Graph drawing by force-directed placement

We present a modification of the spring-embedder model of Eades [Congressus Numerantium, 42, 149–160, (1984)] for drawing undirected graphs with straight edges. Our heuristic strives for uniform edge lengths, and we develop it in analogy to forces in natural systems, for a simple, elegant, conceptually-intuitive, and efficient algorithm.     

Three-dimensional graph drawing

Graph drawing research has been mostly oriented toward two-dimensional drawings. This paper describes an investigation of fundamental aspects of three-dimensional graph drawing. In particular we give three results concerning the space required for three-dimensional drawings. We show how to produce a grid drawing of an arbitraryn-vertex graph with all vertices located at integer grid points, in ann×2n×2n grid, such that no pair of edges cross. This grid size is optimal to within a constant. We also show how to convert an orthogonal two-dimensional drawing in anH×V integer grid to a three-dimensional drawing with volume. Using this technique we show, for example, that three-dimensional drawings of binary trees can be computed with volume . We give an algorithm for producing drawings of rooted trees in which thez-coordinate of a node represents the depth of the node in the tree; our algorithm minimizes thefootprint of the drawing, that is, the size of the projection in thexy plane. Finally, we list significant unsolved problems in algorithms for three-dimensional graph drawing. This work was performed as part of the Information Visualization Group(IVG) at the University of Newcastle. The IVG is supported in part by IBM Toronto Laboratory.     

Design of bi-criteria kanban system using simulated annealing technique

In the kanban system, the main decision parameters are the number of kanbans and lot size. In this paper, an attempt has been made to set the number of kanbans at each station and the lot size required to achieve the best performance using simulated annealing technique. A simulation model with a single-card system has been designed and used for analysis. A bi-criterion objective function comprising of mean throughput rate and aggregate average kanban queue has been used for evaluation. Different perturbation schemes have been experimented and compared.     

Combining multiple clusterings using fast simulated annealing

This paper presents a fast simulated annealing framework for combining multiple clusterings based on agreement measures between partitions, which are originally used to evaluate a clustering algorithm. Although we can follow a greedy strategy to optimize these measures as the objective functions of clustering ensemble, it may suffer from local convergence and simultaneously incur too large computational cost. To avoid local optima, we consider a simulated annealing optimization scheme that operates through single label changes. Moreover, for the measures between partitions based on the relationship (joined or separated) of pairs of objects, we can update them incrementally for each label change, which ensures that our optimization scheme is computationally feasible. The experimental evaluations demonstrate that the proposed framework can achieve promising results.     

Solving power system optimization problems using simulated annealing

Based on the simulated annealing technique and the constrained form of power system optimization problems, this paper develops a simulated-annealing-based optimization algorithm for power-system optimization problems. The algorithm is general, and it possesses the ability to determine the global optimum solution. The developed algorithm is demonstrated by its application to the problem of the economic dispatch of electric power.     

Two-dimensional equilibrium constraint layout using simulated annealing

This paper studies the layout optimization problem with equilibrium constraint. It is a two-dimensional packing problem with the industrial background of simplified satellite module layout design, and is known as NP-hard problem. By incorporating the heuristic neighborhood search mechanism and the adaptive gradient method into the simulated annealing procedure, a heuristic simulated annealing algorithm is put forward for this problem. The special neighborhood search mechanism can avoid the disadvantage of blind search in the simulated annealing algorithm, and the adaptive gradient method is used to execute local search and speed up finding the global optimal solution. Numerical examples are illustrated to verify the effectiveness of the proposed algorithm.     

Applying simulated annealing for designing cellular manufacturing systems using MDmTSP

The design of cellular manufacturing systems involves many structural and operational issues. One of the important design steps is the formation of part families and machine cells (cell formation). Despite a large number of papers on cell formation published worldwide, only a handful incorporates operation sequence in layout design (intra-cell move calculations). We propose a solution to solve the part-family and machine-cell formation problem considering the within-cell layout problem, simultaneously. In this paper, the cellular manufacturing system is formulated as a multiple departures single destination multiple travelling salesman problem (MDmTSP) and a solution methodology based on simulated annealing is proposed to solve the formulated model. Numerical examples show that the proposed method is efficient and effective in finding optimal solutions. The results also indicate that the proposed approach performs well compared to some well-known cell formation methods.     

