Abstract The orienteering problem (OP), which is a selective version of the traveling salesman problem, has been widely studied by many researchers in recent years. The purpose of the OP is to maximise profits collected from customers in a limited time period, during which all customers cannot be visited. In this paper, we introduce a new type of OP called the multi-profit orienteering problem (MPOP). In the MPOP, each customer vertex has a time-dependent profit such that its value varies on the basis of visiting time. To maximise the total profit, a vehicle should carefully select both the customer vertices and visiting time. We introduce a benchmark problem set for the MPOP and propose a mathematical model and a hybrid heuristic algorithm to solve it. Experimental results demonstrate that the proposed algorithm can solve most of the instances well within a reasonable time.

中文翻译：

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多赢定向问题

摘要 定向越野问题（OP）是旅行商问题的一个选择性版本，近年来得到了许多研究人员的广泛研究。OP 的目的是在有限的时间内从客户那里收集到的利润最大化，在此期间不能访问所有客户。在本文中，我们介绍了一种称为多利润定向问题 (MPOP) 的新型 OP。在 MPOP 中，每个客户顶点都有一个与时间相关的利润，因此其价值会根据访问时间而变化。为了最大化总利润，车辆应该仔细选择客户顶点和访问时间。我们为 MPOP 引入了一个基准问题集，并提出了一个数学模型和一个混合启发式算法来解决它。