Annealing Algorithm For Global Optimization Research Articles

New Hybrid Perturbed Projected Gradient and Simulated Annealing Algorithms for Global Optimization

New Hybrid Perturbed Projected Gradient and Simulated Annealing Algorithms for Global Optimization

A hybrid differential evolution and simulated annealing algorithm for global optimization

Differential evolution (DE) is one of the most effective ways to solve global optimization problems. However, considering the traditional DE has lower search efficiency and easily traps into local optimum, a novel DE variant named hybrid DE and simulated annealing (SA) algorithm for global optimization (HDESA) is proposed in this paper. This algorithm introduces the concept of “ranking” into the mutation operation of DE and adds the idea of SA to the selection operation. The former is to improve the exploitation ability and increase the search efficiency, and the latter is to enhance the exploration ability and prevent the algorithm from trapping into the local optimal state. Therefore, a better balance can be achieved. The experimental results and analysis have shown its better or at least equivalent performance on the exploitation and exploration capability for a set of 24 benchmark functions. It is simple but efficient.

Multiple-Try Simulated Annealing Algorithm for Global Optimization

Simulated annealing is a widely used algorithm for the computation of global optimization problems in computational chemistry and industrial engineering. However, global optimum values cannot always be reached by simulated annealing without a logarithmic cooling schedule. In this study, we propose a new stochastic optimization algorithm, i.e., simulated annealing based on the multiple-try Metropolis method, which combines simulated annealing and the multiple-try Metropolis algorithm. The proposed algorithm functions with a rapidly decreasing schedule, while guaranteeing global optimum values. Simulated and real data experiments including a mixture normal model and nonlinear Bayesian model indicate that the proposed algorithm can significantly outperform other approximated algorithms, including simulated annealing and the quasi-Newton method.

Improved modified simulated annealing algorithm for global optimization

Improved modified simulated annealing algorithm for global optimization

A New Dynamic Simulated Annealing Algorithm For Global Optimization

Many problems in system analysis in real world lead to continuous-domain optimization. Existence of sophisticated and many-variable problems in this field emerge need of efficient optimization methods. One of the optimization algorithms for multi-dimensional functions is simulated annealing (SA). In this paper, a modified simulated annealing named Dynamic Simulated Annealing (DSA) is proposed which dynamically switch between two types of generating function on traversed path of continuous Markov chain. Our experiments indicate that this approach can improve convergence and stability and avoid delusive areas in benchmark functions better than SA without any extra mentionable computational cost.

The combination stretching function technique with simulated annealing algorithm for global optimization

A stretching function technique is combined with the simulated annealing (SA) algorithm for the global optimization problems. In the presented algorithm, the obtained local optimum information by SA search is used to build a stretching function. To speed up the convergence of SA, SA is executed iteratively on the stretching function constructed with respect to the previously found local minima instead of on the original objective function. Furthermore, a new next trial point generation scheme in SA is designed to increase the diversity of the trial points to make the introduced technique more effective. In the numerical experiments, we first investigate and compare the effectiveness and efficiency of the combination of the stretching technique with a newly designed SA (SSA), with particle swarm optimization and with differential evolution algorithm, respectively, on eight typical test functions in terms of the average number of the function evaluations and its standard deviation, and the success rate. Second, we systematically compare the numerical results of SSA with the traditional SA with elitist and SA with new generation scheme on 37 benchmark problems. The numerical results show that the hybrid method is effective for global optimization.

A Hybrid Hypergraph Partitioning Algorithm for Scientific Computing

Hypergraph partitioning is an increasingly important and widely studied research topic in parallel scientific computing. In this paper, we present a multiway hypergraph partitioning algorithm, mixed simulated annealing algorithm for global optimization and tabu search algorithm for local optimization. Experiments on the benchmark suite of several unstructured meshes show that, for 2-, 4-, 8-, 16-and 32-way partitioning, the quality of partition produced by our algorithm are on the average 6% and the maximum 17% better than those produced by partitioning software hMETIS in term of the cutsize metric.

