A Problem-Oriented Pareto Evolutionary Algorithm for the Generalized Assignment Problem with Load Balancing

Abstract

Efficient task allocation is essential for improving operational efficiency and maintaining system stability in automated production and logistics systems. Traditional assignment models mainly focus on minimizing assignment cost while neglecting workload balance, which may lead to resource overloading and operational bottlenecks. To address this issue, this paper studies a multi-objective generalized assignment problem with load balancing (MOGAP-LB), where both the total assignment cost and the maximum load occupancy rate are minimized simultaneously. To solve this problem, a problemoriented Pareto evolutionary algorithm (PEA) is proposed. The proposed method integrates three complementary repair rules to efficiently restore feasibility under capacity constraints while promoting balanced workload distribution. In addition, an $\varepsilon$ dominance-based selective local search strategy is introduced to enhance both convergence and diversity of the obtained Pareto solutions. Experimental results on twelve OR-Library benchmark instances demonstrate that the proposed algorithm consistently outperforms several representative multi-objective evolutionary algorithms in terms of IGD and GD metrics. These results verify the effectiveness of the proposed method for loadbalanced resource allocation in automated production and logistics systems.