LP Relaxations for Routing and Wavelength Assignment with Partial Path Protection: Formulations and Computations

TL;DR

This paper develops new LP relaxations and a Benders decomposition algorithm to efficiently compute tight lower bounds for the routing and wavelength assignment problem with partial path protection, improving solution quality assessment.

Contribution

It introduces a novel LP relaxation and a Benders decomposition approach with valid inequalities for RWAP-PPP, enhancing lower bound quality and computational efficiency.

Findings

Achieved average optimality gaps of 8.6% with the new LP relaxation.

Significant improvement over the direct LP relaxation, which has 36.7% gaps.

Demonstrated effectiveness on large practical networks with hundreds of nodes.

Abstract

As a variant of the routing and wavelength assignment problem (RWAP), the RWAP with partial path protection (RWAP-PPP) designs a reliable optical-fiber network for telecommunications. It assigns paths and wavelengths to meet communication requests, not only in normal working situations but also in potential failure cases where an optical link fails. The literature lacks efficient relaxations to produce tight lower bounds on the optimal objective value of the RWAP-PPP. Consequently, the solution quality for the RWAP-PPP cannot be properly assessed, which is critical for telecommunication providers in customer bidding and service improvement. Due to numerous failure scenarios, developing effective lower bounds for the RWAP-PPP is challenging. To address this, we formulate and analyze various linear programming (LP) relaxations of the RWAP-PPP. Among them, we propose a novel LP relaxation yielding promising lower bounds. To solve it, we develop a Benders decomposition algorithm with valid inequalities to enhance performance. Computational results on practical networks, including large ones with hundreds of nodes and edges, demonstrate the effectiveness of the LP relaxation and efficiency of its algorithm. The obtained lower bounds achieve average optimality gaps of 8.6%. Compared with a direct LP relaxation of the RWAP, which has average gaps of 36.7%, significant improvements are observed. Consequently, our LP relaxation and algorithm effectively assess RWAP-PPP solution quality, offering significant research and practical value.