Paper:

# A Compressed Annealing Approach with Pre-Process for the Asymmetric Traveling Salesman Problem with Time Windows

## Tadanobu Mizogaki^{*1}, Masao Sugi^{*2}, Masashi Yamamoto^{*3}, Hidetoshi Nagai^{*3}, Yusuke Shiomi^{*3}, and Jun Ota^{*4}

^{*1}Mori Seiki Co. Ltd.

^{*2}The University of Electro-Communications

^{*3}NS Solutions Corporation

^{*4}The University of Tokyo

This paper proposes a method of rapidly finding a feasible solution to the asymmetric traveling salesman problem with time windows (ATSP-TW). ATSP-TW is a problem that involves determining the route with the minimum travel cost for visiting n cities one time each with time window constraints (the period of time in which the city must be visited is constrained). “Asymmetrical” denotes a difference between the cost of outbound and return trips. For such a combinatorial optimization problem with constraints, we propose a method that combines a pre-process based on the insertion method with metaheuristics called “the compressed annealing approach.” In an experiment using a 3-GHz computer, our method derives a feasible solution that satisfies the time window constraints for all of up to about 300 cities at an average of about 1/7 the computing time of existing methods, an average computing time of 0.57 seconds, and a maximum computing time of 9.40 seconds.

*Int. J. Automation Technol.*, Vol.5, No.5, pp. 669-678, 2011.

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