Simulated Annealing Framework Research Articles

Structured Placement with Topological Regularity Evaluation

This paper introduces a new concept of regularity-oriented floorplanning and block placement — structured placement, it takes the regularity as a criterion of placement so as to improve the performance. We provide the methods to extract regular structures from a placement representation in linear time, and manage to evaluate these structures by quantifying the regularity as an objective function. We also construct a particular simulated annealing framework, which optimizes placement topology and physical dimension separately and alternately so that it attains a solution balancing the trade-off between regularity and area efficiency. Furthermore, we introduce the symmetry-oriented structured placement to produce symmetrical placement. Experiments show that the resultant placements achieve regularity without increased chip area and wire length, compared to those by existing methods.

A dual latent class unfolding model for two-way two-mode preference rating data

In unfolding for two-way two-mode preference ratings data, the categorization of the set of individuals while the categories are represented in a low dimensional space may be an advisable procedure to facilitate their understanding. In addition to considering groups of individuals of a similar preference pattern, homogeneous groups of objects are also considered, such that within each group there are clustered objects perceived to have similar attributes. A dual latent class model is proposed for a matrix of preference ratings data, which will partition the individuals and the objects into classes, and simultaneously represent the cluster centers in a low dimensional space, while individuals and objects retain their preference relationship. Both the categories achieved and the unfolding configuration are estimated to be simultaneously optimal, by means of a conditional maximum likelihood estimation procedure, in a simulated annealing framework that enables us to take a statistical decision about the parameters of the model. The adjusted BIC statistic is employed to test the number of mixture components, and the dimensionality of the representation. Real and artificial data sets are analyzed to illustrate the model’s performance.

Tariff concessions in production sourcing

In this paper, we study a multi-stage production sourcing problem where tariff concessions can be exploited at the firm level using free trade agreements between countries. To solve the problem, an algorithm which embeds a very large-scale neighborhood (VSLN) search into a simulated annealing framework is developed. A numerical study is conducted to verify the effectiveness of the solution approach.

MASTR: multiple alignment and structure prediction of non-coding RNAs using simulated annealing

As more non-coding RNAs are discovered, the importance of methods for RNA analysis increases. Since the structure of ncRNA is intimately tied to the function of the molecule, programs for RNA structure prediction are necessary tools in this growing field of research. Furthermore, it is known that RNA structure is often evolutionarily more conserved than sequence. However, few existing methods are capable of simultaneously considering multiple sequence alignment and structure prediction. We present a novel solution to the problem of simultaneous structure prediction and multiple alignment of RNA sequences. Using Markov chain Monte Carlo in a simulated annealing framework, the algorithm MASTR (Multiple Alignment of STructural RNAs) iteratively improves both sequence alignment and structure prediction for a set of RNA sequences. This is done by minimizing a combined cost function that considers sequence conservation, covariation and basepairing probabilities. The results show that the method is very competitive to similar programs available today, both in terms of accuracy and computational efficiency. Source code available from http://mastr.binf.ku.dk/

Improving inductive logic programming by using simulated annealing

In Inductive Logic Programming (ILP), algorithms that are purely of the bottom-up or top-down type encounter several problems in practice. Since a majority of them are greedy ones, these algorithms stop when finding clauses in local optima, according to the “quality” measure used for evaluating the results. Moreover, when learning clauses one by one, the induced clauses become less and less interesting as the algorithm is progressing to cover few remaining examples. In this paper, we propose a simulated annealing framework to overcome these problems. Using a refinement operator, we define neighborhood relations on clauses and on hypotheses (i.e. sets of clauses). With these relations and appropriate quality measures, we show how to induce clauses (in a coverage approach), or to induce hypotheses directly by using simulated annealing algorithms. We discuss the necessary conditions on the refinement operators and the evaluation measures to increase the effectiveness of the algorithm. Implementations (included a parallelized version of the algorithm) are described and experimentation results in terms of convergence of the method and in terms of accuracy are presented.

Multi-bend bus driven floorplanning

In this paper, the problem of bus-driven floorplanning is addressed. Given a set of blocks and bus specifications (the width of each bus and the blocks that the bus need to go through), we will generate a floorplan solution such that all the buses go through their blocks, with the area of the floorplan and the total area of the buses minimized. The approach proposed is based on a simulated annealing framework. Using the sequence pair representation, we derived and proved some necessary conditions for feasible buses, for which we allow 0-bend, one-bend, or two-bend. A checking will be performed to identify those buses that cannot be placed simultaneously. Finally, a solution will be generated giving the coordinates of the modules and the buses. Comparing with the results of the most updated work on this problem by Xiang et al. [Bus-driven floorplanning, in: Proceedings of IEEE International Conference on Computer-Aided Design, 2003, pp. 66–73], our algorithm can handle buses going through many blocks and the dead space of the floorplan obtained is also reduced. For example, if the buses have to go through more than 10 blocks, the approach in Xiang et al. [Bus-driven floorplanning, in: Proceedings of IEEE International Conference on Computer-Aided Design, 2003, pp. 66–73] is not able to generate any solution while our algorithm can still give solutions of good quality.

