Abstract: Focusing on the issue that emergency resource assignment for multiple demand points and multiple supply points in railway emergencies, an emergency resource assignment model of multiple rescue targets was established, which was based on the concept of "soft time window". The maximum fairness and minimum total assignment cost were considered as the optimization objectives, and parallel selected genetic algorithm was used to solve the model. The population was equally divided into subpopulations by the algorithm. Subpopulations' number was equal to the number of objective functions. An objective function was assigned to each divided subpopulation and the selection work was done independently, by which individuals with high fitness were selected from each subpopulation to form a new population. Crossover and mutation were done to generate the next generation of population. The computing cases show that the parallel selected genetic algorithm reduces the variance of resource satisfaction degree of all demand points by 93.88% and 89.88% respectively, and cuts down the cost by 5% and 0.15% respectively, compared with Particle Swarm Optimization (PSO) and two-phase heuristic algorithm. The proposed algorithm can effectively reduce the variance of the resource satisfaction degree of all demand points, that is, it improves the fairness of each demand point and reduces the cost at the same time, and can obtain higher quality solution when solving multiple objective programming problem.

Key words: railway emergency, resource assignment, soft time window, fairness, parallel selected genetic algorithm

摘要： 针对铁路突发事件多需求点多供应点的应急资源调度问题，结合"软时间窗"的概念，以公平性最大和调度总成本最小为优化目标，设计了有多个救援目标的应急资源调度模型，并利用并列选择遗传算法求解。该算法根据目标函数的个数，将种群均等地划分为与目标函数个数相等的子种群，为划分后的各个子种群各自分配一个目标函数，并对其进行独立的选择运算，将各个子种群中适应度高的个体组成新的种群，对这个新的种群进行交叉、变异，生成下一代种群。算例表明，与粒子群优化（PSO）和两阶段启发式算法相比，利用并列选择遗传算法进行计算，目标函数中所有需求点的资源满足程度的方差分别减小了93.88%、89.88%，成本分别减少了5%、0.15%。所提算法能够有效减小所有需求点的资源满足程度的方差，即提高各需求点的公平性，同时降低成本，其在求解多目标规划问题中能够得到更优的解。

关键词: 铁路突发事件, 资源调度, 软时间窗, 公平性, 并列选择遗传算法