Implementation Of Simulated Annealing Research Articles

New bounds for binary covering arrays using simulated annealing

Covering arrays (CAs) are combinatorial structures specified as a matrix of N rows and k columns over an alphabet on v symbols such that for each set of t columns (called the strength of the array) every t-tuple of symbols is covered. Recently they have been used to represent interaction test suites for software testing given that they provide economical sized test cases while still preserving important fault detection capabilities. This paper introduces an improved implementation of a simulated annealing algorithm, called ISA, for constructing CAs of strengths three through six over a binary alphabet (i.e., binary CAs). Extensive experimentation is carried out, using 127 well-known benchmark instances, for assessing its performance with respect to an existing simulated annealing implementation, a greedy method, and five state-of-the-art algorithms. The results show that our algorithm attains 104 new bounds and equals the best-known solutions for the other 23 instances consuming reasonable computational time. Furthermore, the implications of using these results as ingredients to recursive constructions are also analyzed.

Simulated annealing implementation with shorter Markov chain length to reduce computational burden and its application to the analysis of pulmonary airway architecture

A new way to implement the Simulated Annealing (SA) algorithm was developed and tested that improves computation performance by using shorter Markov chain length (inner iterations) and repeating the entire SA process until the final function value meets the solution criterion. The new approach coupled with the adaptive neighborhood method was tested on the Rosenbrock function in 4 and 13 dimensions. This implementation significantly improved the computation speed without degrading solution quality. The proposed implementation was used to characterize pulmonary architecture from micro CT image data demonstrating the algorithm's effectiveness especially for problems with high computational demand and when the solution quality requirement can be pre-specified. Using this implementation, detailed statistics of the morphometry of conducting airways from 12 male Sprague Dawley rats were obtained for each lobe.

Simulated annealing based parallel genetic algorithm for facility layout problem

The facility layout problem (FLP), a typical combinational optimisation problem, is addressed in this paper by implementing parallel simulated annealing (SA) and genetic algorithms (GAs) based on a coarse-grained model to derive solutions for solving the static FLP with rectangle shape areas. Based on the consideration of minimising the material flow factor cost (MFFC), shape ratio factor (SRF) and area utilisation factor (AUF), a total layout cost (TLC) function is derived by conducting a weighted summation of MFFC, SRF and AUF. The evolution operations (including crossover, mutation, and selection) of GA provide a population-based global search in the space of possible solutions, and the SA algorithm can lead to an efficient local search near the optimal solution. By combing the characteristics of GA and SA, better solutions will be obtained. Moreover, the parallel implementation of simulated annealing based genetic algorithm (SAGA) enables a quick search for the optimal solution. The proposed method is tested by performing a case study simulation and the results confirm its feasibility and superiority to other approaches for solving FLP.

Parallel implementation of simulated annealing to reproduce multiple-point statistics

This paper shows an innovative implementation of simulated annealing in the context of parallel computing. Details regarding the use of parallel computing through a cluster of processors, as well as the implementation decisions, are provided. Simulated annealing is presented aiming at the generation of stochastic realizations of categorical variables reproducing multiple-point statistics. The procedure starts with the use of a training image to determine the frequencies of occurrence of particular configurations of nodes and values. These frequencies are used as target statistics that must be matched by the stochastic images generated with the algorithm. The simulation process considers an initial random image of the spatial distribution of the categories. Nodes are perturbed randomly and after each perturbation the mismatch between the target statistics and the current statistics of the image is calculated. The perturbation is accepted if the statistics are closer to the target, or conditionally rejected if not, based on the annealing schedule. The simulation was implemented using parallel processes with C++ and MPI. The message passing scheme was implemented using a speculative computation framework, by which prior to making the decision of acceptance or rejection of a proposed perturbation, processes already start calculating the next possible perturbation at a second level; one as if the perturbation on level one is accepted, and another process as if the proposed perturbation is rejected. Additional levels can start their calculation as well, conditional to the second level processes. Once a process reaches a decision as to whether accept or reject the suggested perturbation, all processes within the branch incompatible with that decision are dropped. This allows a speed up of up to log n ( p+1), where n is the number of categories and p the number of processes simultaneously active. Examples are provided to demonstrate improvements and speed ups that can be achieved.

