This paper introduces a problem that can be seen as a combination of the traveling salesman problem with profits and the traveling repairman problem with profits, coined as the multi-objective traveling salesman–repairman problem with profits (Mo-TSRPP). The objective of the Mo-TSRPP is to simultaneously optimize three objectives: the total cost, total latency, and total profit. Indirectly, the number of nodes visited is also considered although not as an objective itself since it is determined by the size of every efficient solution in the Pareto front. The Mo-TSRPP emerges as a real-world problem in which a freelancer, which repairs appliances, wants to plan the daily route. Moreover, the daily plan does not require to visit all customers. To solve the problem, first, a greedy randomized adaptive procedure is designed to generate a set of high-quality nondominated solutions and then, a variable neighborhood descent algorithm is applied for further improving the initial set. This procedure allows us to attain a good approximation of the Pareto front. To prove the performance of the proposal a comparison is done against three well-known evolutionary algorithms: NSGA-II, SPEA-2, and MOEA/D. Finally, a realistic problem is shown and solved to illustrate the potential of the algorithm.

中文翻译：

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具有利润的多目标旅行推销员-修理工问题：针对实际场景的可变邻域下降算法的设计和实现

本文介绍了一个可以看作是带有利润的旅行推销员问题和带有利润的旅行修理工问题的组合的问题，被称为带有利润的多目标旅行推销员-修理工问题（Mo-TSRPP）。Mo-TSRPP 的目标是同时优化三个目标：总成本、总延迟和总利润。间接地，访问的节点数量也被考虑，尽管它本身不是一个目标，因为它是由帕累托前沿中每个有效解决方案的大小决定的。Mo-TSRPP 是一个现实世界的问题，其中一名修理电器的自由职业者想要规划每日路线。而且，日常计划不需要拜访所有客户。为了解决该问题，首先，设计贪婪随机自适应过程来生成一组高质量的非支配解，然后应用可变邻域下降算法来进一步改进初始集。这个过程使我们能够很好地近似帕累托前沿。为了证明该提案的性能，与三种著名的进化算法进行了比较：NSGA-II、SPEA-2 和 MOEA/D。最后，展示并解决了一个现实问题，以说明该算法的潜力。