Version Of Simulated Annealing Research Articles

Discrete swarm intelligence optimization algorithms applied to steel–concrete composite bridges

Composite bridge optimization might be challenging because of the significant number of variables involved in the problem. The optimization of a box-girder steel–concrete composite bridge was done in this study with cost and CO2 emissions as objective functions. Given this challenge, this study proposes a hybrid algorithm that integrates the unsupervised learning technique of k-means with continuous swarm intelligence metaheuristics to strengthen the latter’s performance. In particular, the metaheuristics sine-cosine and cuckoo search are discretized. The contribution of the k-means operator regarding the quality of the solutions obtained is studied. First, random operators are designed to use transfer functions later to evaluate and compare the performances. Additionally, to have another point of comparison, a version of simulated annealing was adapted, which has solved related optimization problems efficiently. The results show that our hybrid proposal outperforms the different algorithms designed.

Constructal Design and Simulated Annealing applied to the geometric optimization of an isothermal Double T-shaped cavity

Present numerical work comprises the application of Constructal Design (CD) and Simulated Annealing (SA) for the geometric optimization of a Double T-shaped cavity inserted into a solid wall with internal heat generation. The main goal is to minimize the dimensionless maximum excess of temperature in the solid domain. The cavity is subjected to four constraints and five degrees of freedom (DOF). The Exhaustive Search (ES) and SA methods are employed to optimize the first three DOFs, validating the SA algorithm. From the fourth level onward, new recommendations about the design influence over the system's performance are reached, combining ES and different versions of SA. Results obtained showed the importance of investigating the influence of the DOFs over thermal performance, and corresponding design, using combined SA versions and ES. The proposed methodology reduced the computational effort in comparison with purely ES. For design investigation, the highest insertion of stem and branches led to the best performance. For square solid domains, the Double T-shaped cavity obtained an intermediate performance compared with I, T, Y, H, and ψ shapes. For small height/length solid domain ratios, the best shape found here performed several times better than the best configurations found in the literature.

Mimicking the collective intelligence of human groups as an optimization tool for complex problems

A large number of optimization algorithms have been developed by researchers to solve a variety of complex problems in operations management area. We present a novel optimization algorithm belonging to the class of swarm intelligence optimization methods. The algorithm mimics the decision making process of human groups and exploits the dynamics of such a process as a tool for complex combinatorial problems. In order to achieve this aim, we employ a properly modified version of a recently published decision making model [64,65], to model how humans in a group modify their opinions driven by self-interest and consensus seeking. The dynamics of such a system is governed by three parameters: (i) the reduced temperature βJ, (ii) the self-confidence of each agent β′, (iii) the cognitive level 0 ≤ p ≤ 1 of each agent. Depending on the value of the aforementioned parameters a critical phase transition may occur, which triggers the emergence of a superior collective intelligence of the population. Our algorithm exploits such peculiar state of the system to propose a novel tool for discrete combinatorial optimization problems. The benchmark suite consists of the NK - Kauffman complex landscape, with various sizes and complexities, which is chosen as an exemplar case of classical NP-complete optimization problem.A comparison with genetic algorithms (GA), simulated annealing (SA) as well as with a multiagent version of SA is presented in terms of efficacy in finding optimal solutions. In all cases our method outperforms the others, particularly in presence of limited knowledge of the agent.

Applications of Monte Carlo method to nonlinear regression of rheological data

In rheological study, it is often to determine the parameters of rheological models from experimental data. Since both rheological data and values of the parameters vary in logarithmic scale and the number of the parameters is quite large, conventional method of nonlinear regression such as Levenberg-Marquardt (LM) method is usually ineffective. The gradient-based method such as LM is apt to be caught in local minima which give unphysical values of the parameters whenever the initial guess of the parameters is far from the global optimum. Although this problem could be solved by simulated annealing (SA), the Monte Carlo (MC) method needs adjustable parameter which could be determined in ad hoc manner. We suggest a simplified version of SA, a kind of MC methods which results in effective values of the parameters of most complicated rheological models such as the Carreau-Yasuda model of steady shear viscosity, discrete relaxation spectrum and zero-shear viscosity as a function of concentration and molecular weight.

