An optimal routing search method on the network routing problem using the sequential minimal optimization

Abstract

The network routing problem is one of important problems to consider behaviors of multiple flows on a network with traffic. Some network routing problems can be classified into the selfish routing game in which the behaviors of the flows are competitive and the optimal routing problem in which the behaviors of the flows are cooperative. This study focuses on the optimal routing problem. The optimal routing problem is formulated as an optimization problem with a linear equality constraint and lower limit constraints. The learning problem of the support vector machine (SVM) is formulated as an optimization problem with a linear equality constraint and upper and lower limit constraints. The sequential minimal optimization (SMO) is one of the fast solvers for the learning problem. SMO can be applied to solve the optimal routing problem. This study proposes a new fast optimal routing search method using SMO. In the numerical experiments, the effectiveness of the proposed method on the computational cost is verified with the comparison to the search method using the replicator dynamics.