An exact bidirectional A^⋆ approach for solving resource‐constrained shortest path problems

Abstract

Bidirectional dynamic programming is an algorithm that searches for paths in a network from both the starting and the ending nodes that optimize a given objective function. In recent years, bidirectional dynamic programming has been shown to be an effective means for solving resource-bounded shortest path problems. While many researchers have observed that bidirectional A ⋆ approaches perform poor computationally, we exploit the presence of resource constraints to overcome the source of these computational challenges. Our main contribution in this paper is an exact bidirectional A ⋆ algorithm for resource-constrained shortest path problems (RCSPPs) that is capable of solving large-sized instances that challenge the state-of-the-art in the literature. We also analyze, both computationally and theoretically, the sensitivity of the algorithm's performance to its inputs.

An exact bidirectional pulse algorithm for the constrained shortest path

“…We compare the performance of our proposed bidirectional pulse algorithm (labeled by “BP”) against the original pulse algorithm by Lozano and Medaglia [20] (labeled by “PA”) and the state‐of‐the‐art algorithm by Thomas et al [31] (labeled by “RC‐BDA”). The proposed algorithm “BP” and the original pulse algorithm “PA” were implemented in Java, compiled using Eclipse SDK version 4.8.0, and the experiments executed on a computer with an Intel Core i7‐4610M @ 3.00 GHz with 8 GB of RAM allocated to the memory heap size of the Java Virtual Machine on Windows 10.…”

“…One key aspect of the PA is that it uses a limited number of labels to discard dominated partial paths; however, these labels are never extended, nor the exactness of the algorithm depends on storing the complete set of nondominated labels at each node. We also focus our attention on the recent bidirectional A* algorithm by Thomas et al [31]. Their labeling approach searches for paths in the network from both the starting and ending node, storing the complete set of nondominated labels for each node in both directions until reaching a stopping criterion.…”

“…This notion is commonly known as the “crossing missiles metaphor.” Most of the solutions to solve this problem focus on joining labels created from both search directions and defining a search perimeter. For example, Thomas et al [31] defined a perimeter based on the resource consumption. Specifically, if a label had consumed more than half of the resource, the label is not expanded.…”

“…Since we enforce a strict limit on the number of labels stored at each node, we avoid the curse of dimensionality while still ensuring optimality as the exactness of our algorithm does not depend on storing a complete set of nondominated labels. From a computational perspective, we compare favorably with the state‐of‐the‐art algorithm by Thomas et al [31] over a set of 360 instances from real road networks in the United States commonly used in the literature. Additionally, we embedded our algorithm in a CG scheme to solve the linear relaxation of the multi‐activity shift scheduling problem (MASSP), which involves solving a CSP with multiple resources.…”

Primal column generation framework for vehicle and crew scheduling problems

“…Forward and backward subpaths are joined to form complete s − d paths. The bidirectional search has recently been integrated inside an A* approach by Thomas et al . This approach uses heuristic estimates to evaluate the distance between the nodes of the network to the source and the destination nodes.…”