(untitled) (European Journal of Pure and Applied Mathematics, 2025)
The multi-objective resource allocation problem (MORAP) refers to the challenge of distributing limited resources across multiple projects or business divisions while simultaneously satisfying several, often conflicting, objectives. Such problems are common in engineering, management, and operations research, where decision-makers must balance cost, efficiency, and performance. To address this challenge, this paper introduces a novel Genetic Algorithm with Hybrid Mutation (GA-HM) specifically designed for MORAP. The proposed approach integrates two complementary mutation operators—displacement mutation and inversion mutation—applied in a randomized manner. This hybridization increases the exploration capability of the algorithm, maintains population diversity, and reduces the risk of premature convergence to local optima. To evaluate the effectiveness of GA-HM, two benchmark test problems from the literature are considered, both involving multi-objective workforce-task allocation. Experimental results clearly demonstrate that GA-HM consistently produces superior solutions compared to existing approaches such as fuzzy dynamic programming, fuzzy dynamic optimization, effective GA methods, k-means-based GA, and multi-objective hybrid GAs. Importantly, GA-HM not only identifies optimal trade-offs between cost and efficiency but also provides a well-distributed set of non-dominated solutions, offering decision-makers a broader range of alternatives for resource planning. Overall, the findings confirm that GA-HM is a robust and efficient method for solving MORAPs. By generating diverse Pareto-optimal solutions, the algorithm equips practitioners with practical decision support tools for complex multi-objective optimization tasks. Moreover, the proposed methodology demonstrates strong potential for extension to other real-world engineering and management applications that require effective multi-objective resource allocation strategies.