(ii) show that versions of the two-facility loading problem are strongly NP-hard, but that a shortest path solution provides an asymptotically good heuristic; and (iii) characterize the optimal solution (i.e.,
4.6.4 Shortest Path Routing We now show the connection between shortest path routing presented in Chapter 2 and the single-commodity network flow problem using the node-link formulation. Since we are interested in only the shortest path between two nodes in a network, we simply need to consider...
the paper proposes a resource-constrained shortest path formulation for the SPTDSP-PA along with a tailored label-correcting algorithm used to find an optimal solution. Third, we analyze the impact that parking constraints have on trip duration and compare it to estimated potential costs of disregar...
Reconfiguring two shortest paths in a graph means modifying one shortest path to the other by changing one vertex at a time so that all the intermediate paths are also shortest paths. This problem has several natural applications, namely: (a) repaving road networks, (b) rerouting data packets...
Abstract In most vehicle routing and crew scheduling applications solved by column generation, the subproblem corresponds to a shortest path problem with resource constraints (SPPRC) or one of its variants. This chapter proposes a classification and a generic formulation for the SPPRCs, briefly discus...
Furthermore, Stochastic Time Dependent Shortest Path problems are known to be NP-hard. Emerging Quantum Computing Methods are providing new ways to address these problems. In this paper, the STDSP problem is formulated as a Quadratic Constrained Binary Optimization Problem. We show that in the ...
On the basis of the expected length of the shortest path model () proposed by Beardwood et al. [11], we speculate that the expected length of the shortest path in 3D-TSP may have a linear relationship withor. Therefore, we use the data when the shape of the service area is a cube ...
dent of the path formulation; for instance, in a k-shortest-path model of automatic translation between natural languages [30], a correct translation can be found by a human expert. By listing paths until this known solution appears, one can determine how well the model fits the problem,...
Lin [7] developed a Fuzzy linear programming approach to calculate the Fuzzy Shortest Path and the most vital arc. Kung [6] proposed Fuzzy Shortest Length Heuristic Procedure where the Shortest Path was de- cided by examining the Intersection Area (IA). Hence Fuzzy Similarity Degree [2, 5]...
3.2) The Ideal SP-SDP Problem Formulation for a Stationary Markov process. The focus of this paper is on the formulation of the HEV control problem as a Shortest Path Stochastic Dynamic Program (SP-SDP). This formulation offers two advantages over existing formulations. It allows undiscounted ...