Combinatorial Optimization by Iterative Partial Transcription

TL;DR

This paper introduces an iterative partial transcription method that enhances local search heuristics for combinatorial optimization, significantly improving solution quality for problems like the traveling salesman problem.

Contribution

It presents a novel partial transcription technique that acts as a local search in solution subspaces, outperforming traditional methods like simulated annealing.

Findings

Improved solutions for traveling salesman problem instances.

Partial transcription enhances local search effectiveness.

Outperforms simulated annealing in tested cases.

Abstract

A procedure is presented which considerably improves the performance of local search based heuristic algorithms for combinatorial optimization problems. It increases the average `gain' of the individual local searches by merging pairs of solutions: certain parts of either solution are transcribed by the related parts of the respective other solution, corresponding to flipping clusters of a spin glass. This iterative partial transcription acts as a local search in the subspace spanned by the differing components of both solutions. Embedding it in the simple multi-start-local-search algorithm and in the thermal-cycling method, we demonstrate its effectiveness for several instances of the traveling salesman problem. The obtained results indicate that, for this task, such approaches are far superior to simulated annealing.