A Pareto Local-Branching VNS for a Real-Data-Derived Biobjective Generalized Assignment Problem with Multicriteria Decision Support

Capacity-constrained task allocation requires balancing economic efficiency and resource utilization. This study strengthens a multiobjective decision-support framework for a biobjective Generalized Assignment Problem derived from New York City For-Hire Vehicle records. We propose Pareto Local-Branching Variable Neighborhood Search (PLB-VNS), which combines integer-coded NSGA-II for global Pareto exploration with strictly ε-constrained, time-limited MIP reoptimization inside Hamming neighborhoods. PLB-VNS is compared with a 250,000-evaluation NSGA-II baseline over 30 paired random seeds. PLB-VNS achieved median normalized hypervolume 0.90325 versus 0.86349, winning 28 of 30 pairs (two-sided Wilcoxon p = 1.86 × 10−8; rank-biserial effect size 0.9785), while the local-branching phase improved its 150,000-evaluation initializer in all runs. The pooled nondominated front contained 53 distinct objective vectors. Representative solutions were subsequently evaluated with FITradeoff under a reproducible synthetic preference profile, connecting improved Pareto search to transparent multicriteria recommendation.