Download:
|
by Olivier Martin, Steve W. Otto, Edward W. Felten
Complex Systems
http://ipnweb.in2p3.fr/~lptms/membres/martino/Postscripts/cs.ps.gz
Add To MetaCart
Abstract:
We introduce a new class of Markov chain Monte Carlo search procedures, leading to more powerful optimization methods than simulated annealing. The main idea is to embed deterministic local search techniques into stochastic algorithms. The Monte Carlo explores only local optima, and it is able to make large, global changes, even at low temperatures, thus overcoming large barriers in configuration space. We test these procedures in the case of the Traveling Salesman Problem. The embedded local searches we use are 3-opt and Lin-Kernighan. The large change or step consists of a special kind of 4-change followed by local-opt minimization. We test this algorithm on a number of instances. The power of the method is illustrated by solving to optimality some large problems such as the LIN318, the AT&T532, and the RAT783 problems. For even larger instances with randomly distributed cities, the Markov chain procedure improves 3-opt by over 1.6%, and Lin-Kernighan by 1.3%, leading to a new best heuristic.
Citations
|
2172
|
Optimization by simulated annealing
– Kirkpatrick, Gelatt, et al.
- 1983
|
|
1827
|
Adaptation in Natural and Artificial Systems. The
– Holland
- 1975
|
|
1446
|
The Art of Computer Programming
– Knuth
- 1973
|
|
805
|
Combinatorial Optimization: Algorithms and Complexity
– Papadimitriou, Steiglitz
- 1982
|
|
436
|
Optimization by Simulated Annealing: An Experimental Evaluation
– Johnson, Aragon, et al.
- 1991
|
|
400
|
Neural" computation of decisions in optimization problems
– Hopfield, Tank
- 1985
|
|
273
|
The Traveling Salesman problem
– Lawler, Lenstra
- 1984
|
|
248
|
An Effective Heuristic Algorithm for the Traveling Salesman Problem
– Lin, Kernighan
- 1973
|
|
207
|
Thermodynamical approach to the traveling salesman problem: An efficient simulation algorithm
– Cerny
- 1985
|
|
197
|
Computer Solutions on the Travelling Salesman Problem
– Lin
- 1965
|
|
126
|
The traveling salesman problem and minimum spanning trees
– Held, Karp
- 1970
|
|
76
|
Evolution Algorithms in Combinatorial Optimization. Parallel Computing 7: 65–85
– Mühlenbein, Gorges-Schleuter, et al.
- 1988
|
|
70
|
On the Stability of the Traveling Salesman Problem Algorithm of Hopfield and
– Wilson, Pawley
- 1988
|
|
53
|
Optimization of a 532-city symmetric traveling salesman problem
– Padberg, Rinaldi
- 1987
|
|
32
|
Polyhedral theory
– Grotschel, Padberg
- 1985
|
|
28
|
On the symmetric travelling salesman problem: a computational study
– Padberg, Hong
- 1980
|
|
25
|
Polyhedral computations
– Padberg, Grötschel
- 1985
|
|
20
|
Monte Carlo-minimization approach to the multiple-minima problem in protein folding
– Li, Scheraga
- 1987
|
|
20
|
Empirical analysis of heuristics
– Golden, Stewart
- 1985
|
|
4
|
Searching for Optimal Configurations by Simulated Tunneling ", Zeitschrift fur Physik
– Rujan
- 1988
|
|
4
|
Best-first branch-and-bound on hypercube
– Felten
- 1988
|
|
2
|
Accelerated Branch Exchange Heuristics for Symmetric Traveling Salesman Problems
– Stewart
- 1987
|
|
1
|
A comparison of heuristics for the traveling salesman problem
– Bentley, Johnson
|
|
1
|
Cost distributions in large combinatorial optimization problems
– Burgess, Moore
- 1989
|
