Simulated Annealing Parameters Research Articles

Two metaheuristics for solving the reliability redundancy allocation problem to maximize mean time to failure of a series–parallel system

The redundancy allocation problem is one of the main branches of reliability optimization problems. Traditionally, the redundancy allocation model has focused mainly on maximizing system reliability at a predetermined time. Hence, in this study, we develop a more realistic model, such that the mean time to failure of a system is maximized. To overcome the structural complexity of the model, the Monte Carlo simulation method is applied. Two metaheuristics, Simulated Annealing (SA) and Genetic Algorithm (GA), are proposed to solve the problem. In addition, the design of experiments and response surface methodology are employed for tuning the GA and SA parameters. The metaheuristics are compared, based on their computation time and accuracy, in 30 test problems. Finally, the results are analyzed and discussed, and some conclusions are drawn.

Sensitivity of forest plan value to parameters of simulated annealing

Simulated annealing (SA) is a heuristic technique popular in forest planning, providing solutions close to optimality in reduced computation time. The present study challenges the common approach used to establish the parameters of SA that mimic physical processes by proving that slow cooling or large initial temperatures do not necessarily lead to optimal solutions. The study has two objectives: (1) to identify the parameters (i.e., initial temperature and annealing rate) that could supply close to optimal results with reduced experimentation time and (2) to assess the impact of parameters determining SA performances. Using three forest inventory data sets from British Columbia, we investigated the influence of initial temperature, annealing rate, and numbers of runs on forest planning solutions using a replicated completely randomized design organized as a factorial experiment within a repeated-measures framework. The optimal solution seems to be little influenced by the number of runs; our findings indicate that the combination of initial temperature and rate of annealing is critical in obtaining superior results. Furthermore, the selection of the SA parameters seems to be dependent on the harvest age, which indicates that the parameters should be selected considering whether or not a stand is harvested more than once during the planning period.

Simulated annealing for controlled-source audio-frequency magnetotelluric data inversion

Simulated annealing (SA) is used to invert 1D controlled source audio-frequency magnetotelluric (CSAMT) data. In the annealing process, the system energy is taken as the root-mean-square fitting error between model responses and real data. The model parameters are the natural logarithms of the resistivity and the thickness in each layer of the earth. The annealing temperature decreases exponentially, while the model is refreshed randomly according to the temperature and is accepted according to a Boltzmann probability. We first tested the SA on synthetic data and developed a cooling schedule of model updates specifically for CSAMT data inversion. The redesigned cooling schedule reduces the magnitude of the model updating, and makes the solution converge rapidly and stably. For a three-layer model whose resistivity increases with depth, SA has difficulty in obtaining the global solution for the middle layer. However, the solution for such a layer can be significantly improved by using the mean value of the estimates. The inversion of field data from a northern suburb of Beijing, China, demonstrates that starting from a 1D smooth inversion to determine the range of SA parameters permits the SA to obtain very good results from the CSAMT survey data.

Simultaneous solving of balancing and sequencing problems with station-dependent assembly times for mixed-model assembly lines

In spite of many studies, investigating balancing and sequencing problems in Mixed-Model Assembly Line (MMAL) individually, this paper solves them simultaneously aiming to minimize total utility work. A new Mixed-Integer Linear Programming (MILP) model is developed to provide the exact solution of the problem with station-dependent assembly times. Because of NP-hardness, a Simulated Annealing (SA) is applied and compared to the Co-evolutionary Genetic Algorithm (Co-GA) from the literature. To strengthen the search process, two main hypotheses, namely simultaneous search and feasible search, are developed contrasting Co-GA. Various parameters of SA are reviewed to calibrate the algorithm by means of Taguchi design of experiments. Numerical results statistically show the efficiency and effectiveness of the proposed SA in terms of both the quality of solution and the time of achieving the best solution. Finally, the contribution of each hypothesis in this superiority is analyzed.

