A dynamic programming methodology in very large scale neighborhood search applied to the traveling salesman problem

Authors:
ÖZlem Ergun;James B. Orlin
Affiliations:
Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30339, United States;Sloan School of Management, Massachusetts Institute of Technology, Cambridge, MA 02139, United States
Venue:
Discrete Optimization
Year:
2006

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Abstract

We consider the standard dynamic program to solve the TSP. We then obtain exponentially large neighborhoods by selecting a polynomially bounded number of states, and restricting the dynamic program to those states only. We show how the Balas and Simonetti neighborhood and the insertion dynasearch neighborhood can be viewed in this manner. We also show that one of the dynasearch neighborhoods can be derived directly from the 2-exchange neighborhood using this approach.