A variable fixing heuristic with Local Branching for the fixed charge uncapacitated network design problem with user-optimal flow

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 designing 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 bilevel 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.

Weighted iterated local branching for mathematical programming problems with binary variables

“…In Wang et al (2011) the authors investigated strategies for fixing variables in a tabu search for binary quadratic programming problems. When solving a network design problem, (González et al 2016) used a variable fixing heuristic to generate an initial solution and then a local branching strategy to improve the solution. In Sadykov et al (2019), heuristic schemes involving different forms of variable fixing were explored within a branch-and-price algorithm.…”

On two new formulations for the fixed charge network design problem with shortest path constraints

“…We are interested in a specific variant of the FCNDP, called fixed charge network design problem with shortest path constraints (FCNDP-SPC) [14,11], which consists of adding multiple shortest path problems to the original problem.…”

“…The inclusion of the shortest path requirement makes the problem more difficult to solve exactly. There are few works done for solving exactly the general case of FCNDP-SPC [14,16,17,11,2], and most of the research is dedicated to a particular application. In the literature, the FCNDP-SPC was investigated for the transportation of hazardous materials: the Hazmat transport network design problem (HTNDP) [10,12,9,5,19,13].…”

“…Similar random instances have also been generated for FCNDP-SPC by Mauttone et al [17] and used in [11]. Their instances were not used here for two reasons.…”