A Variable Fixing Heuristic with Local Branching for the Fixed Charge Uncapacitated Network Design Problem with User-optimal Flow

TL;DR

This paper introduces an iterated local search algorithm for the fixed-charge uncapacitated network design problem with user-optimal flow, effectively balancing fixed and variable costs while ensuring shortest path routing for commodities.

Contribution

It proposes a novel combination of variable fixing, local branching, and cycle-based perturbation strategies for solving the FCNDP-UOF efficiently.

Findings

The method consistently finds high-quality solutions.

It operates within reasonable computational times.

The approach effectively balances cost minimization and routing constraints.

Abstract

This paper presents an iterated local search for the fixed-charge uncapacitated network design problem with user-optimal flow (FCNDP-UOF), which concerns routing multiple commodities from its origin to its destination by signing a network through selecting arcs, with an objective of minimizing the sum of the fixed costs of the selected arcs plus the sum of variable costs associated to the flows on each arc. Besides that, since the FCNDP-UOF is a bi-level problem, each commodity has to be transported through a shortest path, concerning the edges length, in the built network. The proposed algorithm generate a initial solution using a variable fixing heuristic. Then a local branching strategy is applied to improve the quality of the solution. At last, an efficient perturbation strategy is presented to perform cycle-based moves to explore different parts of the solution space. Computational experiments shows that the proposed solution method consistently produces high-quality solutions in reasonable computational times.