Adjustment of the primitive parameters of the simulated annealing heuristic

In this paper, the best setting for primitive parameters of simulated annealing fitted on traveling salesman problem is selected by using the design of experiment, response surface methodology and goal programming. There are 6 parameters in that 3 of them are tuned on two-up and down- levels. The three others are tuned on multi levels. A factorial plan 2 3 with 4 central points is used for two-level parameters. Multilevel parameters are tuned by design of experiment. At the end a goal programming model is used to select the best parameters.

Methodologies for optimizing ROP detector layout for CANDU® reactors

The regional overpower protection (ROP) systems protect CANDU® reactors against overpower in the fuel that would reduce the safety margin-to-dryout. Both a localized power peaking within the core (for example, as a result of certain reactivity device configuration) or a general increase in the core power level during a slow-loss-of-regulation (SLOR) event could cause overpower in the fuel. This overpower could lead to fuel sheath dryout. In the CANDU® 600 MW (CANDU 6) design, there are two ROP systems in the core, one for each fast-acting shutdown systems. Each ROP system includes a number of fast-responding, self-powered flux detectors suitably distributed throughout the core within vertical and horizontal assemblies. Traditionally, the placement of these detectors was done using a method called the detector layout optimization (DLO). A new methodology for designing the detector layout for the ROP system has been developed recently. The new method, called the DETPLASA algorithm, utilizes the simulated annealing (SA) technique to optimize the placement of the detectors in the core. Both methodologies will be discussed in detail in this paper. Numerical examples are employed to better illustrate how each method works. Results from some sensitivity studies on three SA parameters are also presented.

Parallel Simulated Annealing with Genetic Enhancement for flowshop problem with Csum

In this paper, parallelisable Simulated Annealing with Genetic Enhancement (SAwGE) algorithm is presented and applied to Permutation Flowshop Scheduling Problem with total flowtime criterion. This problem is proved to be NP -complete in a strong sense for more than one machine. SAwGE is based on a Clustering Algorithm for Simulated Annealing (SA), but introduces a new mechanism for dynamic SA parameters adjustment, based on genetic algorithms. Computational experiments, based on 120 benchmark datasets by Taillard, show that SAwGE outperforms other heuristics and metaheuristics presented recently in literature. Moreover SAwGE obtains 118 best solutions, including 81 newly discovered ones.

Tune-Up Friendly Fast Simulated Annealer for VLSI Analog Module Placement

As an efficient stochastic optimization methodology, simulated annealing (SA) is widely used in the area of very large-scale integration (VLSI) electronic design automation. However, a lot of effort is normally required to tune up SA parameters when being used for distinct applications. In this paper we propose an easy tune-up very fast simulated re-annealing algorithm to solve the problem of analog module placement. Compared to the classical Boltzmann or Cauchy annealing schemes, our method can converge to the global minimum statistically exponentially faster. Moreover, we deploy a re-annealing process to conduct adaptive control on the cooling schedules. Thus, the algorithm tune-up for the analog module placement problem is significantly relieved. Besides the theoretical analysis, our experiments show the proposed algorithm is superior over the other SA derivatives and is able to generate high-quality placement results with significantly less central processing unit (CPU) time.

Fast direct Monte Carlo optimization using the inverse kernel approach

The loss of treatment plan quality after segmentation following fluence optimization is a problem in IMRT. In a previous publication we showed that re-optimization helps to re-establish part of the plan quality. Recently the so-called direct aperture optimization method has been introduced to successfully overcome that difficulty. The aim of the present paper is to present in detail the integration of the inverse kernel method into direct aperture optimization. It can be shown that this integration leads to a system with high performance with regard to time, while Monte Carlo precision is maintained. The integrated simulated annealing optimization algorithm allows easy adaptation to any multi-leaf collimator and it is open to any complex objective function. Investigations of simulated annealing control parameters are performed to improve the performance. The system denoted by direct Monte Carlo optimization (DMCO) is demonstrated on the Carpet phantom and a clinical prostate case as well. Results are compared to inverse kernel optimizations, showing a remarkable time reduction and simultaneously an improvement in plan quality for the Carpet phantom.

