Tree Optimization Based Heuristics and Metaheuristics in Network Construction Problems

TL;DR

This paper introduces heuristic and metaheuristic algorithms for efficiently solving network construction problems, focusing on tree-efficient cases where polynomial solutions are possible, and demonstrates their strong computational performance.

Contribution

It develops a generic local search heuristic and two metaheuristics for tree-efficient network construction problems on general networks, with extensive computational validation.

Findings

Algorithms show excellent computational performance.

Metaheuristics outperform traditional methods.

Effective for NP-hard network construction problems.

Abstract

We consider a recently introduced class of network construction problems where edges of a transportation network need to be constructed by a server (construction crew). The server has a constant construction speed which is much lower than its travel speed, so relocation times are negligible with respect to construction times. It is required to find a construction schedule that minimizes a non-decreasing function of the times when various connections of interest become operational. Most problems of this class are strongly NP-hard on general networks, but are often tree-efficient, that is, polynomially solvable on trees. We develop a generic local search heuristic approach and two metaheuristics (Iterated Local Search and Tabu Search) for solving tree-efficient network construction problems on general networks, and explore them computationally. Results of computational experiments indicate that the methods have excellent performance.