Instance Created:  July 29, 2001
Number of Cities:  71,009
Status:  OPEN
Best Tour:  4,566,506
Best Lower Bound:  4,565,452

History

Date	Gap	Lower Bound	Tour
28.8.01			4,571,895 - Found with linkern (2.5 million kicks, 14,513 seconds on a 500 MHz EV6 Alpha).
12.9.01			4,566,793 - Found by Keld Helsgaun using variants of his LKH code. The running time was approximately 5 days on an 800 MHz Pentium III.
15.9.01	0.029%	4,565,452 - Found by repeated runs on Concorde using -C 20, -C 24, -C 25, up to -C 31 (increasing by 1 in each run). The total running time was 1.7 million seconds.
20.9.01	0.025%		4,566,578 - Improved by Keld Helsgaun with LKH. The additional running time beyond the 9.12.01 tour was approximately 4 days on an 800 MHz Pentium III.
16.3.03	0.024%		4,566,563 - Found by Hung Dinh Nguyen using a hybrid genetic algorithm, starting with the above tour. The running time was 72945 seconds on a single processor of a Sun Ultra 80 (450 MHz).
26.2.04	0.024%		4,566,556 - Found by Keld Helsgaun with LKH. This improved tour was found by combining LKH with a tour-based partitioning scheme and with Karp's partitioning scheme.
25.4.06	0.024%		4,566,552 - Found by Keld Helsgaun with LKH.
10.5.06	0.024%		4,566,551 - Found by Keld Helsgaun with LKH.
21.8.06	0.024%		4,566,542 - Found by Keld Helsgaun with LKH.
10.7.07	0.024%		4,566,506 - Found by Yuichi Nagata.

Notes

1. Concorde is our linear-programming based TSP solver.

2. linkern is an implementation of Martin, Otto, and Felten's Chained Lin-Kernighan heuristic. It is included in the Concorde code.

3. LKH is Keld Helsgaun's powerful implementation of the Lin-Kernighan heuristic.

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