A simulated annealing method for design of laminates with required stiffness properties

Abstract Designing a laminate based on its stiffness properties requires finding the optimum lamination stacking sequence to yield the required stiffness properties. The design variables to be considered are the number of layers and orientation angle of fibers in each layer group, which are treated as discrete-variables. The optimum lamination is then obtained by minimizing a cost function composed of the relative difference between the calculated effective stiffness properties and weight of trial laminate and the desired properties. This error minimization problem was solved using a modified simulated annealing heuristic method. The new simulated annealing implementation comprises a cooling procedure in which the temperature decrease relied adaptively on the objective function evolution. It is shown that the proposed method can give rise to an improvement in convergence speed. To achieve a further improvement in the performance of the method, simulated annealing parallelization implemented using the proposed cooling process. The main features of this algorithm are described and its encouraging results are presented.

PARALLEL TEMPERING FOR THE TRAVELING SALESMAN PROBLEM

We explore the potential of parallel tempering as a combinatorial optimization method, applying it to the traveling salesman problem. We compare simulation results of parallel tempering with a benchmark implementation of simulated annealing, and study how different choices of parameters affect the relative performance of the two methods. We find that a straightforward implementation of parallel tempering can outperform simulated annealing in several crucial respects. When parameters are chosen appropriately, both methods yield close approximation to the actual minimum distance for an instance with 200 nodes. However, parallel tempering yields more consistently accurate results when a series of independent simulations are performed. Our results suggest that parallel tempering might offer a simple but powerful alternative to simulated annealing for combinatorial optimization problems.

Exemplar-Based Clustering via Simulated Annealing

Several authors have touted the p-median model as a plausible alternative to within-cluster sums of squares (i.e., K-means) partitioning. Purported advantages of the p-median model include the provision of “exemplars” as cluster centers, robustness with respect to outliers, and the accommodation of a diverse range of similarity data. We developed a new simulated annealing heuristic for the p-median problem and completed a thorough investigation of its computational performance. The salient findings from our experiments are that our new method substantially outperforms a previous implementation of simulated annealing and is competitive with the most effective metaheuristics for the p-median problem.

A guided simulated annealing search for solving the pick-up and delivery problem with time windows and capacity constraints

Routing and scheduling requests with pick-ups and deliveries is still one of the greatest operative challenges in inter-company logistics. Pick-up and delivery activities have to be bundled into efficient routes and their sequence has to be optimised within the routes without violating time and capacity constraints. The objective is to find a schedule of routes with minimal total costs. These costs result from the arising travelling costs, costs due to waiting and service times, and due to dispatching vehicles. This paper presents a guided local search method based on simulated annealing for solving this kind of routing and scheduling problem. Additionally, a new more realistic objective function that covers the total decision-relevant costs is introduced. The computational results show that the algorithm presented clearly outperforms standard implementations of simulated annealing and hill climber search.

On the Performance of Simulated Annealing for Large-Scale L2 Unidimensional Scaling

In this research note, I present a modified version of G. De Soete, L. Hubert, and P. Arabie’s (1988) simulated annealing approach for the problem of L2 unidimensional scaling via maximization of the Defays criterion. The modifications include efficient storage and computation methods that facilitate rapid evaluation of trial solutions. The results of two experimental studies indicate that the enhanced simulated annealing algorithm is competitive with A. Murillo, J.F. Vera, and W.J. Heiser’s (2005) recently published pertsaus2 procedure in terms of solution quality and computation time. Both Fortran and MatLab versions of this modified simulated annealing implementation are available from the author.

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.

