Evolutionary algorithms for solving unconstrained multilevel lot-sizing problem with series structure

This paper presents a comparative study of evolutionary algorithms which are considered to be effective in solving the multilevel lot-sizing problem in material requirement planning (MRP) systems. Three evolutionary algorithms (simulated annealing (SA), particle swarm optimization (PSO) and genetic algorithm (GA)) are provided. For evaluating the performances of algorithms, the distribution of total cost (objective function) and the average computational time are compared. As a result, both GA and PSO have better cost performances with lower average total costs and smaller standard deviations. When the scale of the multilevel lot-sizing problem becomes larger, PSO is of a shorter computational time.     

基于风险分担的城市公交出行鲁棒优化模型

本文面向城市中需要在给定期限内到达终点的出行者,针对最短耗时公交换 乘问题,利用基于风险分担的鲁棒优化方法进行了建模和求解.公交行车时间和发车间隔 时间是不确定的,本文将其建模为区间数,并基于风险分担的思想给出了这些不确定参 数的集合描述,该集合可以通过一个代表出行者保守程度的参数进行灵活调整,在此基 础上提出了城市公交换乘最短耗时鲁棒优化模型,给出了多项式时间精确算法.通过对一 个算例的求解和仿真实验,展示了该模型求解结果（相对于确定性模型的求解结果）具有 更小的迟到概率;并通过分析讨论,总结出换乘更少,运行更稳定的换乘方案更倾向于成 为鲁棒最优换乘方案.