Two-stage assembly scheduling problem for minimizing total tardiness with setup times

The two-stage assembly flowshop scheduling problem has received much attention from researchers because it is applicable to many real-life environments. The objective of minimizing total tardiness is important because the fulfillment of due dates for customers must be considered when making scheduling decisions. However, the setup times were assumed to be zero in previous studies, which may not be realistic or appropriate for some scheduling environments because treating the setup times separately from the processing times increases the level of machine utilization and reduces total tardiness. In this study, we investigate the two-stage assembly flowshop scheduling problem with separate setup times to minimize the total tardiness. We propose two new algorithms and adapt four existing algorithms, which are different versions of simulated annealing, genetic, and insertion algorithms. Moreover, we formulate the problem mathematically, where we develop a dominance relation and we utilize the dominance relation in our proposed algorithms. Extensive computational experiments indicated that one of the proposed algorithms performed much better than the others on average, i.e., the error using the best algorithm was 54% to 98% less than that with the other algorithms. Computational experiments were also conducted with zero setup times in order to compare the performance of our proposed algorithms with that of the best known previously reported algorithm in the zero setup time case. When the setup times were zero, the best proposed algorithm reduced the error of the best previously reported algorithm by 48% when both algorithms were run for the same computational time. Therefore, our best proposed algorithm can be used for both zero and non-zero setup times. Hence, for the first time, the present study considers the problem with separate setup times as well as proposing much better algorithms for the zero setup time case.

Scalable Feature Selection in High-Dimensional Data Based on GRASP

Feature selection in high-dimensional data is one of the active areas of research in pattern recognition. Most of the algorithms in this area try to select a subset of features in a way to maximize the accuracy of classification regardless of the number of selected features that affect classification time. In this article, a new method for feature selection algorithm in high-dimensional data is proposed that can control the trade-off between accuracy and classification time. This method is based on a greedy metaheuristic algorithm called greedy randomized adaptive search procedure (GRASP). It uses an extended version of a simulated annealing (SA) algorithm for local search. In this version of SA, new parameters are embedded that allow the algorithm to control the trade-off between accuracy and classification time. Experimental results show supremacy of the proposed method over previous versions of GRASP for feature selection. Also, they show how the trade-off between accuracy and classification time is controllable by the parameters introduced in the proposed method.

No-Wait Flowshops to Minimize Total Tardiness with Setup Times

The m-machine no-wait flowshop scheduling problem is addressed where setup times are treated as separate from processing times. The objective is to minimize total tardiness. Different dispatching rules have been investigated and three were found to be superior. Two heuristics, a simulated annealing (SA) and a genetic algorithm (GA), have been proposed by using the best performing dispatching rule as the initial solution for SA, and the three superior dispatching rules as part of the initial population for GA. Moreover, improved versions of SA and GA are proposed using an insertion algorithm. Extensive computational experiments reveal that the improved versions of SA and GA perform about 95% better than SA and GA. The improved version of GA outperforms the improved version of SA by about 3.5%.

A hybrid simulated annealing approach to handle energy resource management considering an intensive use of electric vehicles

The massification of electric vehicles (EVs) can have a significant impact on the power system, requiring a new approach for the energy resource management. The energy resource management has the objective to obtain the optimal scheduling of the available resources considering distributed generators, storage units, demand response and EVs. The large number of resources causes more complexity in the energy resource management, taking several hours to reach the optimal solution which requires a quick solution for the next day. Therefore, it is necessary to use adequate optimization techniques to determine the best solution in a reasonable amount of time.This paper presents a hybrid artificial intelligence technique to solve a complex energy resource management problem with a large number of resources, including EVs, connected to the electric network. The hybrid approach combines simulated annealing (SA) and ant colony optimization (ACO) techniques. The case study concerns different EVs penetration levels. Comparisons with a previous SA approach and a deterministic technique are also presented. For 2000 EVs scenario, the proposed hybrid approach found a solution better than the previous SA version, resulting in a cost reduction of 1.94%. For this scenario, the proposed approach is approximately 94 times faster than the deterministic approach.

