Particle algorithms for optimization on binary spaces

We discuss a unified approach to stochastic optimization of pseudo-Boolean objective functions based on particle methods, including the cross-entropy method and simulated annealing as special cases. We point out the need for auxiliary sampling distributions, that is parametric families on binary spaces, which are able to reproduce complex dependency structures, and illustrate their usefulness in our numerical experiments. We provide numerical evidence that particle-driven optimization algorithms based on parametric families yield superior results on strongly multi-modal optimization problems while local search heuristics outperform them on easier problems

Growth Algorithms for Lattice Heteropolymers at Low Temperatures

Two improved versions of the pruned-enriched-Rosenbluth method (PERM) are proposed and tested on simple models of lattice heteropolymers. Both are found to outperform not only the previous version of PERM, but also all other stochastic algorithms which have been employed on this problem, except for the core directed chain growth method (CG) of Beutler & Dill. In nearly all test cases they are faster in finding low-energy states, and in many cases they found new lowest energy states missed in previous papers. The CG method is superior to our method in some cases, but less efficient in others. On the other hand, the CG method uses heavily heuristics based on presumptions about the hydrophobic core and does not give thermodynamic properties, while the present method is a fully blind general purpose algorithm giving correct Boltzmann-Gibbs weights, and can be applied in principle to any stochastic sampling problem.Comment: 9 pages, 9 figures. J. Chem. Phys., in pres