Objective Integrated Scheduling of Job Shop Problems and Material Handling Robots with Setup Time

Liu, Runze; Jia, Qi; Yu, Hui; Gao, Kaizhou; Fu, Yaping; Yin, Li

doi:10.3390/math13030447

This is an early access version, the complete PDF, HTML, and XML versions will be available soon.

Open AccessArticle

Bi-Objective Integrated Scheduling of Job Shop Problems and Material Handling Robots with Setup Time

by

Runze Liu

^1,2

,

Qi Jia

^1,2

,

Hui Yu

^1,2

,

Kaizhou Gao

^1,2,*

,

Yaping Fu

^3,* and

Li Yin

^1,2

¹

Macau Institute of Systems Engineering, Macau University of Science and Technology, Macao 999078, China

²

Zhuhai MUST Science and Technology Research Institute, Macau University of Science and Technology, Zhuhai 519031, China

³

School of Business, Qingdao University, Qingdao 266071, China

^*

Authors to whom correspondence should be addressed.

Mathematics 2025, 13(3), 447; https://doi.org/10.3390/math13030447

Submission received: 4 January 2025 / Revised: 21 January 2025 / Accepted: 27 January 2025 / Published: 28 January 2025

(This article belongs to the Section E: Applied Mathematics)

Download Versions Notes

Abstract

This work investigates the bi-objective integrated scheduling of job shop problems and material handling robots with setup time. The objective is to minimize the maximum completion time and the mean of earliness and tardiness simultaneously. First, a mathematical model is established to describe the problems. Then, different meta-heuristics and their variants are developed to solve the problems, including genetic algorithms, particle swarm optimization, and artificial bee colonies. To improve the performance of algorithms, seven local search operators are proposed. Moreover, two reinforcement learning algorithms, Q-learning and SARSA, are designed to help the algorithm select appropriate local search operators during iterations, further improving the convergence of algorithms. Finally, based on 82 benchmark cases with different scales, the effectiveness of the suggested algorithms is evaluated by comprehensive numerical experiments. The experimental results and discussions show that the genetic algorithm with SARSA is more competitive than its peers.

Keywords: job shop scheduling; material handling robot; multi-objective optimization; reinforcement learning; meta-heuristics

Share and Cite

MDPI and ACS Style

Liu, R.; Jia, Q.; Yu, H.; Gao, K.; Fu, Y.; Yin, L. Bi-Objective Integrated Scheduling of Job Shop Problems and Material Handling Robots with Setup Time. Mathematics 2025, 13, 447. https://doi.org/10.3390/math13030447

AMA Style

Liu R, Jia Q, Yu H, Gao K, Fu Y, Yin L. Bi-Objective Integrated Scheduling of Job Shop Problems and Material Handling Robots with Setup Time. Mathematics. 2025; 13(3):447. https://doi.org/10.3390/math13030447

Chicago/Turabian Style

Liu, Runze, Qi Jia, Hui Yu, Kaizhou Gao, Yaping Fu, and Li Yin. 2025. "Bi-Objective Integrated Scheduling of Job Shop Problems and Material Handling Robots with Setup Time" Mathematics 13, no. 3: 447. https://doi.org/10.3390/math13030447

APA Style

Liu, R., Jia, Q., Yu, H., Gao, K., Fu, Y., & Yin, L. (2025). Bi-Objective Integrated Scheduling of Job Shop Problems and Material Handling Robots with Setup Time. Mathematics, 13(3), 447. https://doi.org/10.3390/math13030447

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Menu

Bi-Objective Integrated Scheduling of Job Shop Problems and Material Handling Robots with Setup Time

Abstract

Share and Cite

Article Metrics

Article Access Statistics

Further Information

Guidelines

MDPI Initiatives

Follow MDPI