A modification of the simulated annealing algorithm for discrete stochastic optimization

This paper develops a variant of simulated annealing (SA) algorithm for solving discrete stochastic optimization problems where the objective function is stochastic and can be evaluated only through Monte Carlo simulations. In the proposed variant of SA, the Metropolis criterion depends on whether the objective function values indicate statistically significant difference at each iteration. The differences between objective function values are considered to be statistically significant based on confidence intervals associated with these values. Unlike the original SA, our method uses a constant temperature. We show that the configuration that has been visited most often in the first m iterations converges almost surely to a global optimizer.

We present a modification of the simulated annealing algorithm designed for solving discrete stochastic optimization problems. Like the original simulated annealing algorithm, our method has the hi...

A combined strategy of an improved simulated annealing (SA) algorithm and genetic algorithm is presented, with the goal of reducing the computational expenses. The improvements made on the SA algorithm include two parts, i.e., the adaptive regulating for the step vector, and the dynamic testing for the equilibrium of the Metropolis process. The proposed strategy has both the advantage of SA algorithm, the ability to avoid being trapped in a local optimum, and that of genetic algorithm, the ability to use the information about the searched states for the next iteration. A practical application on geometry optimization of pole shoes in large salient pole synchronous generators is effectively implemented using the strategy. The numerical results show that the number of iterations used by executing the combined strategy are only about 75% of those by executing basic SA algorithm.

Simulated annealing for discrete optimization with estimation

Summary The Simulated Annealing (SA) algorithm has been widely used in geophysical data processing. However, the seri al SA algorithm is limited by low computing efficiency. In this paper, the annealing schedule has been improved in the SA algorithm, and a constrained inversion of magnetotelluric (MT) data using the parallel SA algorithm has been applied. The test of synthetic data shows that the improved Very Fast Simulated Annealing (VFSA) method is significantly better than the traditional method. Additionally, the computing efficiency has been improved using the parallel SA inversion algorithm. This method has also been applied in MT data processing for geothermal exploration and good geological results have been achieved.

SUMMARY Many interesting inverse problems in geophysics are non-linear and multimodal. Parametrization of these problems leads to an objective function, or measure of agreement between data and model predictions, that has a complex topography with many local minima. Optimization algorithms that rely on local gradients in the objective function or that search the model space locally may become trapped in these local minima. By combining simulated annealing with the downhill simplex method, a hybrid global search algorithm is presented in this paper for non-linear, multimodal, inverse problems. The hybrid algorithm shares the advantages of both local search methods that perform well if the local model is suitable, and global methods that are able to explore efficiently the full model space. The hybrid algorithm also utilizes a larger and more complex memory to store information on the objective function than simulated annealing algorithms. The effectiveness of this new scheme is evaluated in three problems: minimization of the multidimensional Rosenbrock function, non-linear, 1 -D, acoustic waveform inversion, and residual statics. The performance of the hybrid algorithm is compared with simulated annealing and genetic algorithms and is shown to converge more rapidly and to have a higher success rate of locating the global minimum for the cases investigated.

This paper addressed the modeling and optimization of loading path in T‐shape hydroforming of tubes using Simulated Annealing (SA) algorithm. Analysis of variance shows that some of pre‐selected parameters in loading paths have not significant effect on the deformed tube. Hence, some of optimized parameters found initially, are replaced with their own fixed optimum values in order to seek for the other parameters in more detail by the Simulated Annealing (SA) algorithm. According to the intensity of effectiveness on the deformation, six more important parameters are chosen and their minimum and maximum limitation values are determined. In this case, sixty four different tests for different loading paths are designed by Design of Experiment (DOE) and full factorial method. By using mathematical modeling all required loading parameters are obtained. Proposed models of formability embedded into Simulated Annealing algorithm and optimum value for loading parameters and optimal load paths are found. The obtained results show that more accurate loading path may be found for T‐shape of tube hydroforming.

A hybrid imperialist competitive-simulated annealing algorithm for a multisource multi-product location-routing-inventory problem

This paper presents the solving unit commitment (UC) problem using Modified Subgradient Method (MSG) method combined with Simulated Annealing (SA) algorithm. UC problem is one of the important power system engineering hard-solving problems. The Lagrangian relaxation (LR) based methods are commonly used to solve the UC problem. The main disadvantage of this group of methods is the difference between the dual and the primal solution which gives some significant problems on the quality of the feasible solution. In this paper, MSG method which does not require any convexity and differentiability assumptions is used for solving the UC problem. MSG method depending on the initial value reaches zero duality gap. SA algorithm is used in order to assign the appropriate initial value for MSG method. The major advantage of the proposed approach is that it guarantees the zero duality gap independently from the size of the problem. In order to show the advantages of this proposed approach, the four-unit Tuncbilek thermal plant and ten-unit thermal plant which is usually used in literature are chosen as test systems. Penalty function (PF) method is also used to compare with our proposed method in terms of total cost and UC schedule.