Sequential Triangle Strip Generator Based on Hopfield Networks

The important task of generating the minimum number of sequential triangle strips (tristrips) for a given triangulated surface model is motivated by applications in computer graphics. This hard combinatorial optimization problem is reduced to the minimum energy problem in Hopfield nets by a linear-size construction. In particular, the classes of equivalent optimal stripifications are mapped one to one to the minimum energy states reached by a Hopfield network during sequential computation starting at the zero initial state. Thus, the underlying Hopfield network powered by simulated annealing (i.e., Boltzmann machine), which is implemented in the program HTGEN, can be used for computing the semioptimal stripifications. Practical experiments confirm that one can obtain much better results using HTGEN than by a leading conventional stripification program FTSG (a reference stripification method not based on neural nets), although the running time of simulated annealing grows rapidly near the global optimum. Nevertheless, HTGEN exhibits empirical linear time complexity when the parameters of simulated annealing (i.e., the initial temperature and the stopping criterion) are fixed and thus provides the semioptimal offline solutions, even for huge models of hundreds of thousands of triangles, within a reasonable time.

An Automated Meta-Level Control Framework for Optimizing the Quality–Time Tradeoff of VLSI Algorithms

We address the problem of optimizing the quality-time tradeoff of very large scale integration (VLSI) computer-aided design (CAD) algorithms working under various constrained environments. We present a unified meta-reasoning framework to automatically control the progress of iteratively improving CAD algorithms. The control framework uses profile knowledge about the quality-time relation of the algorithms used and generates a combined strategy for time allocation and parameter control that optimizes the expected tradeoff. We present specific formulations for handling single and multiple problems (both dependent and independent) under various constraints. We use the proposed strategies for adjusting the control parameters of standard simulated annealing and genetic algorithm based techniques used in VLSI optimization along with an appropriate time allocation suited for different constraint specifications. Application on several classical problems in the VLSI domain shows that significant improvement in quality-time tradeoff can be achieved.

A computer method based on simulated annealing to identify aquifer parameters using pumping‐test data

AbstractConventional graphical or computer methods for identifying aquifer parameters have their own inevitable limitations. This paper proposes a computer method based on a drawdown model and a heuristic approach of simulated annealing (SA) to determine the best‐fit aquifer parameters of the confined and unconfined aquifer systems. The drawdown model for the confined aquifer is the Theis solution and the unconfined aquifer is the Neuman solution. The estimated results of proposed method have better accuracy than those of the graphical methods and agree well with those of the computer methods based on the extended Kalman filter and Newton's method. Finally, the sensitivity analyses for the control parameters of SA indicate that the proposed method is very robust and stable in parameter identification procedures. Copyright © 2007 John Wiley & Sons, Ltd.

A two-stage simulated annealing procedure for block layout problems

Rules for setting simulated annealing control parameters are proposed for block layout problems where different material-handling devices are dynamically assigned to individual material movements as layout solutions are perturbed. Recognizing the high cost of computing materials-handling cost in this type of problem, the rules are based on adapting an existing two-stage simulated annealing procedure to accelerate convergence. Experimental results suggest that the application of these rules yields solution quality comparable with other single and two-stage simulated annealing algorithms but with significantly fewer re-evaluations of the objective function.

Simulated annealing applied to test generation: landscape characterization and stopping criteria

This paper investigates a measurement approach to support the implementation of Simulated Annealing (SA) applied to test generation. SA, like other metaheuristics, is a generic technique that must be tuned to the testing problem under consideration. Finding an adequate setting of SA parameters, that will offer good performance for the target problem, is known to be difficult. Our measurement approach is intended to guide the implementation choices to be made. It builds upon advanced research on how to characterize search problems and the dynamics of metaheuristic techniques applied to them. Central to this research is the concept of landscape. Existing measures of landscape have mainly been applied to combinatorial problems considered in complexity theory. We show that some of these measures can be useful for testing problems as well. The diameter and autocorrelation are retained to study the adequacy of alternative settings of SA parameters. A new measure, the Generation Rate of Better Solutions (GRBS), is introduced to monitor convergence of the search process and implement stopping criteria. The measurement approach is experimented on various case studies, and allows us to successfully revisit a problem issued from our previous work on testing control systems.

