ADAPTIVE SIMULATED ANNEALING (ASA) ©Lester Ingberingber@ingber.comingber@alumni.caltech.eduAdaptive Simulated Annealing (ASA) is a C-language code developed to statistically find the bestglobal fit of a nonlinear constrained non-convex cost-function overaD-dimensional space. Thisalgorithm permits an annealing schedule for “temperature”T decreasing exponentially in annealing-timek, T = T

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Adaptive simulated annealing (asa)

In this paper a new meta-heuristic search method, called Cat Swarm Optimization (CSO) algorithm is applied to determine the best optimal impulse response coefficients of FIR low pass, high pass, band pass and band stop filters, trying to meet the respective ideal frequency response characteristics CSO is generated by observing the behaviour of cats and composed of two sub-models In CSO, one can decide how many cats are used in the iteration Every cat has its' own position composed of M dimensions, velocities for each dimension, a fitness value which represents the accommodation of the cat to the fitness function, and a flag to identify whether the cat is in seeking mode or tracing mode The final solution would be the best position of one of the cats CSO keeps the best solution until it reaches the end of the iteration The results of the proposed CSO based approach have been compared to those of other well-known optimization methods such as Real Coded Genetic Algorithm (RGA), standard Particle Swarm Optimization (PSO) and Differential Evolution (DE) The CSO based results confirm the superiority of the proposed CSO for solving FIR filter design problems The performances of the CSO based designed FIR filters have proven to be superior as compared to those obtained by RGA, conventional PSO and DE The simulation results also demonstrate that the CSO is the best optimizer among other relevant techniques, not only in the convergence speed but also in the optimal performances of the designed filters

Cat Swarm Optimization algorithm for optimal linear phase FIR filter design.

Adaptive Simulated Annealing (ASA) is a C-language code that finds the best global fit of a nonlinear cost-function over a D-dimensional space. ASA has over 100 OPTIONS to provide robust tuning over many classes of nonlinear stochastic systems. These many OPTIONS help ensure that ASA can be used robustly across many classes of systems.

Adaptive Simulated Annealing

Simulated annealing SA algorithm is a popular intelligent optimization algorithm which has been successfully applied in many fields. Parameters’ setting is a key factor for its performance, but it is also a tedious work. To simplify parameters setting, we present a list-based simulated annealing LBSA algorithm to solve traveling salesman problem TSP. LBSA algorithm uses a novel list-based cooling schedule to control the decrease of temperature. Specifically, a list of temperatures is created first, and then the maximum temperature in list is used by Metropolis acceptance criterion to decide whether to accept a candidate solution. The temperature list is adapted iteratively according to the topology of the solution space of the problem. The effectiveness and the parameter sensitivity of the list-based cooling schedule are illustrated through benchmark TSP problems. The LBSA algorithm, whose performance is robust on a wide range of parameter values, shows competitive performance compared with some other state-of-the-art algorithms.

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List-Based Simulated Annealing Algorithm for Traveling Salesman Problem

Despite the success statistical physics has enjoyed at predicting the properties of materials for given parameters, the inverse problem, identifying which material parameters produce given, desired properties, is only beginning to be addressed. Recently, several methods have emerged across disciplines that draw upon optimization and simulation to create computer programs that tailor material responses to specified behaviors. However, so far the methods developed either involve black-box techniques, in which the optimizer operates without explicit knowledge of the material’s configuration space, or require carefully tuned algorithms with applicability limited to a narrow subclass of materials. Here we introduce a formalism that can generate optimizers automatically by extending statistical mechanics into the realm of design. The strength of this approach lies in its capability to transform statistical models that describe materials into optimizers to tailor them. By comparing against standard black-box optimization methods, we demonstrate how optimizers generated by this formalism can be faster and more effective, while remaining straightforward to implement. The scope of our approach includes possibilities for solving a variety of complex optimization and design problems concerning materials both in and out of equilibrium.

https://www.pnas.org/content/pnas/113/1/34.full.pdf

Turning statistical physics models into materials design engines

Stochastic global optimization is a very important subject, that hasapplications in virtually all areas of science and technology. Therefore there is nothing more opportune than writing a book about a successful and mature algorithm that turned out to be a good tool in solving difficult problems. Here we present some techniques for solving several problems by means of Fuzzy Adaptive Simulated Annealing (Fuzzy ASA), a fuzzy-controlled version of ASA, and by ASA itself. ASA is a sophisticated global optimization algorithm that is based upon ideas of the simulated annealing paradigm, coded in the C programming language and developed to statistically find the best global fit of a nonlinear constrained, non-convex cost function over a multi-dimensional space. By presenting detailed examples of its application we want to stimulate the readers intuition and make the use of Fuzzy ASA (or regular ASA) easier for everyone wishing to use these tools to solve problems. We kept formal mathematical requirements to a minimum and focused on continuous problems, although ASA isable to handle discrete optimization tasks as well. This book can be used by researchers and practitioners in engineering and industry, in courses on optimization for advanced undergraduate and graduate levels, and also for self-study.

Stochastic Global Optimization and Its Applications with Fuzzy Adaptive Simulated Annealing

An alternative approach to digital filter design is presented. The overall technique is as follows: Starting from frequency domain constraints and a parameterized expression of the filter family under adaptation, a corresponding training set is created, an error function is synthesized and a global minimization process is executed. At the end, the point that minimizes globally the particular cost function at hand determines the optimal filter. The adopted numerical optimization algorithm is based upon the well-known simulated annealing paradigm and its implementation is known as fuzzy adaptive simulated annealing. Although it is used in this paper to fit FIR filters to frequency domain specifications, the method is suitable to application in other problems of digital filter design, where the matter under study can be stated as finding the global minimum of a numerical function of filter parameters. Design examples are shown to verify the effectiveness of the proposed approach.

Frequency Domain FIR Filter Design Using Fuzzy Adaptive Simulated Annealing

Solving nonlinear systems of functional equations with fuzzy adaptive simulated annealing

This work proposes a multi-start global optimization algorithm that uses dimensional reduction techniques based upon approximations of space-filling curves and simulated annealing, aiming to find global minima of real-valued (possibly multimodal) functions that are not necessarily well behaved, that is, are not required to be differentiable or continuous. Given a real-valued function with a multidimensional and compact domain, the method builds an equivalent, onedimensional problem by composing it with a space-filling curve (SFC), searches for a small group of candidates and returns to the original higher-dimensional domain, this time with a small set of “promising” starting points. Finally, these points serve as seeds to the algorithm known as Fuzzy Adaptive Simulated Annealing, aiming to find the global optima of the original cost functions. New SFCs are built with basis on the well-known Sierpinski SFC, a subtle modification of a theorem by Hugo Steinhaus and several results of ergodic theory.

Hime A. e Oliveira

Papers

Stochastic Global Optimization and Its Applications with Fuzzy Adaptive Simulated Annealing

Frequency Domain FIR Filter Design Using Fuzzy Adaptive Simulated Annealing

Solving nonlinear systems of functional equations with fuzzy adaptive simulated annealing

Global Optimization Using Space-Filling Curves and Measure-Preserving Transformations

Establishing Nash equilibria of strategic games: a multistart Fuzzy Adaptive Simulated Annealing approach