On the modeling of breath-by-breath oxygen uptake kinetics at the onset of high-intensity exercises: simulated annealing vs. GRG2 method

Modeling in the time domain, the non-steady-state O2 uptake on-kinetics of high-intensity exercises with empirical models is commonly performed with gradient-descent-based methods. However, these procedures may impair the confidence of the parameter estimation when the modeling functions are not continuously differentiable and when the estimation corresponds to an ill-posed problem. To cope with these problems, an implementation of simulated annealing (SA) methods was compared with the GRG2 algorithm (a gradient-descent method known for its robustness). Forty simulated Vo2 on-responses were generated to mimic the real time course for transitions from light- to high-intensity exercises, with a signal-to-noise ratio equal to 20 dB. They were modeled twice with a discontinuous double-exponential function using both estimation methods. GRG2 significantly biased two estimated kinetic parameters of the first exponential (the time delay td1 and the time constant tau1) and impaired the precision (i.e., standard deviation) of the baseline A0, td1, and tau1 compared with SA. SA significantly improved the precision of the three parameters of the second exponential (the asymptotic increment A2, the time delay td2, and the time constant tau2). Nevertheless, td2 was significantly biased by both procedures, and the large confidence intervals of the whole second component parameters limit their interpretation. To compare both algorithms on experimental data, 26 subjects each performed two transitions from 80 W to 80% maximal O2 uptake on a cycle ergometer and O2 uptake was measured breath by breath. More than 88% of the kinetic parameter estimations done with the SA algorithm produced the lowest residual sum of squares between the experimental data points and the model. Repeatability coefficients were better with GRG2 for A1 although better with SA for A2 and tau2. Our results demonstrate that the implementation of SA improves significantly the estimation of most of these kinetic parameters, but a large inaccuracy remains in estimating the parameter values of the second exponential.

Estimates of Geoacoustic Model Parameters From Inversions of Horizontal and Vertical Line Array Data

This paper describes results from geoacoustic inversion of low-frequency acoustic data recorded at a receiving array divided into two sections, a sparse bottom laid horizontal array (HLA) and a vertical array (VLA) deployed in shallow water. The data are from an experiment conducted by the Norwegian Defence Research Establishment (FFI) in the Barents Sea, using broadband explosives (shot) sources. A two-layer range-independent geoacoustic model, consistent with seismic profiles from the area, described the environment. Inversion for geoacoustic model parameters was carried out using a fast implementation of the hybrid adaptive simplex simulated annealing (ASSA) inversion algorithm, with replica fields computed by the ORCA normal mode code. Low-frequency (40-128 Hz) data from six shot sources at ranges 3-9 km from the array were considered. Estimates of sediment and substrate p-wave velocities and sediment thickness were found to be consistent between independent inversions of data from the two sections of the array

The quadratic assignment problem in the context of the printed circuit board assembly process

The sequencing of placement and the configuration of the feeder is among the main problems involved in printed circuit board (PCB) assembly optimization. In some machine architectures, the latter problem can be formulated as the well known NP-hard quadratic assignment problem (QAP). In this study, a search is made among those metaheuristics that have recently found widespread application in order to identify a heuristic procedure that performs well with the QAP in the PCB assembly context. To this end, specific algorithms reflecting implementations of Taboo Search, Simulated Annealing and Genetic Algorithm-type metaheuristics were tested and compared using real PCB assembly data. The same set of algorithms was also tested on general QAP problems and it was observed that algorithms which performed successfully in the PCB context could perform poorly in the general situation. In the light of this, it can be concluded that ascertaining the best performing heuristic is complicated by the fact that the performance of a heuristic depends on the context of the problem, which determines the structure and relationships of problem parameters.

A Permutation-Translation Simulated Annealing Algorithm for L1 and L2 Unidimensional Scaling

Given a set of objects and a symmetric matrix of dissimilarities between them, Unidimensional Scaling is the problem of finding a representation by locating points on a continuum. Approximating dissimilarities by the absolute value of the difference between coordinates on a line constitutes a serious computational problem. This paper presents an algorithm that implements Simulated Annealing in a new way, via a strategy based on a weighted alternating process that uses permutations and point-wise translations to locate the optimal configuration. Explicit implementation details are given for least squares loss functions and for least absolute deviations. The weighted, alternating process is shown to outperform earlier implementations of Simulated Annealing and other optimization strategies for Unidimensional Scaling in run time efficiency, in solution quality, or in both.