Hybrid genetic algorithm and simulated annealing for two-dimensional non-guillotine rectangular packing problems

In this paper, genetic algorithm (GA) and simulated annealing (SA) with improved bottom left (BL) algorithm were applied to two-dimensional non-guillotine rectangular packing problems. The performance and efficiency of these algorithms on several test problems [Hopper, E., Turton, B.C.H., 2000. An empirical investigation of meta-heuristic and heuristic algorithms for two-dimensional packing problem. European Journal of Operational Research 128 (1), 34–57] were compared. These test problems consist of 17 and 29 individual rectangular pieces to place in main object limited with a size of 200×200 units. Both solution approaches were compared, based on the trim losses of the test problems. Also, the influences of the GA parameters (population sizes, mutation rates, crossover techniques) and of the SA parameters (cooling schedules, neighborhood moves, the number of inner loop, different temperature values) on the solution of these problems were examined. For considering all solutions of the test problems, the hybrid GA produces much better results than the hybrid SA.

A theoretical study on the behavior of simulated annealing leading to a new cooling schedule

This paper presents an empirical study on the efficiency of the simulated annealing (SA) algorithm. It considers various parameters such as landscape and neighborhood. The need for a better understanding of SA, with the additional goal of implementing the algorithm efficiently, motivated this study. The method selected to conduct that study was to carry out experiments to obtain practical data, which could be utilized to carry out a theoretical study simultaneously. Experiments on such a stochastic algorithm as SA were initiated following the observation that it is possible to calculate the exact probability for SA to reach any point in the landscape, provided that the number of solutions and the number of neighbors per solution are small enough. An efficient development of a SA simulator has enabled us to study the influence of the tuning of all the main parameters of SA as well as theoretical concepts such as thermodynamic equilibrium and optimal temperature decrement rules. Interesting results have been obtained in the field of adaptive cooling schedules that enable us to demonstrate that the classical cooling schedules are all equivalent. Finally a new schedule has been proposed that exhibits some useful properties. The proposed cooling schedule has been successfully implemented in the SA algorithm to solve the well known traveling salesman problem.

A part-and-tool assignment method for the workload-balance between machines and the minimisation of tool-shortage occurrences in an FMS

In this paper, we look into the loading problem of a flexible manufacturing system (FMS) that is made up of several identical flexible manufacturing machines (CMMs). These machines are capable of different operations as long as the required tools are provided to them. The loading problem studied in this paper is a pre-release problem that deals with the pre-assignment of parts and tools before the process of an FMS begins. There are two objectives that one would like to achieve. They include minimising the number of tool-shortage occurrences and balancing the workload between machines. Since one cannot directly minimise the number of tool-shortage occurrences at the current pre-release stage, a surrogate objective of minimising the total tool-capacity shortage (TTCS) is adopted. Furthermore, because of the ‘tool movement policy’ assumption, our loading problem only involves assigning parts and tools to each machine. In this paper, we propose a part-and-tool assignment method that combines fuzzy c-means, SA (simulated annealing), and an optimal tool-assignment algorithm. The proposed part-and-tool assignment method is designed to be interactive. Because of this interactive nature, human designers can experiment with different evaluation criteria or reset the parameters of SA to look for alternative solutions. An example is given which illustrates the proposed part-and-tool assignment method. From the example, one can see that the proposed method is very efficient and effective in finding good-quality solutions.

