基于可信性测度的三角模糊多目标机会约束应急物资调度模型与改进遗传算法

Triangular Fuzzy Multi-Objective Chance-Constrained Emergency Material Scheduling Model Based on Credibility Measure and Its Improved Genetic Algorithm

摘要: 针对城市洪涝灾害初期应急物资调度中受灾点需求与路网通行状态的双重模糊不确定性，建立一类基于可信性测度的三角模糊多目标机会约束规划模型。以三角模糊数刻画物资需求，以道路通行可靠度约束刻画路网损毁风险；在库存约束和通行可靠度约束下，以配送时效、运输成本和道路损毁风险为目标函数，构造模糊多目标机会约束优化问题。利用可信性测度及其等价刻画，将模糊机会约束转化为确定性等价形式。针对标准遗传算法易早熟、Pareto解集分布均匀性差的问题，设计自适应交叉变异算子，引入外部档案维护非支配解多样性，提出改进非支配排序遗传算法。基于地级市应急调拨数据开展数值实验，采用超体积HV指标和迭代收敛曲线评价Pareto解集的收敛性与多样性，并对需求置信水平和道路可靠度进行双参数灵敏度分析。数值结果表明，所提模型能刻画模糊不确定性与路网损毁对调度方案的耦合影响，改进算法在收敛性和多样性上优于对比算法。

Abstract: To address the dual fuzzy uncertainties in demand at disaster-affected sites and road network connectivity during the early response phase of urban flood disasters, this paper develops a triangular fuzzy multi-objective chance-constrained programming model on the basis of credibility measure. Triangular fuzzy numbers are employed to quantify material requirements, while road connectivity reliability constraints are formulated to capture the risk of road network disruption. Subject to inventory and connectivity reliability constraints, a fuzzy multi-objective chance-constrained optimization framework is established, with distribution timeliness, transportation cost and road disruption risk defined as objective functions. By virtue of credibility measure and its equivalent transformation, the fuzzy chance constraints are converted into their deterministic counterparts. To remedy the inherent limitations of the conventional genetic algorithm, including premature convergence and uneven distribution of the Pareto solution set, adaptive crossover and mutation operators are devised, and an external archive strategy is incorporated to preserve the diversity of non-dominated solutions. On this basis, an improved non-dominated sorting genetic algorithm is put forward. Numerical experiments are implemented using emergency allocation data from a prefecture-level city. The hypervolume (HV) metric and iterative convergence profiles are adopted to assess the convergence and diversity of the Pareto solution set, and a two-parameter sensitivity analysis is conducted with respect to the demand confidence level and road reliability. Computational results demonstrate that the proposed model is capable of characterizing the coupled impacts of fuzzy uncertainty and road network disruption on emergency scheduling strategies. Moreover, the developed algorithm achieves superior performance over benchmark algorithms in both convergence and solution diversity.