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. (C) 2010 Elsevier Ltd. All rights reserved.