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...
(ii) show that versions of the twofacility loading problem are strongly NP-hard, but that a shortest path solution provides an asymptotically "good" heuristic; and (iii) characterize the optimal solution (that is, specify a linear programming formulation with integer solutions) of the common ...
We compare the MRS algorithm with the following algorithms: 1) the shortest path tree (SPT) algorithm in IP network, 2) the Node-Link algorithm employing Mix Integer Linear Programming (MILP) formulation proposed in section III, which finds the optimal solution of the routing problem in HSDN,...
Furthermore, we propose a mathematical programming formulation for the shortest paths problem on time-dependent networks, that gives rise to integer programs. Within the context of solving Mixed-Integer Linear Programs through a Branch-and-Bound algorithm, we propose a new strategy for branching, ...
By introducing a duality theorem, we successfully formulate our problem as an LP formulation that can be easily solved yielding the desired split ratios. Numerical results show that the proposed scheme dramatically reduces the network congestion ratio compared to the classical shortest path routing ...
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...
linear programming; digraphs; shortest path Abstract In this paper, we are interested in the shortest path problem between two specified vertices in digraphs containing negative cycles. We study two integer linear formulations and their linear relaxations. A first formulation, close in spirit to a cl...
findingthekshortestpaths寻找最短路径 系统标签: shortestpaths短路径findingdigraphpath FindingthekShortestPaths DavidEppstein ∗ March31,1997 Abstract Wegivealgorithmsforfindingthekshortestpaths(notrequiredtobesimple)connectinga pairofverticesinadigraph.Ouralgorithmsoutputanimplicitrepresentationofthesepathsina...
Additionally, we analyze the solution times of MIP formulation (F3). The remainder of this section is organized as follows. Section 5.1 describes Conclusion In this paper we consider the shortest path problem, where the arc costs are governed by some probability distribution, which is itself ...
In their paper, a decomposition of the shortest path problem in transfer graph is proposed to optimize the computation time. Horn [27] presented a comprehensive cost-minimizing formulation and an algorithm for planning multi-modal passenger journeys. This algorithm can solve the problems with an “...