Continuous Simulated Annealing Research Articles

Fuzzy c-means and simulated annealing for planar location-routing problem

Location-routing problem (LRP) contains two Np-hard problems as, facility location (FL) and vehicle routing problem (VRP), in the same content. Since both problems directly affect the cost of distributions of the products and supply chain, the decision of location and routing is important for the success of companies. Therefore, many attempts are made to solve LRP problem in the literature. Researchers proposed exact and heuristic methods for LRP. However, exact methods cannot provide solutions for considerably large instances. In this paper, a new heuristic method is proposed for continuous or planar LRP. The proposed method contains fuzzy c-means for continuous location problem and simulated annealing algorithm for vehicle routing problem, respectively. The proposed method is applied to both capacitated and uncapacitated LRP instances that are widely used in the literature. Results of the proposed method are compared with successful researches that are made on this problem in terms of the total cost.

A committee machine with intelligent experts (CMIE) for estimation of fast and slow shear wave velocities utilizing petrophysical logs

Petrophysical properties determination of a reservoir such as shear wave velocity plays a crucial role in exploration and production management. The purpose of this study is to develop a robust committee machine model for estimating fast and slow shear wave velocities from petrophysical logs. To this end, appropriate inputs were determined and different algorithms including artificial neural network, fuzzy logic and neuro-fuzzy were applied. Afterward, the obtained outputs were merged by utilizing optimization methods consisting of Ant Colony Optimization for Continuous Domain, Genetic and Simulated Annealing approaches. The construction of the committee machine was done using a case study including 2000 data samples from the Sarvak Formation in one of the southwestern Iran oilfields. The utilized dataset was divided into training and testing data which contain 1600 and 400 samples, respectively. Mean Squared Error was presented as a determinative factor for evaluating system performance. To obtain the best system performance with the lowest Mean Squared Error, the parameters setting of each algorithm were coded in different ranges. A total 52416, 76896 and 29400 cases were run to optimize the parameter settings of genetic algorithms, simulated annealing and continues ant colony optimization models, respectively. A weight factor is assigned to each method indicating their contribution in the final estimation. The desirable weights' combination is acquired using optimization methods. Among the individual systems, fuzzy logic and artificial neural network obtained the best performance for estimating fast and slow shear wave velocities, respectively. Also, the results of committee machine algorithms indicate a well optimization on individual systems and have superior performance over them. The most efficient optimization algorithms in the structure of committee machines for fast shear wave velocity are Genetic and Simulated Annealing and for slow shear wave velocity is Genetic Algorithm, in terms of Mean Squared Error criteria.

Rigid Point Set Registration Based on Cubature Kalman Filter and Its Application in Intelligent Vehicles

Point set registration is a key problem in intelligent vehicle localization and mapping. This paper presents a rigid point set registration algorithm based on the cubature Kalman filter (CKF). First, the point set registration problem is cast into the state space model assuming that the correspondence between these two point sets is previously unknown. Then, CKF is used to solve this nonlinear filtering problem. At every iterative step, all the points in the moving point set will be considered, and the corresponding points in the model point set will be updated accordingly. In the time update, the scale of the free space that can be explored is significant for this registration algorithm. Herein, continuous simulated annealing (CSA) is adopted to gradually optimize the covariance of the model noise to speed up convergence. Tests on public data sets show that the CKF-based point set registration algorithm is robust to outliers, noise, and initialization misalignment. Then, the application of this algorithm on intelligent vehicles and intelligent transportation systems is demonstrated through mapping and localization experiments. The precision and robustness are both validated compared with the traditional ICP, NDT, and CPD based point set registrations in the localization experiments. Thus, the contributions of this paper are threefold. First, a CKF scheme is utilized in the point set registration problem. Second, CSA serves as the local optimizer to speed up the convergence process and make it more accurate. Third, this filtering-based method is adopted in intelligent vehicles and SLAM applications.

