救灾物资高维多目标自适应分配问题建模与求解

针对救灾物资分配中效率和公平性的均衡问题，提出一种基于二维整数编码的高维多目标自适应分配算法。首先构建了一个综合考虑应急响应总时间、灾民恐慌度、救灾物资未满足度、物资分配公平性、灾民损失、应急响应总成本的高维多目标优化模型，然后采用二维整数编码和自适应个体修正（AIR）解决潜在的应急资源冲突，最后引入移位密度估计和第二代强度帕累托进化算法（SPEA2）设计了一个救灾物资高维多目标分配算法。在仿真实验中，与带有编码修正机制的非支配排序差异演化算法（ERNS-DE）和基于贪心搜索的多目标遗传算法（GSMOGA）相比，所提算法在两种应急环境中的覆盖值分别提高了34.87%、100%和23.59%、100%，同时所提算法的超体积值也远远高于两种对比算法。实验结果表明，所提模型和算法可以让决策者根据实际应急需求选择应急方案，具有更好的灵活性和求解效率。

Modeling and solving of high-dimensional multi-objective adaptive allocation for emergency relief supplies

To seek a good balance between efficiency and fairness in emergency relief supply allocation, a high-dimensional multi-objective adaptive allocation algorithm based on two-dimensional integer encoding was developed. First of all, a high-dimensional multi-objective optimization model was constructed with the consideration of total emergency response time, panic degree of the victims, unsatisfactory degree of relief supplies, fairness of supply allocation, loss of the victims, and total cost of emergency response. Then, two-dimensional integer encoding and Adaptive Individual Repair (AIR) were adopted to resolve potential emergency resource conflicts. Finally, the shift-based density estimation and Strength Pareto Evolutionary Algorithm 2 (SPEA2) were introduced to design a high-dimensional multi-objective allocation algorithm for disaster relief supplies. Simulation results show that compared with Encoding Repair and Non-dominated Sorting based Differential Evolution algorithm (ERNS-DE) and Greedy-Search-based Multi-Objective Genetic Algorithm (GSMOGA), the proposed algorithm had coverage values increased by 34.87%, 100% and 23.59%, 100% in two emergency environments, respectively. Moreover, the hypervolume values of the proposed algorithm were much higher than those of the two comparison algorithms. Experimental results verify that the proposed model and algorithm allow decision makers to select emergency schemes according to actual emergency needs, and have better flexibility and efficiency.