A Method for Determining the k Most Vital Arcs in Maximum Flow Problem

최대유통문제에서 k-MVA를 결정하는 방법

The purpose of this study is to present a method for determining the k most vital arcs in the maximum flow problem using genetic algorithms. Generally, the problem which determine the k most vital arcs in maximum flow problem has known as NP-hard. Therefore, in this study we propose a method for determining all the k most vital arcs in maximum flow problem using genetic algorithms. First, we propose a genetic algorithm to find the k most vital arcs removed at the same time and then present the expression and determination method of individuals compatible with the characteristics of the problem, and specify the genetic parameter values of constitution, population size, crossover rate, mutation rate and etc. of the initial population which makes detecting efficiency better. Finally, using the proposed algorithms, we analyzed the performance of searching optimal solution through computer experiment. The proposed algorithms found all alternatives within shorter time than other heuristic methods. The method presented in this study can determine all the alternatives when there exists other alternative solutions.