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.     

A theoretical framework for simulated annealing

Simulated Annealing has been a very successful general algorithm for the solution of large, complex combinatorial optimization problems. Since its introduction, several applications in different fields of engineering, such as integrated circuit placement, optimal encoding, resource allocation, logic synthesis, have been developed. In parallel, theoretical studies have been focusing on the reasons for the excellent behavior of the algorithm. This paper reviews most of the important results on the theory of Simulated Annealing, placing them in a unified framework. New results are reported as well.This research was sponsored by SRC and DARPA monitored by SNWSC under contract numbers N00039-87-C-012 and N00039-88-C-0292.     

Looking for narrow interfaces in automatic differentiation using graph drawing

Automatic differentiation is a powerful technique for evaluating derivatives of functions given in the form of a high-level programming language such as Fortran, C, or C++. This technique is superior, in terms of accuracy, to numerical differentiation because it avoids the truncation error involved in divided difference approximations. In automatic differentiation, the program is treated as a potentially very long composition of elementary functions to which the chain rule of differential calculus is applied over and over again. Because of the associativity of the chain rule, there is room for different strategies computing the same numerical results but whose computational cost may vary significantly. Several strategies exploiting high-level structure of the underlying computer code are known to reduce computational cost as opposed to blindly applying automatic differentiation. An example includes “interface contraction” where one takes advantage of the fact that the number of variables passed between subroutines is small compared with the number of propagated directional derivatives. Unfortunately, these so-called narrow interfaces are not immediately available. The present study investigates the use of the VCG graph drawing tool to recognize narrow interfaces in the computational graph, a certain directed acyclic graph used to represent data dependences of variables in the underlying computer code.     

Modified simulated annealing for multiple-objective engineering design optimization

Simulated annealing is adopted as a tool for engineering design optimization. The annealing algorithm was originally designed for single-objective, discrete variable problems. In this study, the annealing algorithm has been significantly modified to handle multiple-objective, continuous variable problems. Cam design is used as a test-bed for the modified annealing algorithm. The result is compared with those from other cam design methods. Computational experience with the modified annealing algorithm is presented and discussed.     

一种新的模糊自适应模拟退火遗传算法

针对遗传算法收敛速度慢、容易"早熟"等缺点,结合模糊推理、模拟退火算法和自适应机制,提出一种改进的遗传算法--模糊自适应模拟退火遗传算法(FASAGA),并分析了该算法的性能和特点,实验研究表明,该算法比标准的遗传算法(SGA)具有更快的收敛速度和寻优效果.     

Efficient simulated annealing on fractal energy landscapes

We present a new theoretical framework for analyzing simulated annealing. The behavior of simulated annealing depends crucially on the ldergy landscape associated with the optimization problem: the landscape must have special properties if annealing is to be efficient.We prove that certain fractal properties are sufficient for simulated annealing to be efficient in the following sense: If a problem is scaled to have best solutions of energy 0 and worst solutions of energy 1, a solution of expected energy no more than can be found in time polynomial in 1/, where the exponent of the polynomial depends on certain parameters of the fractal. Higher-dimensional versions of the problem can be solved with almost identical efficiency.The cooling schedule used to achieve this result is the familiar geometric schedule of annealing practice, rather than the logarithmic schedule of previous theory. Our analysis is more realistic than those of previous studies of annealing in the constraints we place on the problem space and the conclusions we draw about annealing's performance.The mode of analysis is also new: Annealing is modeled as a random walk on a graph, and recent theorems relating the conductance of a graph to the mixing rate of its associated Markov chain generate both a new conceptual approach to annealing and new analytical, quantitative methods.The efficiency of annealing is compared with that of random sampling and descent algorithms. While these algorithms are more efficient for some fractals, their run times increase exponentially with the number of dimensions, making annealing better for problems of high dimensionality.We find that a number of circuit placement problems have energy landscapes with fractal properties, thus giving for the first time a reasonable explanation of the successful application of simulated annealing to problems in the VLSI domain.This work was done while the author was on leave from IBM Research, and was also sponsored by DARPA and monitored by SNWSC under contract numbers N00039-87-C-0182 and N00039-88-C-0292. The author is completing his doctoral studies with Prof. Alberto Sangiovanni-Vincentelli. He is on leave from the I.B.M. Thomas J. Watson Research Center.     

