We develop a quantum algorithm to solve combinatorial optimization problems through quantum simulation of a classical annealing process. Our algorithm combines techniques from quantum walks, quantum phase estimation, and quantum Zeno effect. It can be viewed as a quantum analogue of the discrete-time Markov chain Monte Carlo implementation of classical simulated annealing. Our implementation re...

There is a deep and useful connection between statistical mechanics (the behavior of systems with many degrees of freedom in thermal equilibrium at a finite temperature) and multivariate or combinatorial optimization (finding the minimum of a given function depending on many parameters). A detailed analogy with annealing in solids provides a framework for optimization of the properties of very ...

The question of satissability for a given proposi-tional formula arises in many areas of AI. Especially nding a model for a satissable formula is very important though known to be NP-complete. There exist complete algorithms for satissability testing like the Davis-Putnam-Algorithm, but they often do not construct a satisfying assignment for the formula , are not practically applicable for more...

We undertake a set of studies using simulated annealing, concerning the prediction of the structures of compounds of the type ATiO3 (A = Ca, Ba). A tremendous increase of the efficiency in obtaining the correct structure and in the accuracy of the atomic coordinates was obtained by the incorporation of space symmetry elements obtainable from powder diffraction. In a second stage we also used a ...

An algorithm is developed to statistically find the best global fit of a nonlinear non-convex cost-function over a D-dimensional space. It is argued that this algorithm permits an annealing schedule for ''temperature'' T decreasing exponentially in annealing-time k, T = T 0 exp(−ck 1/D). The introduction of re-annealing also permits adaptation to changing sensitivities in the multi-dimensional ...

We propose a new stochastic algorithm (generalized simulated annealing) for computationally finding the global minimum of a given (not necessarily convex) energy/cost function defined in a continuous D-dimensional space. This algorithm recovers, as particular cases, the so called classical (“Boltzmann machine”) and fast (“Cauchy machine”) simulated annealings, and can be quicker than both. Key-...

fuzzy cognitive maps (fcms) have successfully been applied in numerous domains to show the relations between essential components in complex systems. in this paper, a novel learning method is proposed to construct fcms based on historical data and by using meta-heuristic: genetic algorithm (ga), simulated annealing (sa), and tabu search (ts). implementation of the proposed method has demonstrat...

The paper addresses the problem of scheduling production orders (jobs). First an approach based on simulated annealing and Hopfield nets is described. Since performance was unsatisfactory for real-world applications, we changed problem representation and tuned the scheduling method, dropping features of the Hopfield net and retaining simulated annealing. Both computing time and solution quality...