The objective is to minimize the maximum relative regret of the path from the source to the destination. This problem is known as the minmax relative regret RSP and it is NP-Hard. We propose a mixed integer linear programming formulation for this problem. The CPLEX branch-and-bound algorithm...
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...
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...
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...
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,...
The Shortest-path problem with timewindows and capacity constraints (SPPTWCC) is a problem used for solving vehicle-routing and crewscheduling applications. The SPPTWCC occurs as a sub-problem used to implicitly generate the set of all feasible routes and schedules in the columngeneration formulat...
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 ...
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]...
Our aim in the next section is to provide a state-of-the-art mixed integer programming (MIP)-based algorithm to solve the TDTSP in full generality. We begin by formally defining time-expanded graphs and establishing both an arc-based and a path-based formulation, since it is not immediatel...
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 ...