Antonio Petraglia

Adaptive Simulated Annealing

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.

Stochastic Global Optimization and Its Applications with Fuzzy Adaptive Simulated Annealing - Volume 35

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.

Global Optimization and Its Applications

In this chapter we will introduce ideas about global optimization methods, their types and limitations, exposing, in a succint way, several of their main characteristics. As our focus in this book will be on adaptive simulated annealing and its applications, we’ll start to pave the way that will take us to pragmatic utilization of that method and stochastic optimization methods, in general.

Nonlinear Equation Solving

This chapter introduces a global optimization approach for finding solutions of nonlinear systems of functional equations using Fuzzy ASA. The original problem is transformed into a global optimization one by synthesizing objective functions whose global minima, if any, are also solutions to the original system. The global minimization process is triggered from different starting points so as to find as many solutions as possible. To demonstrate its utility, the method is applied to several types of equations, presenting very good results. The equation systems are composed of n equations on n-dimensional Euclidean spaces.

Space-Filling Curves and Fuzzy ASA

This chapter introduces a multi-start global optimization algorithm that uses dimensional reduction techniques based upon approximations of space-filling curves and fuzzy adaptive simulated annealing, aiming at finding global minima of real-valued (possibly multimodal) functions that are not necessarily well behaved, that is, are not required to be differentiable, continuous, or even satisfying Lipschitz conditions. The overall idea is as follows: 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, 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. In this fashion, it is possible to overcome difficulties related to capture in inconvenient attraction basins and, simultaneously, to bypass the complexity associated to finding the global minimum of the auxiliary one dimensional problem, whose graph is typically fractal-like, as we shall see along the chapter. New space-filling curves 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.

Applications to Signal Processing - Blind Source Separation

In this chapter an alternative method to make independent component analysis and source separation is introduced. It is based upon Fuzzy Adaptive Simulated Annealing and uses mainly mutual information measures to achieve its final goals. After presenting the central arguments of the method, some experimental results are shown and comparison to previous work is done.

Fuzzy Modeling with Fuzzy Adaptive Simulated Annealing

Data-based fuzzy system modeling usually depends on effective optimization methods to fit experimental data to parametric fuzzy models. Here, an approach that uses Takagi-Sugeno models and Adaptive Simulated Annealing (ASA) is presented and discussed, showing that (Fuzzy) ASA could also be helpful in such a kind of task. The problem to solve is well-defined - given a training set containing a finite number of input-output pairs, construct a fuzzy system approximating the behavior of the actual system that originated that set, within a pre-established precision. Such an approximation must have generalization ability to be useful in the real world, considering the finiteness of the training set and other constraints. Besides, other suggestions for application of (Fuzzy) ASA to fuzzy logic related problems are offered.

Statistical Estimation and Global Optimization

A very popular method for the estimation of probability density functions (PDFs) associated to a set of random samples of a given population or process is the so-called Maximum Likelihood Estimation Method, based upon the premise that the best estimative for the set of parameters corresponding to the actual PDF of the population under study is that one maximizing the likelihood function, relative to that set of sample points. To find global maximizers for that function it is common practice to submit it, or its logarithm, to gradient based deterministic algorithms, aiming at better numerical conditioning. The present work presents an alternative approach to obtain the global maximum, based on Fuzzy ASA. After a brief theoretical introduction, several experimental results will be presented to illustrate the effectiveness of the proposed method.