First vs. best improvement: An empirical study

Authors:
Pierre Hansen;Nenad Mladenović
Affiliations:
GERAD and HEC Montréal, 3000, chemin de la Côte-Sainte-Catherine, Montréal, Qué., Canada H3T 2A7;GERAD and HEC Montréal, 3000, chemin de la Côte-Sainte-Catherine, Montréal, Qué., Canada H3T 2A7
Venue:
Discrete Applied Mathematics - Special issue: IV ALIO/EURO workshop on applied combinatorial optimization
Year:
2006

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Abstract

When applying the 2-opt heuristic to the travelling salesman problem, selecting the best improvement at each iteration gives worse results on average than selecting the first improvement, if the initial solution is chosen at random. However, starting with 'greedy' or 'nearest neighbor' constructive heuristics, the best improvement is better and faster on average. Reasons for this behavior are investigated. It appears to be better to use exchanges introducing into the solution a very small edge and fairly large one, which can easily be removed later, than two small ones which are much harder to remove.