A combined procedure for discrete simulation–optimization problems based on the simulated annealing framework

This paper addresses the problem of optimizing a function over a finite or countable infinite set of alternatives, whenever the objective function cannot be evaluated exactly, but has to be estimated via simulation. We present an iterative method, based on the simulated annealing framework, for solving such discrete stochastic optimization problems. In the proposed method, we combine the robustness of this metaheuristic method with a statistical procedure for comparing the solutions that are generated. The focus of our work is on devising an effective procedure rather than addressing theoretical issues. In fact, in our opinion, although significant progresses have been made in studying the convergence of a number of simulation---optimization algorithms, at present there is no procedure able to consistently provide good results in a reasonable amount of time. In addition, we present a parallelization strategy for allocating simulation runs on computing resources.

Registration of lung nodules using a semi‐rigid model: Method and preliminary results

The tracking of lung nodules across computed tomography (CT) scans acquired at different times for the same patient is helpful for the determination of malignancy. We are developing a nodule registration system to facilitate this process. We propose to use a semi-rigid method that considers principal structures surrounding the nodule and allows relative movements among the structures. The proposed similarity metric, which evaluates both the image correlation and the degree of elastic deformation amongst the structures, is maximized by a two-layered optimization method, employing a simulated annealing framework. We tested our method by simulating five cases that represent physiological deformation as well as different nodule shape/size changes with time. Each case is made up of a source and target scan, where the source scan consists of a nodule-free patient CT volume into which we inserted ten simulated lung nodules, and the target scan is the result of applying a known, physiologically based nonrigid transformation to the nodule-free source scan, into which we inserted modified versions of the corresponding nodules at the same, known locations. Five different modification strategies were used, one for each of the five cases: (1) nodules maintain size and shape, (2) nodules disappear, (3) nodules shrink uniformly by a factor of 2, (4) nodules grow uniformly by a factor of 2, and (5) nodules grow nonuniformly. We also matched 97 real nodules in pairs of scans (acquired at different times) from 12 patients and compared our registration to a radiologist's visual determination. In the simulation experiments, the mean absolute registration errors were 1.0+/-0.8 mm (s.d.), 1.1+/-0.7 mm (s.d.), 1.0+/-0.7 mm (s.d.), 1.0+/-0.6 mm (s.d.), and 1.1+/- 0.9 mm (s.d.) for the five cases, respectively. For the 97 nodule pairs in 12 patient scans, the mean absolute registration error was 1.4+/-0.8 mm (s.d.).

Phasor Measurement Unit Placement Techniques for Complete and Incomplete Observability

This paper presents techniques for identifying placement sites for phasor measurement units (PMUs) in a power system based on incomplete observability. The novel concept of depth of unobservability is introduced and its impact on the number of PMU placements is explained. Initially, we make use of spanning trees of the power system graph and a tree search technique to find the optimal location of PMUs. We then extend the modeling to recognize limitations in the availability of communication facilities around the network and pose the constrained placement problem within the framework of Simulated Annealing (SA). The SA formulation was further extended to solve the pragmatic phased installation of PMUs. The performance of these methods is tested on two electric utility systems and IEEE test systems. Results show that these techniques provide utilities with systematic approaches for incrementally placing PMUs thereby cushioning their cost impact.

A co-operative parallel heuristic for mixed zero–one linear programming: Combining simulated annealing with branch and bound

This paper considers the exact approach of branch and bound (B&B) and the metaheuristic known as simulated annealing (SA) for processing integer programs (IP). We extend an existing SA implementation (GPSIMAN) for pure zero–one integer programs (PZIP) to process a wider class of IP models, namely mixed zero–one integer programs (MZIP). The extensions are based on depth-first B&B searches at different points within the SA framework. We refer to the resultant SA implementation as MIPSA. Furthermore, we have exploited the use of parallel computers by designing a co-operative parallel heuristic whereby concurrent executions of B&B and MIPSA, linked through a parallel computer, exchange information in order to influence their searches. Results reported for a wide range of models taken from a library of MIP benchmarks demonstrate the effectiveness of using a parallel computing approach which combines B&B with SA.

