Combining simulated annealing with local search heuristics

We introduce a meta-heuristic to combine simulated annealing with local search methods for CO problems. This new class of Markov chains leads to significantly more powerful optimization methods than either simulated annealing or local search. The main idea is to embed deterministic local search techniques into simulated annealing so that the chain explores only local optima. It makes large, global changes, even at low temperatures, thus overcoming large barriers in configuration space. We have tested this meta-heuristic for the traveling salesman and graph partitioning problems. Tests on instances from public libraries and random ensembles quantify the power of the method. Our algorithm is able to solve large instances to optimality, improving upon local search methods very significantly. For the traveling salesman problem with randomly distributed cities, in a square, the procedure improves on 3-opt by 1.6%, and on Lin-Kernighan local search by 1.3%. For the partitioning of sparse random graphs of average degree equal to 5, the improvement over Kernighan-Lin local search is 8.9%. For both CO problems, we obtain new best heuristics.

[1]  J. P. Secrétan,et al.  Der Saccus endolymphaticus bei Entzündungsprozessen , 1944 .

[2]  Shen Lin.  Computer solutions of the traveling salesman problem , 1965 .

[3]  Brian W. Kernighan,et al.  An efficient heuristic procedure for partitioning graphs , 1970, Bell Syst. Tech. J..

[4]  Maurice Hanan,et al.  A review of the placement and quadratic assignment problems , 1972 .

[5]  Brian W. Kernighan,et al.  An Effective Heuristic Algorithm for the Traveling-Salesman Problem , 1973, Oper. Res..

[6]  Alex Pothen,et al.  PARTITIONING SPARSE MATRICES WITH EIGENVECTORS OF GRAPHS* , 1990 .

[7]  H. Crowder,et al.  Solving Large-Scale Symmetric Travelling Salesman Problems to Optimality , 1980 .

[8]  R. M. Mattheyses,et al.  A Linear-Time Heuristic for Improving Network Partitions , 1982, 19th Design Automation Conference.

[9]  Charles M. Fiduccia,et al.  A linear-time heuristic for improving network partitions , 1988, 25 years of DAC.

[10]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[11]  Scott Kirkpatrick,et al.  Optimization by simulated annealing: Quantitative studies , 1984 .

[12]  Brian W. Kernighan,et al.  A Procedure for Placement of Standard-Cell VLSI Circuits , 1985, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[13]  V. Cerný.  Thermodynamical approach to the traveling salesman problem: An efficient simulation algorithm , 1985 .

[14]  Editors , 1986, Brain Research Bulletin.

[15]  P. Anderson,et al.  Application of statistical mechanics to NP-complete problems in combinatorial optimisation , 1986 .

[16]  E. Baum.  Towards practical `neural' computation for combinatorial optimization problems , 1987 .

[17]  Shahid H. Bokhari,et al.  A Partitioning Strategy for Nonuniform Problems on Multiprocessors , 1987, IEEE Transactions on Computers.

[18]  H. Scheraga,et al.  Monte Carlo-minimization approach to the multiple-minima problem in protein folding. , 1987, Proceedings of the National Academy of Sciences of the United States of America.

[19]  Heinz Mühlenbein,et al.  Evolution algorithms in combinatorial optimization , 1988, Parallel Comput..

[20]  F. Barahona,et al.  On the magnetisation of the ground states in two dimensional Ising spin glasses , 1988 .

[21]  Cecilia R. Aragon,et al.  Optimization by Simulated Annealing: An Experimental Evaluation; Part I, Graph Partitioning , 1989, Oper. Res..

[22]  Frank Thomson Leighton,et al.  Improving the Performance of the Kernighan-Lin and Simulated Annealing Graph Bisection Algorithms , 1989, 26th ACM/IEEE Design Automation Conference.

[23]  M. Padberg,et al.  Addendum: Optimization of a 532-city symmetric traveling salesman problem by branch and cut , 1990 .

[24]  David S. Johnson,et al.  Local Optimization and the Traveling Salesman Problem , 1990, ICALP.

[25]  Gerhard Reinelt,et al.  TSPLIB - A Traveling Salesman Problem Library , 1991, INFORMS J. Comput..

[26]  Edward W. Felten,et al.  Large-Step Markov Chains for the Traveling Salesman Problem , 1991, Complex Syst..

[27]  Giovanni Rinaldi,et al.  A Branch-and-Cut Algorithm for the Resolution of Large-Scale Symmetric Traveling Salesman Problems , 1991, SIAM Rev..

[28]  Jack Dongarra,et al.  Heterogeneous network computing , 1991 .

[29]  Edward W. Felten,et al.  Large-step markov chains for the TSP incorporating local search heuristics , 1992, Oper. Res. Lett..

[30]  Jack Dongarra,et al.  Integrated Pvm Framework Supports Heterogeneous Network Computing , 1993 .

[31]  Jack Dongarra,et al.  PVM and HeNCE: tools for heterogeneous network computing , 1993 .

[32]  Olivier C. Martin,et al.  Partitioning of unstructured meshes for load balancing , 1995, Concurr. Pract. Exp..