A Mixed Integer Model for the Stamina-Aware Sightseeing Tour Problem

Personal navigation systems have experienced a rising interest in the past few years thanks to the ever-increasing ubiquity of smartphones and in-car navigation systems. In their simplest forms, the goal is to calculate routes that are optimized with respect to criteria such as travel time and distance. Various systems have been proposed that allow for additional dynamic aspects to be included in the optimization process such as a user’s current context [1], multimodal transportation [2] and weather [3]. The stamina-aware sightseeing tour problem (SASTP) was first proposed by Wu et al. [4] and is defined as follows: Given is a tourist with a time and stamina budget and a number of sightseeing spots. Each spot can be visited by using one of several available methods (e.g., short tour, guided tour, extensive tour, etc.) and each method requires a certain amount of time and stamina, but gives a certain degree of satisfaction in return. Traveling between sightseeing spots takes time and also consumes stamina. After visiting a spot, the tourist may spend some time to take a break and regain stamina. The goal is to construct a sightseeing tour that contains a selection of spots with corresponding visiting methods that maximizes the tourist’s overall satisfaction and does not exceed his time and stamina budget. In [4] a predator search (PS) metaheuristic was proposed for this problem. Solutions are represented in a straightforward way by a set of quadruples, each specifying the spot to be visited, the order in the final tour, the visiting method, and the length of the break after the visit. The algorithm uses two phases: First an auxiliary solution is generated on the basis of a randomized algorithm. Then it is improved by a neighborhood search phase that optimizes each of the solution attributes. A drawback of this approach is that the search space is very large, therefore only instances with 10 to 20 sightseeing spots were considered.