During the last decade, a number of challenging applications in logistics, tourism and other fields were modelled as orienteering problems (OP). In the orienteering problem, a set of vertices is given, each with a score. The goal is to determine a path, limited in length, that visits some vertices and maximises the sum of the collected scores. In this paper, the literature about the orienteering problem and its applications is reviewed. The OP is formally described and many relevant variants are presented. All published exact solution approaches and (meta)heuristics are discussed and compared. Interesting open research questions concerning the OP conclude this paper.

The Orienteering Problem (OP) has received a lot of attention in the past few decades. The OP is a routing problem in which the goal is to determine a subset of nodes to visit, and in which order, so that the total collected score is maximized and a given time budget is not exceeded. A number of typical variants has been studied, such as the Team OP, the (Team) OP with Time Windows and the Time Dependent OP. Recently, a number of new variants of the OP was introduced, such as the Stochastic OP, the Generalized OP, the Arc OP, the Multi-agent OP, the Clustered OP and others. This paper focuses on a comprehensive and thorough survey of recent variants of the OP, including the proposed solution approaches. Moreover, the OP has been used as a model in many different practical applications. The most recent applications of the OP, such as the Tourist Trip Design Problem and the mobile-crowdsourcing problem are discussed. Finally, we also present some promising topics for future research.

In the Team Orienteering Problem with Time Windows (TOPTW) a set of locations is given, each with a score, a service time and a time window. The goal is to determine a fixed number of routes, limited in length, that visit, at the right time, some locations and maximise the sum of the collected scores. This paper describes a simple, fast and effective iterated local search meta-heuristic to solve the TOPTW. An insert step is combined with a shake step to escape local optima.The specific shake step implementation produces a heuristic that performs very well on a large set of instances with up to 288 locations. The obtained results have an average gap with the optimal solution of only 1.8% for instances with only a single route and 2.1% for instances with three to twenty routes.

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