Jamming Model for the Extremal Optimization Heuristic

Extremal optimization, a recently introduced meta-heuristic for hard optimization problems, is analysed on a simple model of jamming. The model is motivated first by the problem of finding lowest energy configurations for a disordered spin system on a fixed-valence graph. The numerical results for the spin system exhibit the same phenomenology found in all earlier studies of extremal optimization, and our analytical results for the model reproduce many of these features.

[1]  Alex M. Andrew,et al.  Modern Heuristic Search Methods , 1998 .

[2]  James P. Sethna,et al.  Multicanonical methods, molecular dynamics, and Monte Carlo methods: Comparison for Lennard-Jones glasses , 1998 .

[3]  Stefan Boettcher,et al.  Optimization with Extremal Dynamics , 2000, Complex..

[4]  Faster Monte Carlo simulations at low temperatures. The waiting time method , 2001, cond-mat/0107475.

[5]  A P Young,et al.  Nature of the spin glass state. , 2000, Physical review letters.

[6]  Victor J. Rayward-Smith,et al.  Modern Heuristic Search Methods , 1996 .

[7]  R. Monasson,et al.  Statistical physics analysis of the computational complexity of solving random satisfiability problems using backtrack algorithms , 2000, cond-mat/0012191.

[8]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[9]  P. Salamon,et al.  Best possible strategy for finding ground states. , 2001, Physical review letters.

[10]  Nils J. Nilsson,et al.  Artificial Intelligence , 1974, IFIP Congress.

[11]  Julian F. Miller,et al.  Genetic and Evolutionary Computation — GECCO 2003 , 2003, Lecture Notes in Computer Science.

[12]  S Cocco,et al.  Trajectories in phase diagrams, growth processes, and computational complexity: how search algorithms solve the 3-satisfiability problem. , 2001, Physical review letters.

[13]  Ritort.  Glassiness in a Model without Energy Barriers. , 1995, Physical review letters.

[14]  M. Mézard,et al.  Mean-field theory of randomly frustrated systems with finite connectivity , 1987 .

[15]  G. Rinaldi,et al.  Exact ground states of Ising spin glasses: New experimental results with a branch-and-cut algorithm , 1995 .

[16]  Riccardo Zecchina,et al.  Exact solutions for diluted spin glasses and optimization problems , 2001, Physical review letters.

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

[18]  A. Bray,et al.  Phase diagrams for dilute spin glasses , 1985 .

[19]  A K Hartmann.  Calculation of ground states of four-dimensional +/-J Ising spin glasses. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[20]  Slow relaxation in granular compaction , 1996, cond-mat/9603150.

[21]  K. F. Pál.  The ground state of the cubic spin glass with short-range interactions of Gaussian distribution , 1996 .

[22]  D. Sherrington,et al.  Graph bipartitioning and statistical mechanics , 1987 .

[23]  R. Palmer,et al.  Models of hierarchically constrained dynamics for glassy relaxation , 1984 .

[24]  Riccardo Zecchina,et al.  Simplest random K-satisfiability problem , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Alexander K. Hartmann.  GROUND-STATE BEHAVIOR OF THE THREE-DIMENSIONAL J RANDOM-BOND ISING MODEL , 1999 .

[26]  S. Boettcher.  Extremal Optimization of Graph Partitioning at the Percolation Threshold , 1999, cond-mat/9901353.

[27]  Stefan Boettcher,et al.  Extremal Optimization for Graph Partitioning , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  R. Palmer,et al.  Ground States for Large Samples of Two-Dimensional Ising Spin Glasses , 1999 .

[29]  Rémi Monasson,et al.  Determining computational complexity from characteristic ‘phase transitions’ , 1999, Nature.

[30]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[31]  Károly F. Pál,et al.  The ground state energy of the Edwards-Anderson Ising spin glass with a hybrid genetic algorithm , 1996 .

[32]  H. Jaeger,et al.  Granular solids, liquids, and gases , 1996 .

[33]  D. Sherrington,et al.  Graph bipartitioning and spin glasses on a random network of fixed finite valence , 1987 .

[34]  S. Kirkpatrick,et al.  2+p-SAT: relation of typical-case complexity to the nature of the phase transition , 1999 .

[35]  Glassy dynamics of protein folding. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.