The regular language-constrained orienteering problem with time windows

Abstract

Several application domains of the Orienteering Problem (OP) entail the categorization of graph nodes. Specific categories of nodes may be preferred to be included in the solution, while nodes of other categories should be limited to a certain extent or even excluded. Additionally, precedence constraints may apply among nodes from different categories. We contend that regular expressions, which describe patterns of node categories and specify constraints for solution paths, can effectively capture practical tourist tour planning aspects. Hence, we introduce the Regular Language-Constrained OP with Time Windows (RLC-OPTW) as an extension of the OP, where regular expressions are utilized to describe the admissible category patterns in solution paths. Our approach leverages the simplicity, elegance, and expressive power of regular languages, which excel in applications involving pattern recognition and matching. Given that RLC-OPTW is NP-hard, we initially provide an exact solution for small instances of the problem. Then, we present two efficient heuristic approaches: The first heuristic iteratively appends nodes to the solution to generate an initial feasible (i.e., regular expression-constrained) solution and then replaces nodes in search of higher quality solutions. The second heuristic iteratively inserts nodes at any point within the solution and then replaces sets of consecutive nodes upon reaching a local optimum. The efficiency of our proposed algorithms has been assessed using publicly available datasets. We have also showcased the effectiveness of our methods in generating meaningful tourist trips that adhere to practical user constraints using a real dataset with tourist attractions in Athens (Greece) as a case study. Although our algorithmic approaches and experimental evaluation of RLC-OPTW primarily focus on tourist trip planning, the proposed algorithms can be applied to finding paths under constraints in numerous other application domains of the OP.