Dynamic optimization with simulated annealing

In this paper we present an approach for the dynamic optimization of energy and chemical engineering processes with the simulated annealing (SA) algorithm. The aim of this work is to develop an optimization methodology which finds optimal control strategies requiring a minimum of user input. The methodology we propose uses rigorous dynamic Simulink models based on first principles in a black-box approach. If any, only slight modifications have to be done for existing Simulink models to be able to be optimized. The presented approach based on the SA algorithm has the potential to find the global optimum and it does not need any additional information than the dynamic model itself. Both control profiles and time-invariant parameters, such as PI control parameters can be optimized simultaneously. The simulated annealing algorithm is implemented in a set of MATLAB script files together with a graphical user interface (GUI) as an independent module of the OptControlCentre (OCC). All parameters of the simulated annealing algorithm and of the model can be specified in the GUI as well as the course of the optimization itself is made visible at runtime. The proposed methodology is tested on a set of example problems and the influence of several simulated annealing parameters on the optimization is shown.

Metaheurística Simulated Annealing para solução de problemas de planejamento florestal com restrições de integridade

Os objetivos deste trabalho foram desenvolver e testar a metaheurística SA para solução de problemas de gerenciamento florestal com restrições de integridade. O algoritmo SA desenvolvido foi testado em quatro problemas, contendo entre 93 e 423 variáveis de decisão, sujeitos às restrições de singularidade, produção mínima e produção máxima, periodicamente. Todos os problemas tiveram como objetivo a maximização do valor presente líquido. O algoritmo SA foi codificado em liguagem delphi 5.0 e os testes foram efetuados em um microcomputador AMD K6II 500 MHZ, com memória RAM de 64 MB e disco rígido de 15GB. O desempenho da SA foi avaliado de acordo com as medidas de eficácia e eficiência. Os diferentes valores ou categorias dos parâmetros da SA foram testados e comparados quanto aos seus efeitos na eficácia do algoritmo. A seleção da melhor configuração de parâmetros foi feita com o teste L&O, a 1% de probabilidade, e as análises foram realizadas através de estatísticas descritivas. A melhor configuração de parâmetros propiciou à SA eficácia média de 95,36%, valor mínimo de 83,66%, valor máximo de 100% e coeficiente de variação igual a 3,18% do ótimo matemático obtido pelo algoritmo exato branch and bound. Para o problema de maior porte, a eficiência da SA foi dez vezes superior à eficiência do algoritmo exato branch and bound. O bom desempenho desta heurística reforçou as conclusões, tiradas em outros trabalhos, do seu enorme potencial para resolver importantes problemas de gerenciamento florestal de difícil solução pelos instrumentos computacionais da atualidade.

SW—Soil and Water: Application of the Simulated Annealing Method to Agricultural Water Resource Management

This work presents a model based on the on-farm irrigation scheduling and the simulated annealing (SA) optimization method for agricultural water resource management. The proposed model is applied to an irrigation project located in Delta, Utah of 394·6 ha area for optimizing economic profits, simulating the water demand and crop yields and estimating the related crop area percentages with specified water supply and planted area constraints.The application of SA to irrigated project planning in this study can be divided into nine steps: (1) to receive the output from the on-farm irrigation scheduling module; (2) to enter three simulated annealing parameters; (3) to define the design ‘chromosome’ representing the problem; (4) to generate the random initial design ‘chromosome’; (5) to decode the design ‘chromosome’ into a real number; (6) to apply constraints; (7) to apply an objective function and a fitness value; (8) to implement the annealing schedule by the Boltzmann probability; and (9) to set the ‘cooling rate’ and criterion for termination.The irrigation water requirements from the on-farm irrigation scheduling module are: (1) 1067·9, 441·7, and 471·8 mm for alfalfa, barley and maize, respectively, in one unit command area; and (2) 1039·5, 531·4, 490·9, and 539·4 mm for alfalfa, barley, maize and wheat, respectively, in the other unit command area. The simulation results demonstrate that the most appropriate parameters of SA for this study are as follows: (1) initial simulation ‘temperature’ of 1000; (2) number of moves equal to 90; and (3) ‘cooling rate’ of 0·95.