Minimizing total tardiness in no-wait flowshops

AbstractWe address the m-machine no-wait flowshop scheduling problem; where the objective is to minimize total tardiness. To the best of our knowledge, the considered problem has not been addressed so far. We propose heuristic solutions since the problem is NP-hard. Initially, we consider a number of dispatching rules commonly used for the considered objective in other scheduling environments. We identify through computational experiments the best performing dispatching rule; and then propose simulated annealing (SA) and genetic algorithms (GA) by using the best performing dispatching rule as an initial solution. This achieves at least 50% improvement in the SA and GA performances. Next, we propose enhanced versions of SA and GA and show through computational experiments that the enhanced versions provide over 90% further improvement. The performance of enhanced GA is slightly better than that of enhanced SA; however, the computation time of enhanced GA is about 10 times that of enhanced SA. Therefore, we conclude that the enhanced SA outperforms the enhanced GA.

An efficient implementation of parallel simulated annealing algorithm in GPUs

In this work we propose a highly optimized version of a simulated annealing (SA) algorithm adapted to the more recently developed graphic processor units (GPUs). The programming has been carried out with compute unified device architecture (CUDA) toolkit, specially designed for Nvidia GPUs. For this purpose, efficient versions of SA have been first analyzed and adapted to GPUs. Thus, an appropriate sequential SA algorithm has been developed as starting point. Next, a straightforward asynchronous parallel version has been implemented and then a specific and more efficient synchronous version has been developed. A wide appropriate benchmark to illustrate the performance properties of the implementation has been considered. Among all tests, a classical sample problem provided by the minimization of the normalized Schwefel function has been selected to compare the behavior of the sequential, asynchronous and synchronous versions, the last one being more advantageous in terms of balance between convergence, accuracy and computational cost. Also the implementation of a hybrid method combining SA with a local minimizer method has been developed. Note that the generic feature of the SA algorithm allows its application in a wide set of real problems arising in a large variety of fields, such as biology, physics, engineering, finance and industrial processes.

Bayesian variable selection in generalized linear models using a combination of stochastic optimization methods

In this paper the usage of a stochastic optimization algorithm as a model search tool is proposed for the Bayesian variable selection problem in generalized linear models. Combining aspects of three well known stochastic optimization algorithms, namely, simulated annealing, genetic algorithm and tabu search, a powerful model search algorithm is produced. After choosing suitable priors, the posterior model probability is used as a criterion function for the algorithm; in cases when it is not analytically tractable Laplace approximation is used. The proposed algorithm is illustrated on normal linear and logistic regression models, for simulated and real-life examples, and it is shown that, with a very low computational cost, it achieves improved performance when compared with popular MCMC algorithms, such as the MCMC model composition, as well as with “vanilla” versions of simulated annealing, genetic algorithm and tabu search.

A local search method for continuous global optimization

A large number of algorithms introduced in the literature to find the global minimum of a real function rely on iterative executions of searches of a local minimum. Multistart, tunneling and some versions of simulated annealing are methods that produce well-known procedures. A crucial point of these algorithms is to decide whether to perform or not a new local search. In this paper we look for the optimal probability value to be set at each iteration so that by moving from a local minimum to a new one, the average number of function evaluations evals is minimal. We find that this probability has to be 0 or 1 depending on the number of function evaluations required by the local search and by the size of the level set at the current point. An implementation based on the above result is introduced. The values required to calculate evals are estimated from the history of the algorithm at running time. The algorithm has been tested both for sample problems constructed by the GKLS package and for problems often used in the literature. The outcome is compared with recent results.

