On DC optimization algorithms for solving minmax flow problems

Abstract

We formulate minmax flow problems as a DC. optimization problem. We then apply a DC. primal-dual algorithm to solve the resulting problem. The obtained computational results show that the proposed algorithm is efficient thanks to particular structures of the minmax flow problems.

A Mixed Integer Programming Approach for the Minimum Maximal Flow

“…It can be seen that our running times are less than theirs for all the instances. By regression analysis, we obtain that log(MIP Running Time) = 0.0022n − 2.129, R 2 = 0.6685, log(Muu and Thuy [9] Running Time) = 0.0248n − 0.2729, R 2 = 0.86433. [11] no.…”

“…First, we construct networks whose minimum maximal flow values are known, so that we can check whether the exact optimal solutions are computed. Then we use the MMF problems presented in Shigeno et al [11] and Muu and Thuy [9], so that we can compare our approach with theirs. We also make experiments on relatively large instances.…”

“…We use the problems with the same size of Muu and Thuy [9] to compare with theirs. The results of the experiments are shown in Table 3, where the sizes of generated networks are based on their experiments [9]. In Figure 4, we show the natural logarithm of the running time by Muu and Thuy's algorithm and ours.…”

“…As far as we know, the largest-scaled instance of the MMF problem is solved in Muu and Thuy [9] where n = 200. The results of computational experiments for large-scaled instances are shown in Table 4.…”

“…In 2009, Chen et al [3,8] use non-homogeneous Farkas' Theorem to define the set of maximal flows and propose an algorithm. In 2014, Muu and Thuy [9] use smoothing technique on DC algorithm to solve the problem locally. In those algorithms, the computational time highly depends on the size of n. Some papers mentioned above report results of computational experiments for solving the MMF problems, but the size of n is at most 200.…”