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首页> 外文期刊>International journal of unconventional computing >Two-Stage Multi-objective Evolutionary Algorithm Based on Classified Population for Tri-objective VRPTW
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Two-Stage Multi-objective Evolutionary Algorithm Based on Classified Population for Tri-objective VRPTW

机译：基于分类群体的三级多目标进化算法，用于三目标VRPTW

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This paper presents a two-stage multi-objective evolutionary algorithm based on classified population (TSCEA) to solve vehicle routing problem with time windows (VRPTW). It is a well-known NP-hard discrete optimization problem with three objectives: to minimize the total distance cost, to minimize the number of vehicles, and to optimize the balance of routes within a limited time. For TSCEA, there are two stages: In the first stage, a population is explored using the proposed algorithm and then classified according to the number of vehicles, we call this process population classification; In the second stage, Pareto solution set of tri-objective VRPTW is obtained by optimizing the classified population again. The advantages of classified population structure are that for the first stage, this population that the number of vehicles of each individual is in this range composed of the upper and lower bounds of vehicles can be classified as different small populations with the same number of vehicles. Due to the evolution of small population, Pareto solution set with better extensibility can be searched. For the second one, it can reduce the dimension of tri-objective function, that is, three objective functions can be reduced to two objective functions because one of them has been identified in the first stage. Moreover, to resolve the nonlinear discrete problems, the computational approach of crowding degree is modified. The paper chooses Solomon benchmark instances as testing sets and the simulated results show that TSCEA outperforms the compared algorithms in terms of quality or extension, which verified the feasibility of the algorithm in solving tri-objective VRPTW.
机译：本文介绍了一种基于分类群体（TSCEA）的两级多目标进化算法，以解决时间窗口（VRPTW）的车辆路由问题。它是一个着名的NP硬离散优化问题，具有三个目标：以最小化总距离成本，以最大限度地减少车辆数量，并在有限时间内优化路线的平衡。对于TSCEA，有两个阶段：在第一阶段，使用所提出的算法探索一群人口，然后根据车辆的数量进行分类，我们称之为人口分类;在第二阶段，通过再次优化分类群体，获得了三目标VRPTW的Pareto解决方案集。分类人口结构的优点是，对于第一阶段，该人群在这个范围内，每个人的车辆数量由车辆的上下边界组成，可以被归类为具有相同数量的车辆的不同小群体。由于小人口的演变，可以搜索具有更好可扩展性的Pareto解决方案。对于第二个，它可以减少三目标函数的维度，即三个客观函数可以减少到两个目标函数，因为它们中的一个已经在第一阶段识别。此外，为了解决非线性离散问题，修改了拥挤程度的计算方法。本文选择所罗门基准实例作为测试集，模拟结果表明，TSCEA在质量或扩展方面优于比较算法，这验证了算法在解决三目标VRPTW中的可行性。

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