In metropolitan areas, drivers share their vehicles with people who commute daily via carpooling. In this paper, we first defined a multiobjective carpool service problem with time windows (MOCSPTW) by considering four optimized objectives; subsequently, we propose a coevolutionary algorithm for two solution sets, population and archive, using objective-wise local search and set-based simulated binary operation in order to address the MOCSPTW. In the evolution module of the proposed algorithm, three different methods, namely, objective-wise local search in an archive, set-based simulated binary operation in a population, and set-based simulated binary operation both in a population and in an archive, were used to generate the offspring. Meanwhile, the $\epsilon $ -domination and normal domination in the update module were adopted to control the convergence and diversity of the population and archive. In the experimental result, 48 sets of tests, including three moving patterns in a metropolitan area for the MOCSPTW, were prepared. The results of the quantitative comparison and objective visualization showed that the proposed algorithm can obtain superior Pareto-optimal solutions regarding convergence and diversity compared with a fast nondominated sorting genetic algorithm.

中文翻译：

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用时间窗解决拼车服务问题的协同进化中的全局和局部帕累托最优

在大都市地区，司机与每天通过拼车上下班的人共享他们的车辆。在本文中，我们首先通过考虑四个优化目标来定义具有时间窗的多目标拼车服务问题（MOCSPTW）；随后，我们为两个解决方案集（人口和档案）提出了一种协同进化算法，使用客观局部搜索和基于集合的模拟二元运算来解决 MOCSPTW。在所提出算法的进化模块中，三种不同的方法，即档案中的客观局部搜索，群体中基于集合的模拟二元运算，以及群体和档案中的基于集合的模拟二元运算，被用来产生后代。同时，更新模块中的 $\epsilon $ -dommination 和 normal domination 被用来控制种群和档案的收敛性和多样性。在实验结果中，为 MOCSPTW 准备了 48 组测试，包括在大都市区的三个移动模式。定量比较和客观可视化的结果表明，与快速非支配排序遗传算法相比，所提出的算法在收敛性和多样性方面可以获得优越的帕累托最优解。