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

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.