Simulation-based optimization using simulated annealing with ranking and selection

We discuss the choice of the estimation of the optimal solution when random search methods are applied to solve discrete stochastic optimization problems. At the present time, such optimization methods usually estimate the optimal solution using either the feasible solution the method is currently exploring or the feasible solution visited most often so far by the method. We propose using all the observed objective function values generated as the random search method moves around the feasible region seeking an optimal solution to obtain increasingly more precise estimates of the objective function values at the different points in the feasible region. At any given time, the feasible solution that has the best estimated objective function value (largest one for maximization problems; the smallest one for minimization problems) is used as the estimate of the optimal solution. We discuss the advantages of using this approach for estimating the optimal solution and present numerical results showing that modifying an existing random search method to use tnhis approach for estimating the optimal soluation appears to yield improved performance. We also present sereval rate of convergence results for random search methods using our approach for estimating the optimal solution. One these random search methods is a new variant of the stochastic comparison method; in addition to specifying the rate of convergence of this method, we prove that it is guaranteed to converge almost surely to the set of global optimal solutions and present a result that demonstrates that this method is likely to perform well in practice.

For the congestion problems in asynchronous transfer mode (ATM) networks, a hybrid intelligent controller based on simulated annealing (SA) and reinforcement learning (RL) algorithm is proposed. The SA algorithm is a powerful way to solve hard combinatorial optimization problems, which is used to adjust the parameters of the controller. The RL algorithm shows the particular superiority in ATM networks, which is independent of the mathematic model and just needs simple fuzzy information obtained through trial-and-error and interaction with the environment. With the advantages of the two algorithms, the proposed controller forces the queue size in the multiplexer buffer to the desired value by adjusting the source transmission rate of the available bit rate (ABR) service. Simulation results show that the proposed method can promote the performance of the networks and avoid the occurrence of congestion effectively.

Voltage stability constrained reactive power planning (RPP) or VAr planning is a very challenging issue in power systems. This paper proposes a new approach for modeling and solving VAr planning problem taking into account the static voltage stability constraint. First, the fuzzy clustering method is employed to select new candidate VAr source locations. Then, modified Gray code is proposed and used to represent a series of non-uniform VAr capacity intervals at different candidate buses. Under the new ordering of the VAr capacity intervals, a simplified piecewise linear function between the total transfer capability (TTC) and new VAr capacity is derived and applied as static voltage stability constraint in RPP. Finally, the RPP optimization model is solved by an enhanced simulated annealing (SA) algorithm taking advantage of the modified Gray code. In the SA algorithm, a modified definition of the neighborhood selection and a novel approach to generate new random solutions are proposed. In the case study, fuzzy clustering method, the modified Gray code, and the improved SA are applied to the IEEE 30-bus system. Test results conclude that the proposed method is a simplified and effective approach for voltage stability constrained VAr planning with contingency considered.

In this paper, simulated annealing (SA) algorithm is employed to solve the flowshop scheduling problem with the objective of minimising the completion time variance (CTV) of jobs. Four variants of the two-phase SA algorithm (SA-I to SA-IV) are proposed to solve flowshop scheduling problem with the objective of minimising the CTV of jobs without considering the right shifting of completion time of jobs on the last machine. The proposed SA algorithms have been tested on 90 benchmark flowshop scheduling problems. The solutions yielded by the proposed SA variants are compared with the best CTV of jobs reported in the literature, and the proposed SA-III is found to perform well in minimising the chosen performance measure (CTV) particularly in medium and large size problems.

As demonstrated in Chap. 3, different evolutionary algorithms, including genetic algorithm (GA), simulated annealing (SA) algorithm, hybrid GASA algorithm, particle swarm optimization (PSO) algorithm, continuous ant colony optimization (CACO) algorithm, artificial bee colony (ABC) algorithm, and immune algorithm (IA), are employed to determine suitable for parameter combination of an SVR-based electric load forecasting model. These forecasting results indicate that almost all SVR-based models with different evolutionary algorithms are superior to other competitive forecasting models (including ARIMA, HW, GRNN, and BPNN models); however, these algorithms almost lack knowledge memory or storage mechanisms which would be neither time-consuming nor inefficient in searching the suitable parameters, that is, premature convergence (being trapped in local optimum). For example, for SVRGA model, in GA processing, new individuals are generated by the following operators, selection, crossover, and mutation. For all types of objective functions, the generation begins with a binary coding for the parameter set. Based on this special binary coding process, GA is able to solve some specified problems which are not easily to be solved by traditional algorithms. GA can empirically provide a few best fitted offsprings from the whole population; however, after some generations, due to low diversity of the population, it might lead to a premature convergence [1]. For SVRSA model, SA algorithm is a generic probabilistic search technique that simulates the material physical process of heating and controlled cooling. Each step of SA attempts to replace the current state by a random move. The new state may then be accepted with a probability that depends both on the difference between the corresponding function values and also on a global parameter, temperature. Thus, SA has some institution to reach more ideal solutions. However, SA algorithm requires the subtle and skillful adjustment in the annealing schedule; therefore, the settings of the size of the temperature steps during annealing, the temperature range, the number of restarts, and the redirection of the search will be taken into account carefully [1]; in addition, its Monte Carlo scheme and lack of knowledge memory mechanism will also lead to time-consuming and inefficient searching in annealing process.