Determination of initial temperature in fast simulated annealing

In this paper, we propose a method of determining the initial temperature for continuous fast simulated annealing from the perspective of state variation. While the conventional method utilizes fitness variation, the proposed method additionally considers genotype variation. The proposed scheme is based on the fact that the annealing temperature, which includes the initial temperature, not only appears in the acceptance probability but serves as the scale parameter of a state generating probability distribution. We theoretically derive an expression for the probability of generating states to cover the state space in conjunction with the convergence property of the fast simulated annealing. We then numerically solve the expression to determine the initial temperature. We empirically show that the proposed method outperforms the conventional one in optimizing various benchmarking functions.

Performance Analysis of Metaheuristic Approaches for Single-Snapshot DOA Estimation

This letter addresses the application of metaheuristics to the single-snapshot direction-of-arrival estimation. The performances of five of the most popular optimization algorithms—Particle Swarm Optimization, Ant Colony Optimization for Continuous Domains, Simulated Annealing, Genetic Algorithms, and Differential Evolution—are compared in terms of convergence, accuracy, resolution, and computational cost in order to find the most suitable one. Also, running parameters are suggested for all of them. The featured numerical simulations include both uniform and nonuniform arrays and different noise scenarios. Results show that all of the presented optimization algorithms are capable of solving the problem, but Ant Colony Optimization for Continuous Domains is the most recommendable .

A derivative-free variant called DFSA of Dekkers and Aarts’ continuous simulated annealing algorithm

We propose a derivative-free implementation of Dekkers and Aarts’ continuous simulated annealing (SA). Essential in DFSA is the ’random direction’ local technique that we introduce. We study the convergence properties of the resulting algorithm and test its performance on a set of 50 problems. Numerical results are presented which show the robustness of the algorithm. Numerical comparisons with SA, two derivative-free simulated annealing algorithms and three population-based global optimization algorithms show that the derivative-free SA, DFSA, offers a reasonable alternative to some recent global optimization algorithms, especially for problems requiring a ‘direct search’ type algorithm.

Constrained optimization of spatial sampling in salt contaminated coastal farmland using EMI and continuous simulated annealing.

Coastal farmland along the Venice Lagoon catchment is threatened by saltwater contamination posing a serious risk for agricultural activities. A research project was recently started to understand the dynamics of salt water intrusion and soil desertification. The spatial simulated annealing (SSA) was used to optimize the soil sampling scheme in a 25ha study area taking into account sampling constraints, the field shape, and apparent electrical conductivity (ECa) investigations as auxiliary information. The results show how the sampling procedure is able to consider the heterogeneous nature of the site.

A simulated annealing driven multi-start algorithm for bound constrained global optimization

A derivative-free simulated annealing driven multi-start algorithm for continuous global optimization is presented. We first propose a trial point generation scheme in continuous simulated annealing which eliminates the need for the gradient-based trial point generation. We then suitably embed the multi-start procedure within the simulated annealing algorithm. We modify the derivative-free pattern search method and use it as the local search in the multi-start procedure. We study the convergence properties of the algorithm and test its performance on a set of 50 problems. Numerical results are presented which show the robustness of the algorithm. Numerical comparisons with a gradient-based simulated annealing algorithm and three population-based global optimization algorithms show that the new algorithm could offer a reasonable alternative to many currently available global optimization algorithms, specially for problems requiring ‘direct search’ type algorithm.

Optimal In-Situ Biormediation System Design Using Simulated Annealing

The presented procedure combines continuous simulated annealing (CSA) heuristic optimization with BIOPLUME II simulation for optimizing in-situ bioremediation system design. The design goal is to minimize the total cost of facility installation and operation needed to achieve contaminant plume containment and cleanup. System design elements include pumping rates and well locations. During optimization, pumping rates are treated as continuous variables, differing from previously reported simulated annealing combinatorial optimization for groundwater management. To improve computation efficiency, CSA annealing schedules employing four different temperature update functions (TUF) are contrasted. Each yields somewhat different optimal designs and requires different computation effort. An adaptive TUF used almost 4,000 simulations to develop the lowest-cost design. A geometric TUF used 5% fewer simulations to create a design costing about 3% more. Site characteristics significantly affect optimal system design features. For a specific design, bioremediation improves with increasing hydraulic conductivity, longitudinal dispersivity, and remediation period and with decreasing retardation factor.

