A penalized best‐response algorithm for nonlinear single‐path routing problems

Abstract

This article is devoted to nonlinear single‐path routing problems, which are known to be NP‐hard even in the simplest cases. For solving these problems, we propose an algorithm inspired from Game Theory in which individual flows are allowed to independently select their path to minimize their own cost function. We design the cost function of the flows so that the resulting Nash equilibrium of the game provides an efficient approximation of the optimal solution. We establish the convergence of the algorithm and show that every optimal solution is a Nash equilibrium of the game. We also prove that if the objective function is a polynomial of degree d ≥ 1 , then the approximation ratio of the algorithm is ( 2 1 / d − 1 ) − d . Experimental results show that the algorithm provides single‐path routings with modest relative errors with respect to optimal solutions, while being several orders of magnitude faster than existing techniques. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 69(1), 52–66 2017

A Game-Theoretic Algorithm for the Joint Routing and VNF Placement Problem

“…The problem differs however significantly from traditional single-path routing problems as on one hand the same resource appears at different layers of the expanded network and on the other hand the volume of a traffic demand may change from one layer to the other. Nevertheless the heuristic algorithm that we propose in this section is directly inspired from an algorithm proposed in [15] for solving such problems. The idea of the algorithm is to view the traffic demands as the players of a non-cooperative game in which each each player independently optimizes its own objective function.…”

“…The pseudocode of our heuristic is given in Algorithm 1. Note that it is fully similar to the algorithm in [15], the only difference being in the way the traffic flowing on a resource is computed. The algorithm starts from an initial feasible solution π (0) .…”

“…We show that the VNF placement and chaining problem can be formulated as a non-linear single-path routing problem in an extended graph. To solve this problem, we adapt a single-path routing algorithm inspired from Game Theory which was proposed in [15]. We show that this algorithm converges and establishes its approximation ratio in a number of cases.…”

The invisible‐hand heuristic for origin‐destination integer multicommodity network flows

“…Amiri et al [3,4], Rolland et al [29], and recently Fortz et al [12] present Lagrangian-relaxation-based heuristics for ODIMCF. And Brun et al [9] develop an approximation heuristic inspired by game theory's Nash equilibrium.…”

Preface: Static and dynamic optimization models for network routing problems

“…Brun et al consider nonlinear single path routing problems, which are known to be NP‐hard even in the simplest cases. The authors propose an algorithm inspired from Game Theory in which individual flows are allowed to independently select their path to minimize their own cost function.…”