Convergence in Probability of Compressed Annealing

We consider combinatorial optimization problems for which the formation of a neighborhood structure of feasible solutions is impeded by a set of constraints. Neighborhoods are recovered by relaxing the complicating constraints into the objective function within a penalty term. We examine a heuristic called compressed annealing that integrates a variable penalty multiplier approach within the framework of simulated annealing. We refer to the value of the penalty multiplier as “pressure.” We analyze the behavior of compressed annealing by exploring the interaction between temperature (which controls the ability of compressed annealing to climb hills) and pressure (which controls the height of the hills). We develop a necessary and sufficient condition on the joint cooling and compression schedules for compressed annealing to converge in probability to the set of global minima. Our work generalizes the results of Hajek (1988) in the sense that when there are no relaxed constraints, our results reduce to his.

Purposeful mobility for relaying and surveillance in mobile ad hoc sensor networks

We consider a mobile ad hoc sensor network. The mobility of the sensor nodes is designed with the cost of communication and mobility in mind along with consideration of the possible scanning tasks of the nodes. Our mobility algorithm is developed in the context of a distributed system where, for any single mobile node, only local information about associated energy costs is known. We use a distributed simulated annealing framework to govern the motion of the nodes and prove that, in a limiting sense, a global objective function comprising mobility and communication energy costs are minimized. This paper concludes with a simulation study focusing on mobile sensors with dual roles of scanning and relaying higher priority tracking traffic from tracking nodes.

Assigning cells to switches in cellular networks by incorporating a pricing mechanism into simulated annealing.

Handoff and cabling costs play key roles in the design of cellular telecommunications networks. Efficient homing of cells to switches can have a significant impact on each of these costs. In the presence of capacity constraints at the switches, the problem of assigning cells to switches becomes a difficult one to solve, with all effective solution approaches being based on heuristic techniques. This paper presents a hybrid heuristic which integrates ideas from linear programming into a simulated annealing framework. Extensive computational results are presented comparing the performance of the heuristic with the lower bound obtained from the linear programming relaxation. These results indicate that this price influenced simulated annealing (PISA) procedure is extremely efficient, usually providing solutions with gaps around 1% in less than 1 s.

Simulated annealing in lot sizing problems

This paper provides a brief presentation of simulated annealing techniques and their application in lot sizing problems. By using a binary matrix to describe lot sizing decisions, it is ready to model this type of production/inventory system as a combinatorial optimisation problem and solve it within the simulated annealing framework. Experiments are conducted in order to understand how different aspects of the algorithm, especially the annealing schedule, affect the quality of the solution.

Study of population heterogeneity in innovation diffusion model: Estimation based on simulated annealing

Parameter variability randomness in diffusion (PVRD) models based on random differential equations have recently been developed to study stochastic evolution of adopters. Analysis of such models is found to generate multimodal life cycle patterns (or intervening slumps) besides the conventional unimodal pattern. Application of these models to real data sets necessitate estimation of parameters of the model. Nonlinear least squares estimation problem is formulated to deal with the minimization of high-dimensional cost function. Using the simulated annealing (SA) framework, effectiveness of the estimation approach and the fitting algorithm is demonstrated in terms of “fit statistics.” An important finding from empirical studies reveal that even in unimodal life cycle patterns, parameters of innovation diffusion process are found to possess considerable variability. This finding amply demonstrates the presence of heterogeneity on account of population variability.

ADAPTIVE AND MONOTONE SPLINE ESTIMATION OF THE CROSS-SECTIONAL TERM STRUCTURE

A number of numerical methods based on a piecewise polynomial approximation have been proposed for the estimation of the term structure of interest rates. Some drawbacks have been pointed out, such as a possible non monotonic estimated discount function and a highly fluctuating spot and forward rates. In order to overcome these kind of problems, we study the feasibility of an adaptive regression spline technique which use a monotone basis together with two alternative knot location procedures: a deterministic greedy algorithm and its randomized version in a simulated annealing framework. The features of the proposed method are tested on a set of data.

Global Optimization with Exploration/Selection Algorithms and Simulated Annealing

This article studies a stochastic model of an evolutionary algorithm that evolves a “population” of potential solutions to a minimization problem. The minimization process is based on two operators. First, each solution is regarded as an individual that attempts a random search on a graph, involving a probabilistic operator called exploration. The second operator is called selection. This deterministic operator creates interaction between individuals. The convergence of the evolutionary process is described within the framework of simulated annealing. It can be quantified by means of two quantities called the critical height and the optimal convergence exponent, which both measure the difficulty of the algorithm to deal with the minimization problem. This work describes the critical height for large enough population sizes. Explicit bounds are given for the optimal convergence exponent, using a few geometric quantities. As an application, this work allows comparisons of the evolutionary strategy with independent parallel runs of the simulated annealing algorithm, and it helps deciding when one method should be preferred to the other.

