A Preference-Driven SPEA2 for Hyper-Rectangular Regions of Interest with Application to Emergency Resource Allocation

Many existing preference-based multi-objective evolutionary algorithms compress decision-maker preferences into a single point or direction, which limits their ability to specify desired objective ranges. This paper proposes Dual-Layer SPEA2 with Preference Differential Evolution (DLSPEA2-PDE), which guides populations toward hyper-rectangular preference regions of interest through three mechanisms: virtual boundary reference-point guidance, dual-layer fitness assignment, and region-aware differential evolution. The algorithm is validated on ZDT and DTLZ benchmark suites under single-ROI, multi-ROI, and infeasible-ROI scenarios, and comparisons with diverse types of preference-based MOEAs confirm its robustness and coverage uniformity under diverse ROI configurations. To demonstrate practical utility, the algorithm is applied to a multi-stage emergency resource allocation model that accounts for pre-disaster prediction uncertainty and employs conditional value-at-risk to control tail risk, capturing how prediction biases propagate and amplify through inter-stage coupling. On this problem, DLSPEA2-PDE significantly outperforms SPEA2 across all indicators, and runs substantially faster than T-NSGA-II at comparable solution quality.