Adaptive search with stochastic acceptance probabilities for global optimization

We present an extension of continuous domain Simulated Annealing. Our algorithm employs a globally reaching candidate generator, adaptive stochastic acceptance probabilities, and converges in probability to the optimal value. An application to simulation–optimization problems with asymptotically diminishing errors is presented. Numerical results on a noisy protein-folding problem are included.

Spacecraft optimal rendezvous controller design using simulated annealing

A new global approach for rendezvous Linear Quadratic controller design is presented in this paper. Instead of solving the algebraic Riccati equation, a continuous simulated annealing (SA) algorithm is used to design rendezvous LQ controller. Optimization of one automatic rendezvous controller with 18 design parameters is illustrated. The results show that the SA algorithm can locate the global solution effectively and robust, besides a great number of global solutions have been obtained by the SA. The SA has demonstrated better performance than other optimization algorithms such as floating-coded Genetic Algorithm, Simplex method and Powell algorithm.

Optimization of the Operating Parameters of a Proton Exchange Membrane Fuel Cell for Maximum Power Density

The performance of fuel cells can be significantly improved by using optimum operating conditions that maximize the power density subject to constraints. Despite its significance, relatively scant work is reported in the open literature on the model-assisted optimization of fuel cells. In this paper, a methodology for model-based optimization is presented by considering a one-dimensional nonisothermal description of a fuel cell operating on reformate feed. The numerical model is coupled with a continuous search simulated annealing optimization scheme to determine the optimum solutions for selected process constraints. Optimization results are presented over a range of fuel cell design parameters to assess the effects of membrane thickness, electrode thickness, constraint values, and CO concentration on the optimum operating conditions.

Simulated Annealing for Missile Optimization: Developing Method and Formulation Techniques

Hide-and-seek is a continuous simulated annealing algorithm that uses an adaptive cooling schedule. A number of improvements are proposed for the global optimum estimation required for the cooling schedule. To handle equality constraints, two approaches are examined: the rejection method and augmentation of constraints to cost using penalty coefficients. It is demonstrated that a faster convergence is possible if, in the penalty coefficients approach, equality constraints are replaced with tight inequality constraints. The missile trajectory optimization problem is formulated using nodes equally spaced in time until burnout and equally spaced in energy consumption after burnout. This approach is shown to be superior to the use of all nodes equally spaced in time. Also investigated is the effect of node number on the performance of the algorithm. The problem of combined optimization of design and control variables is also addressed. For this purpose a two-loop approach, where each loop has its own temperature and cooling schedule, is proposed, and its effectiveness is demonstrated.

Optimal Temperature and Current Cycles for Curing of Composites Using Embedded Resistive Heating Elements

Curing is an important and time consuming step in the fabrication of thermosetting-matrix composite products. The use of embedded resistive heating elements providing supplemental heating from within the material being cured has been shown in previous studies (Ramakrishnan, Zhu, and Pitchumani, 2000, J. Manuf. Sci. Eng., 122, pp. 124–131; and Zhu and Pitchumani, 2000, Compos. Sci. Technol., 60, 2699–2712.) to offer significant improvements in cure cycle time and cure uniformity, due to the inside-out curing. This paper addresses the problem of determining the temperature and electrical current cycles, as well as the placement configuration of the conductive mats, for time-optimal curing of composites using embedded resistive heating elements. A continuous search simulated annealing optimization technique is utilized coupled with a numerical process simulation model to determine the optimal solutions for selected process constraints. Optimization results are presented over a range of material systems and different numbers of conductive mats to assess the effects of materials reactivity on the optimal number of conductive mats.