Coupled Simulated Annealing

We present a new class of methods for the global optimization of continuous variables based on simulated annealing (SA). The coupled SA (CSA) class is characterized by a set of parallel SA processes coupled by their acceptance probabilities. The coupling is performed by a term in the acceptance probability function, which is a function of the energies of the current states of all SA processes. A particular CSA instance method is distinguished by the form of its coupling term and acceptance probability. In this paper, we present three CSA instance methods and compare them with the uncoupled case, i.e., multistart SA. The primary objective of the coupling in CSA is to create cooperative behavior via information exchange. This aim helps in the decision of whether uphill moves will be accepted. In addition, coupling can provide information that can be used online to steer the overall optimization process toward the global optimum. We present an example where we use the acceptance temperature to control the variance of the acceptance probabilities with a simple control scheme. This approach leads to much better optimization efficiency, because it reduces the sensitivity of the algorithm to initialization parameters while guiding the optimization process to quasioptimal runs. We present the results of extensive experiments and show that the addition of the coupling and the variance control leads to considerable improvements with respect to the uncoupled case and a more recently proposed distributed version of SA.

Comparing Stochastic Optimization Methods for Variable Selection in Binary Outcome Prediction, With Application to Health Policy

Traditional variable-selection strategies in generalized linear models (GLMs) seek to optimize a measure of predictive accuracy without regard for the cost of data collection. When the purpose of such model building is the creation of predictive scales to be used in future studies with constrained budgets, the standard approach may not be optimal. We propose a Bayesian decision-theoretic framework for variable selection in binary-outcome GLMs where the budget for data collection is constrained and potential predictors may vary considerably in cost. The method is illustrated using data from a large study of quality of hospital care in the U.S. in the 1980s. Especially when the number of available predictors p is large, it is important to use an appropriate technique for optimization (e.g., in an application presented here where p = 83, the space over which we search has 283 ≐ 1025 elements, which is too large to explore using brute force enumeration). Specifically, we investigate simulated annealing (SA), genetic algorithms (GAs), and the tabu search (TS) method used in operations research, and we develop a context-specific version of SA, improved simulated annealing (ISA), that performs better than its generic counterpart. When p was modest in our study, we found that GAs performed relatively poorly for all but the very best user-defined input configurations, generic SA did not perform well, and TS had excellent median performance and was much less sensitive to suboptimal choice of user-defined inputs. When p was large in our study, the best versions of GA and ISA outperformed TS and generic SA. Our results are presented in the context of health policy but can apply to other quality assessment settings with dichotomous outcomes as well.

Self-interacting diffusions: a simulated annealing version

We study asymptotic properties of processes X, living in a Riemannian compact manifold M, solution of the stochastic differential equation (SDE) $$dX_t = dW_t(X_t) - \beta(t)\nabla V\mu_t(X_t)dt$$ with W a Brownian vector field, β(t) = alog(t + 1), \(\mu_t = \frac{1}{t} \int_0^t \delta_{X_s}ds\) and \(V\mu_t(x) = \frac{1}{t}\int_0^t V(x, X_s)ds\), V being a smooth function. We show that the asymptotic behavior of μ t can be described by a non-autonomous differential equation. This class of processes extends simulated annealing processes for which V(x, y) is only a function of x. In particular we study the case \(M = {\mathbb{S}}^n\) , the n-dimensional sphere, and V(x, y) = −cos(d(x, y)), where d(x, y) is the distance on \({\mathbb{S}}^n\) , which corresponds to a process attracted by its past trajectory. In this case, it is proved that μ t converges almost surely towards a Dirac measure.

How to Maximize the Likelihood Function for a DSGE Model

This paper extends two optimization routines to deal with objective functions for DSGE models. The optimization routines are i) a version of Simulated Annealing developed by Corana, Marchesi & Ridella (1987), and ii) the evolutionary algorithm CMA-ES developed by Hansen, Muller & Koumoutsakos (2003). Following these extensions, we examine the ability of the two routines to maximize the likelihood function for a sequence of test economies. Our results show that the CMA-ES routine clearly outperforms Simulated Annealing in its ability to find the global optimum and in efficiency. With 10 unknown structural parameters in the likelihood function, the CMA-ES routine finds the global optimum in 95% of our test economies compared to 89% for Simulated Annealing. When the number of unknown structural parameters in the likelihood function increases to 20 and 35, then the CMA-ES routine finds the global optimum in 85% and 71% of our test economies, respectively. The corresponding numbers for Simulated Annealing are 70% and 0%.

