The planning of cycle trips in the province of East Flanders

Traditional route planners assist in finding the shortest or fastest route from one place to another. This paper presents a novel approach to path finding in a directed graph, namely a target distance, motivated by the problem that a recreational cyclist deals with when searching a nice route of a certain length. The problem is defined as a variant of the arc orienteering problem (AOP), a new combinatorial optimisation problem in which the score of a route in a directed graph has to be maximised by visiting arcs, while each arc can be visited at most once and the total cost of the route should not exceed a predefined cost. The contribution of this paper is threefold: (1) a mathematical model of the AOP is provided, (2) a metaheuristic method that solves AOP instances to near optimality in 1 s of execution time, is proposed and evaluated, and (3) two real-life applications of the method are presented. An on-line cycle route planning application offers personalised cycle routes based on user preferences, and an SMS service provides cyclists "in the field" with routes on demand.