Related papers: Probing spin glasses with heuristic optimization a…
Spin-glass systems are universal models for representing many-body phenomena in statistical physics and computer science. High quality solutions of NP-hard combinatorial optimization problems can be encoded into low energy states of…
This PhD thesis is organized as follows. In the first two chapters I will review some basic notions of statistical physics of disordered systems, such as random graph theory, the mean-field approximation, spin glasses and combinatorial…
Vehicle routing is a well-known optimization research topic with significant practical importance. Among different approaches to solving vehicle routing, heuristics can produce a satisfactory solution at a reasonable computational cost.…
In these two lectures I review our theoretical understanding of spin glasses paying a particular attention to the basic physical ideas. We introduce the replica method and we describe its probabilistic consequences (we stress the recently…
It is a folklore belief in the theory of spin glasses and disordered systems that out-of-equilibrium dynamics fail to find stable local optima exhibiting e.g. local strict convexity on physical time-scales. In the context of the…
This paper surveys the recent attempts at leveraging machine learning to solve constrained optimization problems. It focuses on surveying the work on integrating combinatorial solvers and optimization methods with machine learning…
The odds theorem and the corresponding solution algorithm (odds algorithm) are tools to solve a wide range of optimal stopping problems. Its generality and tractability have caught much attention. (Google for instance "Bruss odds" to obtain…
Evaluating solutions to optimization problems is arguably the most important step for heuristic algorithms, as it is used to guide the algorithms towards the optimal solution in the solution search space. Research has shown evaluation…
Recently, Smajic et al. published an article on numerical structural opti- mizations of two-dimensional photonic crystals using two different classes of optimization algorithms i.e, deterministic for local searches and stochastic for…
This chapter collects several probabilistic tools that proved to be useful in the analysis of randomized search heuristics. This includes classic material like Markov, Chebyshev and Chernoff inequalities, but also lesser known topics like…
In a previous paper (q-alg/9501022) we suggested some algorithms that could be useful in solving the problem of knot classification. Here we continue this discussion by answering questions raised in that paper and by commenting on practical…
Spin glasses are quintessential examples of complex matter. Although much about their order remains uncertain, abstract models of them inform, e.g., the classification of combinatorial optimization problems, the magnetic ordering in metals…
Here we review the approach to glassy systems based on the replica method and we introduce the main ingredients of replica symmetry breaking. We explain why the replica method has been successful in spin glass and why it should be…
The race to heuristically solve non-deterministic polynomial-time (NP) problems through efficient methods is ongoing. Recently, optics was demonstrated as a promising tool to find the ground state of a spin-glass Ising Hamiltonian, which…
Ignoring uncertainty in combinatorial optimization leads to suboptimal decisions in practice. Nevertheless, the focus is often on deterministic combinatorial optimization problems, mainly because they are already challenging enough without…
In spin glass models one can remove minimization of free energy by some order parameter. One can consider hierarchy of order parameters. It is possible to divide energy among these parts. We can consider relaxation process in glass system…
This work considers infinite-horizon optimal control of positive linear systems applied to the case of network routing problems. We demonstrate the equivalence between Stochastic Shortest Path (SSP) problems and optimal control of a certain…
This talk describes how techniques developed by Computer Scientists have helped our understanding of certain problems in statistical physics which involve randomness and ``frustration''. Examples will be given from two problems that have…
We discuss the metastate, a probability measure on thermodynamic states, and its usefulness in addressing difficult questions pertaining to the statistical mechanics of systems with quenched disorder, in particular short-range spin glasses.…
In these lectures I will review some theoretical results that have been obtained for spin glasses. I will concentrate my attention on the formulation of the mean field approach and on its numerical and experimental verifications. I will…