An integrated Lagrangean relaxation-simulated annealing approach to the multi-level multi-item capacitated lot sizing problem

This study proposes a heuristic approach for the solution of the dynamic multi-level multi-item capacitated lot sizing problem (MLCLSP) with general product structures. The difficulty in solving MLCLSP is to provide capacity-feasible lot-sizes while maintaining the non-negativity of the inventories belonging to the items in the lower levels of the product structures. The proposed technique aims to resolve this issue by combining the capability of the Lagrangean relaxation to decompose the hard-to-solve problems into smaller subproblems and the intensive search capability of the simulated annealing. As the first attempt, two Lagrangean relaxation schemes are designed and different versions of simulated annealing are incorporated into relaxation designs as the Lagrangean heuristic. Then in order to improve the performance of the heuristic, a Phase-1 procedure is developed as a recursive algorithm to restore capacity feasibility. It is observed that the best results are obtained by executing first Phase-1 procedure and then simulated annealing approach with only improving moves in each Lagrangean cycle. The performance of these approaches is compared by using the benchmark problems available in literature.

A Feedback Algorithm for Determining Search Parameters for Monte Carlo Optimization

Monte Carlo methods have become popular for obtaining solutions to global optimization problems. One such Monte Carlo optimization technique is simulated annealing (SA). Typically in SA the parameters of the search are determineda priori. Using an aggregated, orlumped, version of SA's associated Markov chain and the concept of expected hitting time, we adjust the search parameters dynamically using information gained from the SA search process. We present an algorithm that varies the SA search parameters dynamically, and show that, on average, dynamic adjustment of the parameters attains better solutions on a set of test problems than those attained with a logarithmic cooling schedule.

Simulated annealing for order spread minimization in sequencing cutting patterns

The Order Spread Minimization Problem (OSMP) is a sequencing problem that arises in the process of planning industrial cutting operations. As it can be looked upon as a generalization of the Travelling-Salesman Problem (TSP), it has to be classified as NP-complete. Thus heuristic algorithms are required in order to solve large problem instances. In this paper the authors suggest to apply Simulated Annealing (SA) to the OSMP. A specific version of SA is developed and compared to both an approach previously introduced into the literature by Madsen and a traditional 3-opt-procedure. The performance of these methods is compared on a set of 2400 randomly generated problem instances. SA appears to provide solutions which - in terms of solution quality - are equivalent to those generated by the 3-opt-procedure. However, computing times of the latter for solving large instances are prohibitive. In relation to Madsen's approach SA provides significantly improved solutions at the expense of a moderate increase in computing times.

DYNAMIC FINITE ELEMENT MODEL UPDATING USING SIMULATED ANNEALING AND GENETIC ALGORITHMS

Dynamic finite element (FE) model updating may be considered as an optimisation process. Over the past few years, two powerful new optimisation algorithms have been developed independently of each other; namely, the genetic algorithm (GA) and simulated annealing (SA). These algorithms are both probabilistic search algorithms capable of finding the global minimum amongst many local minima. This paper compares various implementations of the two algorithms for model updating purposes. A new variant of simulated annealing is suggested and is found to be the most effective of all the optimisation algorithms considered. This version of simulated annealing is then tested using several objective functions for simulated model updating in the frequency domain. In the second part of this paper, both SA and GAs are applied to a practical FE model updating problem using measured data. The new variation of the SA algorithm, termed the blended SA algorithm, performed better than the traditional GA algorithm. However, the results obtained show a significant dependence on the choice of updating parameters. It was concluded that model updating using these optimisation algorithms is a promising and viable approach, but the appropriate choice of updating parameters is of paramount importance.