State-based accelerations and bidirectional search for bi-objective multi-modal shortest paths

Abstract

Taking into account the multi-modality of urban transportation networks for computing the itinerary of an individual passenger introduces a number of additional constraints such as mode restrictions and various objective functions. In this paper, constraints on modes are gathered under the concept of viable path, modeled by a non deterministic finite state automaton (NFA). The goal is to find the non-dominated viable shortest paths considering the minimization of the travel time and of the number of modal transfers. We show that the problem, initially considered by Lozano and Storchi [15], is a polynomially-solvable bi-objective variant of the mono-objective regular language-constrained shortest path problem [2,8].We propose several label setting algorithms for solving the problem: a topological label-setting algorithm improving on algorithms proposed by Pallottino and Scutellà [23] and Lozano and Storchi [15], a multi-label algorithm using buckets and its bidirectional variant, as well as dedicated goal oriented techniques. Furthermore, we propose a new NFA state-based dominance rule. The computational experiments, carried-out on a realistic urban network, show that the state-based dominance rule associated with bidirectional search yields significant average speed-ups. On an expanded graph comprising 1 859 350 nodes, we obtain on average 3.5 non-dominated shortest paths in less than 180 ms.keywords: bi-objective regular language-constrained shortest path problem, multimodal transportation, finite state automaton, label-setting algorithms, state-based dominance rule, bidirectional search, state-based estimated travel times.

K-Objective Time-Varying Shortest Path Problem with Zero Waiting Times at Vertices

“…They considered two objectives and assumed that travel time to be constant for the duration of travel along that arc, i.e., they considered the model of travel time is known as a frozen arc model. Artigues et al (2013) proposed a bi objective shortest path problem in a multi-modal urban transportation network. They modeled their problem by a multi-layered network.…”

“…A comprehensive survey on multi-criteria shortest path algorithm is given by Ehrgott and Gandibleux (2002). The reader is referred to Ahuja et al (1993), Artigues et al (2013), Bertsekas (1991), Getachew et al (2000), Reinhardt and Pisinger (2011) and Schrijver (2003) for developments in that area.…”

“…Brumbaugh-Smith and Shier (1989) proposed the linear time algorithm to solve the bi-criteria shortest path problems. Several algorithm to solve bi-objective multi-model shortest paths by using bidirectional search were presented by Artigues et al (2013), where path viability constraints are modeled by a finite state automaton. A comprehensive survey on multi-criteria shortest path algorithm is given by Ehrgott and Gandibleux (2002).…”

“…A comprehensive survey on multi-criteria shortest path algorithm is given by Ehrgott and Gandibleux (2002). The reader is referred to Ahuja et al (1993), Artigues et al (2013), Bertsekas (1991, Getachew et al (2000), Reinhardt andPisinger (2011) andSchrijver (2003) for developments in that area.In time-dependent version of problem, Cooke and Halsey (1966) described the fastest path problem. Kostreva and Wiecek (1993) extended the research of Cooke and Halsey (1966) to the multi-criteria case.…”

A bi-objective model for uncertain multi-modal shortest path problems

“…Thus, investigating the multi-modal shortest path problem in the indeterministic environment becomes a significant and challenging issue for the practical applications. We here note that finding the shortest path in a multi-modal network has been studied in various forms such as static [22], dynamic [26,28], stochastic [29,30], fuzzy [27], constrained [23], and multi-criteria [24,25,31,32]. However, to the best of our knowledge, few studies have been considered in the uncertain environment within the framework of uncertain programming.…”