Parallel continuous simulated annealing for global optimization simulated annealing*

In this paper a parallel algorithm for simulated annealing (SA) in the continuous case, the Multiple Trials and Adaptive Supplementary Search, MTASS algorithm, is presented. It is based on a combination of multiple trials, local improved searches and an adaptive cooling schedule. The results in optimizing some standard test problems are compared with some SA sequential algorithms and another parallel probabilistic algorithm

ＳＡを用いた複合型アルゴリズム

As a new procedure of a global optimization for nonlinear systems, a hybrid algorithm between a global optimization technique called a Hide-and-Seek method, a kind of continuous simulated annealing method, and a conventional local optimization technique is proposed. To show performance of this method, comparison between this and other methods are made through several bench mark and engineering optimization problems.

Constrained Optimization of Spatial Sampling using Continuous Simulated Annealing

AbstractSpatial sampling is an important issue in environmental studies because the sample configuration influences both costs and effectiveness of a survey. Practical sampling constraints and available preinformation can help to optimize the sampling scheme. In this paper, spatial simulated annealing (SSA) is presented as a method to optimize spatial environmental sampling schemes. Sampling schemes are optimized at the point‐level, taking into account sampling constraints and preliminary observations. Two optimization criteria have been used. The first optimizes even spreading of the points over a region, whereas the second optimizes variogram estimation using a proposed criterion from the literature. For several examples it is shown that SSA is superior to conventional methods of designing sampling schemes. Improvements up to 30% occur for the first criterion, and an almost complete solution is found for the second criterion. Spatial simulated annealing is especially useful in studies with many sampling constraints. It is flexible in implementing additional, quantitative criteria.

On-Line Learning Fokker-Planck Machine

In this letter we present an on-line learning version of the Fokker-Planck machine. The method makes use of a regularized constrained normalized LMS algorithm in order to estimate the time-derivative of the parameter vector of a radial basis function network. The RBF network parametrizes a transition density which satisfies a Fokker-Planck equation, associated to continuous simulated annealing. On-line learning using the constrained normalized LMS method is necessary in order to make the Fokker-Planck machine applicable to large scale nonlinear optimization problems.

Machining condition optimization by genetic algorithms and simulated annealing

Optimal machining conditions are the key to economical machining operations. In this work, some benchmark machining models are evaluated for optimal machining conditions. These machining models are complex because of non-linearities and non-convexity. In this research, we have used Genetic Algorithms and Simulated Annealing as optimization methods for solving the benchmark models. An extension of the Simulated Annealing algorithm, Continuous Simulated Annealing is also used. The results are evaluated and compared with each other as well as with previously published results which used gradient based methods, such as, SUMT (Sequential Unconstrained Minimization Technique), Box's Complex Search, Hill Algorithm (Sequential search technique), GRG (Generalized Reduced Gradient), etc. We conclude that Genetic Algorithms, Simulated Annealing and the Continuous Simulated Annealing which are non-gradient based optimization techniques are reliable and accurate for solving machining optimization problems and offer certain advantages over gradient based methods.

Simulated annealing for constrained global optimization

Hide-and-Seek is a powerful yet simple and easily implemented continuous simulated annealing algorithm for finding the maximum of a continuous function over an arbitrary closed, bounded and full-dimensional body. The function may be nondifferentiable and the feasible region may be nonconvex or even disconnected. The algorithm begins with any feasible interior point. In each iteration it generates a candidate successor point by generating a uniformly distributed point along a direction chosen at random from the current iteration point. In contrast to the discrete case, a single step of this algorithm may generateany point in the feasible region as a candidate point. The candidate point is then accepted as the next iteration point according to the Metropolis criterion parametrized by anadaptive cooling schedule. Again in contrast to discrete simulated annealing, the sequence of iteration points converges in probability to a global optimum regardless of how rapidly the temperatures converge to zero. Empirical comparisons with other algorithms suggest competitive performance by Hide-and-Seek.