Handling soft modules in general nonslicing floorplan using Lagrangian relaxation

In the early stage of floorplan design, many modules have large flexibilities in shape (soft modules). Handling soft modules in general nonslicing floorplan is a complicated problem. Many previous works have attempted to tackle this problem using heuristics or numerical methods, but none of them can solve it optimally and efficiently. In this paper, we show how this problem can be solved optimally by geometric programming using the Lagrangian relaxation technique. The resulting Lagrangian relaxation subproblem is so simple that the optimal size of each module can be computed in linear time. We implemented this method in a simulated annealing framework based on the sequence pair representation. The geometric program is invoked in every iteration of the annealing process to compute the optimal size of each module to give the best packing. The execution time is much faster (at least 15 times faster for data sets with more than 50 modules) than that of the most updated previous work by Murata and Kuh (1998). For a benchmark data with 49 modules, we take 3.7 h in total for the whole annealing process using a 600-MHz Pentium III processor while the convex programming approach described by Murata and Koh needs seven days using a 250-MHz DEC Alpha. Our technique will also be applicable to other floorplanning algorithms that use constraint graphs to find module positions in the final packing.

Influence of solvation on the helix-forming tendency of nonpolar amino acids

This paper presents a computational study on helix folding and unfolding of length 10 homopeptides composed of the nonpolar amino acids methionine, alanine, leucine, phenylalanine, isoleucine, valine and glycine. We apply a Monte Carlo Simulated Annealing (MCSA) framework to derive energetic parameters which allow to differentiate between α-helix formers and helix breakers within this group of peptides, and especially emphasize solvation effects, modeled via a continuum approximation, on folding pathways and respective α-helix stability. Computed differences in potential energies of random coil and folded states clearly show methionine, alanine and leucine as helix formers, whereas phenylalanine, and in particular isoleucine, valine and glycine may be considered as helix destabilizing. This finding is also reflected by helix unfolding simulations, which indicate considerable helix stability for the first group of peptides, but enhanced unfolding for the latter four.Solvation effects do certainly affect the putative helix formation pathways for the seven model peptides considered and the paper presents a detailed analysis on correlations between changes in potential energy as well as changes in total solvation (which is also factorized into its contributions derived from hydrophobic and hydrophilic surface areas) in respective folding and unfolding pathways.Correlation analysis of MCSA runs under co-optimization of potential and solvation energies shows that solvation, in particular during the early stage, counteracts the potential energy-driven folding process. Decreases and increases of potential and solvation energies are inversely correlated. We interpret these results as such that potential energy minima are frequently associated with solvation energy maxima on the folding energy landscape, in particular at the early stage of folding. This on the one hand prevents folds from being trapped in local minima of potential energy. On the other hand this mechanism could decrease the total number of actually accessible points on the folding energy landscape (which have to be characterized as a co-optimum of potential and solvation energy), which would better define the folding pathway towards the native structure. The correlation analysis shows that the helix formers methionine, alanine, and leucine have reached such a combined optimum of potential and solvation energy at the α-helical state, whereas helix destabilizing residues as isoleucine, valine and glycine unfold the helix, driven by a combination of both, potential energies and solvation energy status.

Circular dichroic constrained structure optimization of homoalanine peptides

This article describes a new method for peptide structure optimization within a Monte Carlo Simulated Annealing (MCSA) framework, namely the cominimization of potential energies under the constraint of a calculated Circular Dichroism (CD) spectrum. We compute potential energy as well as the CD spectrum of every structure generated within the course of the MCSA run, and cooptimize the mean deviation of this calculated spectrum to a corresponding experimental spectrum together with the potential energies of the respective structures using a modified Metropolis Criterion within the MCSA scheme. We compare the performance of this technique with two other MCSA optimization variants—first, a cominimization of potential energies and free energies of solvation; and second, the standard minimization of potential energy alone. We use homoalanines in lengths of 10 and 15, whose optimized structures are highly α-helical, and correspondingly give α-helix characteristic CD signals as the test peptides. This circular dichroic constrained optimization of potential energies is, compared to the other methods, highly efficient in locating α-helical structures with lowest potential energies in both the 10 alanine and the 15 alanine peptide system, within short MCSA runs. The overall structural information embedded in the CD spectrum efficiently guides the optimization towards the native peptide structure. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 270–281, 2000