An Efficient Algorithm for Solving Minimum Cost Flow Problem with Complementarity Slack Conditions

Abstract

This paper presents an algorithm for solving a minimum cost flow (MCF) problem with a dual approach. The algorithm holds the complementary slackness at each iteration and finds an augmenting path by updating node potential iteratively. Then, flow can be augmented at the original network. In contrast to other popular algorithms, the presented algorithm does not find a residual network, nor find a shortest path. Furthermore, our algorithm holds information of node potential at each iteration, and we update node potential within finite iterations for expanding the admissible network. The validity of our algorithm is given. Numerical experiments show that our algorithm is an efficient algorithm for the MCF problem, especially for the network with a small interval of cost of per unit flow.

A Network Flow Algorithm for Solving Generalized Assignment Problem

“…Although several algorithms are presented for optimizing minimum-cost flow problem, both cost and capacity are to be considered for iteratively defining residual network. Hu et al [29] introduced an approach that can solve min-cost flow. Unlike the traditional algorithms, the proposed algorithm in [29] can find an augmenting path in the original network by updating node potentials.…”

“…Hu et al [29] introduced an approach that can solve min-cost flow. Unlike the traditional algorithms, the proposed algorithm in [29] can find an augmenting path in the original network by updating node potentials. We will describe an algorithm for optimizing GAP based on the network model defined above in the next section.…”

“…It is well known that AP is thought of as a special min-cost flow problem, which suggests that classical AP or GAP can be solved by some methods with network flow theory. Recently, an efficient algorithm was proposed for solving min-cost flow problem [29]. is paper attempts to give a variation of the algorithm presented in [29] for GAP based on the advantage of the special structure of the transformed network model.…”

“…Recently, an efficient algorithm was proposed for solving min-cost flow problem [29]. is paper attempts to give a variation of the algorithm presented in [29] for GAP based on the advantage of the special structure of the transformed network model. is paper is organized as follows.…”

An Interactive Approach for Solving the Multiobjective Minimum Cost Flow Problem in the Fuzzy Environment

“…In his earlier work, Osman and El-Banna [26] analyzed the concepts of the solvability set and the stability set of the first and second kinds for parametric convex nonlinear programming problems. Hu et al [27] introduced the stability of fuzzy multiobjective nonlinear programming problems. Hu and Lee [28] presented a method for the MCF problem which holds complementary slackness and found an augmenting path with the dual approach.…”