Using grammars to generate very large scale neighborhoods for the traveling salesman problem and other sequencing problems

Authors:
Agustin Bompadre;James B. Orlin
Affiliations:
Operations Research Center, MIT, Cambridge, MA;Sloan School of Management, MIT, Cambridge, MA
Venue:
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Year:
2005

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Abstract

Local search heuristics are among the most popular approaches to solve hard optimization problems. Among them, Very Large Scale Neighborhood Search techniques present a good balance between the quality of local optima and the time to search a neighborhood. We develop a language to generate exponentially large neighborhoods for sequencing problems using grammars. We develop efficient generic dynamic programming solvers that determine the optimal neighbor in a neighborhood generated by a grammar for sequencing problems such as the Traveling Salesman Problem or the Linear Ordering Problem. This framework unifies a variety of previous results on exponentially large neighborhood for the Traveling Salesman Problem and generalizes them to other sequencing problems.