A note on simulated annealing to computer laboratory scheduling

The concepts, principles and implementation of simulated Annealing as a modem heuristic technique is presented. Simulated Annealing algorithm is used in solving real life problem of Computer Laboratory scheduling in order to maximize the use of scarce and insufficient resources. KEY WORDS: Simulated Annealing (SA), Computer Laboratory Scheduling, Statistical Thermodynamics, Energy Function, and Heuristic etc. Global Jnl of Pure and Applied Sciences Vol.10(4) 2004: 607-610

Robust and efficient image segmentation approaches using Markov random field models

Modified implementations of simulated annealing (SA) for image segmentation are proposed and evaluated. The segmentation procedure is based on a Markov random field (MRF) model for describing regions within an image. SA offers an iterative approach for computing a set of labels with maximum a posteriori (MAP) probability. However, this approach is computationally expensive and lacks robustness in noisy environments. We propose a random cost function (RCF) for computing a posterior energy function in SA. The proposed modified SA (SA-RCF) method depicts more robust performance for image segmentation than standard SA at the same computational cost. Alternatively, we proposed a multi-resolution (MR) approach based on MRF, which offers robust segmentation for noisy images with significant reduction in the computational cost. Computational cost and segmentation accuracy of each algorithm were examined using a set of simulated head computerized tomography (CT) phantoms.

VLSI placement and area optimization using a genetic algorithm to breed normalized postfix expressions

We present a genetic algorithm (GA) that uses a slicing tree construction process for the placement and area optimization of soft modules in very large scale integration floorplan design. We have overcome the serious representational problems usually associated with encoding slicing floorplans into GAs and have obtained excellent (often optimal) results for module sets with up to 100 rectangles. The slicing tree construction process used by our GA to generate the floorplans has a runtime scaling of O(n lg n). This compares very favorably with other recent approaches based on nonslicing floorplans that require much longer runtimes. We demonstrate that our GA outperforms a simulated annealing implementation with the same representation and mutation operators as the GA.

A robust simulated annealing based examination timetabling system

This paper is concerned with the development of an examination scheduling system that is sufficiently flexible to deal with the many different objectives and constraints found across a broad spectrum of universities and colleges. The problem is solved in two phases using simulated annealing. The first phase seeks out a feasible solution and the second finds an improvement in terms of meeting the secondary objectives and soft constraints. As the quality of a simulated annealing solution is known to depend on the parameters used to control the algorithm and the way in which the problem is modelled within the simulated annealing framework a successful implemetation relies on judicious choices in both areas. A number of different choices are suggested and compared using a test-bed of problems derived from data from a variety of institutions. The final result is a robust system that is capable of dealing with a wide range of problem specifications and data characteristics.The examination scheduling problem varies in detail from institution to institution. Thus any generic approach must be robust enough to work well over the full spectrum of problem characteristics. It is well-known that the quality of solutions produced by any simulated annealing implementation depends on the correct choice of solution space and neighbourhood, as well as the parameters that govern the cooling schedule. As these choices are sensitive to the precise problem details the design of a generic simulated annealing based approach to examination scheduling needs to address this issue carefully. This paper examines this problem with respect to an implementation that has already been shown to work well at a single institution. The basic framework is used to test different neighbourhoods and cooling schedules over a variety of problems and to examine whether or not biases in sampling have a significant effect on solution quality. The results indicate that the choice of neighbourhood is the most important decision and that neighbourhoods based on the graph-theoretic concept of Kempe chains are the most effective regardless of the objectives or size of the problem.

A branch and bound algorithm for scheduling projects to maximize net present value: The case of time dependent, contingent cash flows

The problem of scheduling activities in a project to maximize its net present value (NPV) has been solved recently for the case where net cash flow magnitudes are dependent on the time of realization. In this problem, incentive payments and penalties for early and late event occurrences respectively, as well as the cost of resources over time, are time dependent. We present a branch and bound solution approach for this problem. We compare the NPVs of the solutions obtained from the branch and bound algorithm with those of a simulated annealing approach developed earlier. Our computational results show that the branch and bound approach outperforms the best known simulated annealing implementation.

Implementation of Ensemble-Based Simulated Annealing with dynamic load balancing under MPI

This paper describes an implementation of Ensemble Based Simulated Annealing (EBSA) with dynamic load balancing. It is running under the MPI Message Passing Library allowing parallel execution on various types of computers. The load balancing is used to get maximum use of the available processing power, even on hetegeneous workstation clusters where the machines differ a lot in computing power.