Minimizing makespan in a flow shop with two batch-processing machines using simulated annealing

This paper aims at minimizing the makespan of two batch-processing machines in a flow shop. The processing times and the sizes of the jobs are known and non-identical. The machines can process a batch as long as its capacity is not exceeded. The processing time of a batch is the longest processing time among all the jobs in that batch. The problem under study is NP-hard for makespan objective. Consequently, a heuristic based on Johnson's algorithm and a simulated annealing (SA) algorithm is proposed. Random instances were generated to verify the effectiveness of the proposed approaches. The results obtained from SA were compared with the proposed heuristic and a commercial solver. The SA outperformed both the heuristic and the commercial solver. On larger problem instances, the heuristic outperformed the commercial solver.     

Parameter determination of support vector machine and feature selection using simulated annealing approach

Support vector machine (SVM) is a novel pattern classification method that is valuable in many applications. Kernel parameter setting in the SVM training process, along with the feature selection, significantly affects classification accuracy. The objective of this study is to obtain the better parameter values while also finding a subset of features that does not degrade the SVM classification accuracy. This study develops a simulated annealing (SA) approach for parameter determination and feature selection in the SVM, termed SA-SVM.To measure the proposed SA-SVM approach, several datasets in UCI machine learning repository are adopted to calculate the classification accuracy rate. The proposed approach was compared with grid search which is a conventional method of performing parameter setting, and various other methods. Experimental results indicate that the classification accuracy rates of the proposed approach exceed those of grid search and other approaches. The SA-SVM is thus useful for parameter determination and feature selection in the SVM.     

Music playlist generation by adapted simulated annealing

We present the design of an algorithm for use in an interactive music system that automatically generates music playlists that fit the music preferences of a user. To this end, we introduce a formal model, define the problem of automatic playlist generation (APG), and prove its NP-hardness. We use a local search (LS) procedure employing a heuristic improvement to standard simulated annealing (SA) to solve the APG problem. In order to employ this LS procedure, we introduce an optimization variant of the APG problem, which includes the definition of penalty functions and a neighborhood structure. To improve upon the performance of the standard SA algorithm, we incorporated three heuristics referred to as song domain reduction, partial constraint voting, and a two-level neighborhood structure. We evaluate the developed algorithm by comparing it to a previously developed approach based on constraint satisfaction (CS), both in terms of run time performance and quality of the solutions. For the latter we not only considered the penalty of the resulting solutions, but we also performed a conclusive user evaluation to assess the subjective quality of the playlists generated by both algorithms. In all tests, the LS algorithm was shown to be a dramatic improvement over the CS algorithm.     

Multiprocessor scheduling using mean-field annealing

This paper presents our work on the static task scheduling model using the mean-field annealing (MFA) technique. Meanfield annealing is a technique of thermostatic annealing that takes the statistical properties of particles as its learning paradigm. It combines good features from the Hopfield neural network and simulated annealing, to overcome their weaknesses and improve on their performances. Our MFA model for task scheduling is derived from its prototype, namely, the graph partitioning problem. MFA is deterministic in nature and this has the advantage of faster convergence to the equilibrium temperature, compared to simulated annealing. Our experimental work verifies this finding, besides making comparison on the effectiveness of the model on various network and task graph sizes. Our work also includes the simulation of the MFA model on several network topologies using varying parameters. The MFA simulation model is targeted on nonpreemptive and precedence-related tasks with communication costs.     

A robust design of simulated annealing approach for mixed-model sequencing

The effectiveness of the solution method based on simulated annealing (SA) mainly depends on how to determine the SA-related parameters. A scheme as well as parameter values for defining an annealing schedule should be appropriately determined, since various schemes and their corresponding parameter values have a significant impact on the performance of SA algorithms. In this paper, based on robust design we propose a new annealing parameter design method for the mixed-model sequencing problem which is known to be NP-hard. To show the effectiveness of the proposed method, extensive computation experiments are conducted. It was found that the robust designed method outperforms the SA algorithm by McMullen and Frazier [McMullen, P.R., & Frazier, G.V. (2000). A simulated annealing approach to mixed-model sequencing with multiple objectives on a just-in-time line. IIE Transactions, 32, 679–686].