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Algorithms
Volume 18
Issue 12
10.3390/a18120746
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Bi-Objective Optimization with Mode-Oriented Genetic Algorithm for Multi-Mode Resource-Constrained Project Scheduling

by
Mingcong Xia
1,2,
Guokai Liang
1,
Rui Tong
1,
Jianxin Zhu
1,
Xin Xie
1,
Jintao Chen
1,
Weihua Tan
3,4,* and
Yuting Liu
5
1
Guangzhou Power Supply Bureau, Guangdong Power Grid Co., Ltd., Guangzhou, 510510, China
2
School of Electric Power Engineering, South China University of Technology, Guangzhou, 510006, China
3
School of Information and Electrical Engineering, Hunan University of Science and Technology, Xiangtan, 411201, China
4
Sanya Institute of Hunan University of Science and Technology, Sanya, 572024, China
5
College of Electrical and Information Engineering, Hunan University, Changsha, 410082, China
*
Author to whom correspondence should be addressed.
Algorithms 2025, 18(12), 746; https://doi.org/10.3390/a18120746 (registering DOI)
Submission received: 4 November 2025 / Revised: 22 November 2025 / Accepted: 26 November 2025 / Published: 27 November 2025
(This article belongs to the Section Algorithms for Multidisciplinary Applications)
Versions Notes

Abstract

To address the time–cost trade-off challenge in real-world practices, a bi-objective optimization model of the Multi-mode Resource-Constrained Project Scheduling Problem is proposed with simultaneously minimizing both the project makespan and the resource cost. A mode-oriented Non-dominated Sorting Genetic Algorithm II is developed to solve the formulated problem. Two key improvements are introduced: a mode-repair mechanism is incorporated during the initialization phase to generate feasible execution modes, thereby improving the quality of initial solutions and accelerating search efficiency, and four neighborhood structures based on mode and task execution lists are designed for local search, enabling fine-grained solution refinement in each iteration. Extensive experimental studies are conducted to verify the effectiveness of the proposed strategies, and comparative evaluations with state-of-the-art algorithms demonstrate that MNSGA-II achieves superior performance across multiple metrics, including lower mean ideal distance, better solution quality, improved diversity, and more uniform distribution of Pareto-optimal solutions.
Keywords: resource-constrained project scheduling problem; multi-objective optimization; neighborhood search; heuristic resource-constrained project scheduling problem; multi-objective optimization; neighborhood search; heuristic

Share and Cite

MDPI and ACS Style

Xia, M.; Liang, G.; Tong, R.; Zhu, J.; Xie, X.; Chen, J.; Tan, W.; Liu, Y. Bi-Objective Optimization with Mode-Oriented Genetic Algorithm for Multi-Mode Resource-Constrained Project Scheduling. Algorithms 2025, 18, 746. https://doi.org/10.3390/a18120746

AMA Style

Xia M, Liang G, Tong R, Zhu J, Xie X, Chen J, Tan W, Liu Y. Bi-Objective Optimization with Mode-Oriented Genetic Algorithm for Multi-Mode Resource-Constrained Project Scheduling. Algorithms. 2025; 18(12):746. https://doi.org/10.3390/a18120746

Chicago/Turabian Style

Xia, Mingcong, Guokai Liang, Rui Tong, Jianxin Zhu, Xin Xie, Jintao Chen, Weihua Tan, and Yuting Liu. 2025. "Bi-Objective Optimization with Mode-Oriented Genetic Algorithm for Multi-Mode Resource-Constrained Project Scheduling" Algorithms 18, no. 12: 746. https://doi.org/10.3390/a18120746

APA Style

Xia, M., Liang, G., Tong, R., Zhu, J., Xie, X., Chen, J., Tan, W., & Liu, Y. (2025). Bi-Objective Optimization with Mode-Oriented Genetic Algorithm for Multi-Mode Resource-Constrained Project Scheduling. Algorithms, 18(12), 746. https://doi.org/10.3390/a18120746

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