Road Graph Simplification for Minimum Cost Flow Problem

V této práci se zaměřujeme na problém výpočtu nejlevnějších toků jako na klíčový problém pro řízení dopravního provozu. Tento problém se řeší pravidelně během dne, tj. nejde o nalezení řešení jednou, ale o dlouhodobý proces, ve kterém se pořád hledá řešení toho samého problémů s různými vstupy. Proto představujeme řešení, které může být úspěšně použito v dlouhodobém horizontu. Předpokládáme, že v poptávce existuje periodický vzor, tj. směr vozidel se obecně opakuje denně. Naše zlepšení je založeno na metodě generování sloupců, která umožňuje opětovné použití cest vozidel z předchozích dnů při vyhledávání řešení. Dosáhli jsme snížení výpočetního času o 40% při zachování optimality řešení.In this work we consider the Minimum Cost Multicommodity Network Flow (MCMNF) problem as a key problem for traffic routing. The routing problem is recurring, it should be solved many times a day on a daily basis. So we present a solution that may be successfully used in the long term. We make use of a periodic demand pattern, i.e. vehicles' directions are in general recurring daily. Our improvement is based on column generation method, that allows us to reuse vehicles paths from previous days in the solution process. We achieved a 40% reduction of computational time, while the optimal solution is preserved

Parallel primal-dual methods for the minimum cost flow problem

"This report is a substantial revision of report LIDS-P-1998, September 1990."Includes bibliographical references (p. 20-21).Supported by the BM/C3 Technology branch of the U.S. Army Strategic Defense Command.by Dimitri P. Bertsekas and David A. Castañon

Parallel asynchronous primal-dual methods for the minimum cost flow problem

Cover title. "September 1990."Includes bibliographical references (p. 18-19).Research supported by the BM/C3 Technology branch of the United States Army Strategic Defense Command.by Dimitri P. Bertsekas and David A. Castañon

Dynamic Network Flows with Uncertain Costs belonging to Interval

This paper considers minimum cost flow problem in dynamic networks with uncertain costs. First, we present a short introduction of dynamic minimum cost flow. Then, we survey discrete and continuous dynamic minimum cost flow problems, their properties and relationships between them. After that, the minimum cost flow problem in discrete dynamic network with uncertainty in the cost vector is considered such that the arc cost can be changed within an interval. Finally, we propose an algorithm to find the optimal solution of the proposed model

A bi-objective column generation algorithm for the multi-commodity minimum cost flow problem

We present a column generation algorithm for solving the bi-objective multi-commodity minimum cost flow problem. This method is based on the bi-objective simplex method and Dantzig–Wolfe decomposition. The method is initialised by optimising the problem with respect to the first objective, a single objective multi-commodity flow problem, which is solved using Dantzig–Wolfe decomposition. Then, similar to the bi-objective simplex method, our algorithm iteratively moves from one non-dominated extreme point to the next one by finding entering variables with the maximum ratio of improvement of the second objective over deterioration of the first objective. Our method reformulates the problem into a bi-objective master problem over a set of capacity constraints and several single objective linear fractional sub-problems each over a set of network flow conservation constraints. The master problem iteratively updates cost coefficients for the fractional sub-problems. Based on these cost coefficients an optimal solution of each sub-problem is obtained. The solution with the best ratio objective value out of all sub-problems represents the entering variable for the master basis. The algorithm terminates when there is no entering variable which can improve the second objective by deteriorating the first objective. This implies that all non-dominated extreme points of the original problem are obtained. We report on the performance of the algorithm on several directed bi-objective network instances with different characteristics and different numbers of commodities