Structural Shape Optimization Using an Adaptive Simulated Annealing

In structural design optimization, numerical techniques are increasingly used. In typical structural optimization problems there may be many locally minimum configurations. For that reason, the application of a global method, which may escape from the locally minimum points, remain essential. In this paper, a new hybrid simulated annealing algorithm for global optimization with constraints is proposed. We have developed a new algorithm called Adaptive Simulated Annealing algorithm (ASA); ASA is a series of modifications done to the Basic Simulated Annealing algorithm ( BSA) that gives the region containing the global solution of an objective function. In addition, the stochastic method Simultaneous Perturbation Stochastic Approximation (SPSA), for solving unconstrained optimization problems, is used to refine the solution. We also propose Penalty SPSA (PSPSA) for solving constrained optimization problems. The constraints are handled using exterior point penalty functions. The proposed method is applicable for any problem where the topology of the structure is not fixed, it is simple and capable of handling problems subject to any number of nonlinear constraints. Extensive tests on the ASA as a global optimization method are presented, its performance as a viable optimization method is demonstrated by applying it first to a series of benchmark functions with 2 - 30 dimensions and then it is used in structural design to demonstrate its applicability and efficiency. It is found that the best results are obtained by ASA compared to those provided by the commercial software ANSYS.

Global optimization using ab initio quantum mechanical potentials and simulated annealing of the classical Liouville equation

The routine location of the global minimum energy structures of a molecular system remains a challenging problem in chemical physics. Recently Straub and co-workers [J. Ma et al., J. Chem. Phys. 99, 4024 (1993) and 101, 533 (1994)] have introduced a number of novel dynamic simulated annealing algorithms for global optimization. Instead of using Newton’s equations, they are based on Liouville’s equation and the particles are described with phase space distributions. The methods were shown to have significantly enhanced effectiveness over traditional methods when used to locate the global minima of Lennard-Jones clusters. In this paper the extensions necessary to use these methods with ab initio quantum mechanical potentials are presented and their application is illustrated by the simulated annealing of a small lithium atom cluster.

Simulated annealing using coarse grained classical dynamics: Smoluchowski dynamics in the Gaussian density approximation

A dynamical annealing algorithm for global optimization based on approximate solution of the Smoluchowski equation is presented. The equations of motion in the Gaussian density approximation are interpreted as a steepest descent quench on a time dependent effective potential energy surface. A relation between the convexity condition for the effective potential surface and the size of thermal fluctuations provides a definition of the critical temperature above which the distribution is delocalized and the effective potential is smooth and convex during an annealing run. This critical temperature may be significantly less than the temperature characteristic of escape from a local energy minimum.

An adaptive simulated annealing algorithm for global optimization over continuous variables

A method is presented for attempting global minimization for a function of continuous variables subject to constraints. The method, calledAdaptive Simulated Annealing (ASA), is distinguished by the fact that the fixed temperature schedules and step generation routines that characterize other implementations are here replaced by heuristic-based methods that effectively eliminate the dependence of the algorithm's overall performance on user-specified control parameters. A parallelprocessing version of ASA that gives increased efficiency is presented and applied to two standard problems for illustration and comparison.

Metropolis-Type Annealing Algorithms for Global Optimization in $\mathbb{R}^d $

The convergence of a class of Metropolis-type Markov-chain annealing algorithms for global optimization of a smooth function $U( \cdot )$ on $\mathbb{R}^d $ is established. No prior information is assumed as to what bounded region contains a global minimum. The analysis contained herein is based on writing the Metropolis-type algorithm in the form of a recursive stochastic algorithm $X_{k + 1} = X_k - a_k (\nabla U(X_k ) + \xi _k ) + b_k W_k $, where $\{ {W_k } \}$ is a standard white Gaussian sequence, $\{ {\xi _k } \}$ are random variables, and $a_k = {A / k}$, $b_k = {{\sqrt B } / {\sqrt {k\log \log k} }}$ for k large. Convergence results for $\{ {X_k } \}$ are then applied from our previous work [SIAM Journal on Control and Optimization, 29 (1991), pp. 999–1018]. Since the analysis of $\{ {X_k } \}$ is based on the asymptotic behavior of the related Langevin-type Markov diffusion annealing algorithm $dY(t) = - \nabla U(Y(t))dt + c(t)dW(t)$, where $W( \cdot )$ is a standard Wiener process and $c(t) = {...

The demon algorithm

This paper introduces a generalization of the simulated annealing algorithm for global optimization. Simulated annealing has been successfully applied to a number of combinatorial and continuous optimization problems. The original approach has been significantly improved by introducing adaptive annealing schedules and annealing several copies of the problem in parallel. In this paper we make a further step and propose a generalized simulated annealing algorithm called Demon Algorithm. This algorithm is constructed in analogy to the action of Maxwell's Demon and has been motivated by an information-theoretic analysis of simulated annealing. The algorithm is based on an ensemble of identical systems that are annealed in parallel. The ensemble evolves according to a sequence of target distributions with the aim to end up in a distribution that is concentrated on optimal solutions. The evolution of the ensemble is based on collective moves. The algorithm is implemented for the problem of graph bipartitioning ...