Search For A Method

From one of the 20th century’s most profound philosophers and writers, comes a thought provoking essay that seeks to reconcile Marxism with existentialism. Exploring the complicated relationship the two philosophical schools of thought have with one another, Sartre supposes that the two are in fact compatible and complimentary towards one another, with poignant analysis and reasoning. An important work of modern philosophy, Search for a Method has a major influence on the current perceptions of existentialism and Marxism. “This is the most important philosophical work by Sartre to be translated since Being and Nothingness.”—James Collings, America

The book is intended for graduate students and researchers in mathematics, computer science, and operational research. The book presents a new derivative-free optimization method/algorithm based on randomly generated trial points in specified domains and where the best ones are selected at each iteration by using a number of rules. This method is different from many other well established methods presented in the literature and proves to be competitive for solving many unconstrained optimization problems with different structures and complexities, with a relative large number of variables. Intensive numerical experiments with 140 unconstrained optimization problems, with up to 500 variables, have shown that this approach is efficient and robust. Structured into 4 chapters, Chapter 1 is introductory. Chapter 2 is dedicated to presenting a two level derivative-free random search method for unconstrained optimization. It is assumed that the minimizing function is continuous, lower bounded and its minimum value is known. Chapter 3 proves the convergence of the algorithm. In Chapter 4, the numerical performances of the algorithm are shown for solving 140 unconstrained optimization problems, out of which 16 are real applications. This shows that the optimization process has two phases: the reduction phase and the stalling one. Finally, the performances of the algorithm for solving a number of 30 large-scale unconstrained optimization problems up to 500 variables are presented. These numerical results show that this approach based on the two level random search method for unconstrained optimization is able to solve a large diversity of problems with different structures and complexities. There are a number of open problems which refer to the following aspects: the selection of the number of trial or the number of the local trial points, the selection of the bounds of the domains where the trial points and the local trial points are randomly generated and a criterion for initiating the line search.

An infinite number of mathematical models can be created to describe naturally occurring physical systems. In addition there is a smaller, but large, number of criteria which can be used to measure the goodness of fit of a model to a physical process. Together, a selected criterion and a mathematical model define an objective function to be optimized.

This brief provides a detailed introduction, discussion and bibliographic review of the nature1-inspired optimization algorithm called Harmony Search. It uses a large number of simulation results to demonstrate the advantages of Harmony Search and its variants and also their drawbacks. The authors show how weaknesses can be amended by hybridization with other optimization methods. The Harmony Search Method with Applications will be of value to researchers in computational intelligence in demonstrating the state of the art of research on an algorithm of current interest. It also helps researchers and practitioners of electrical and computer engineering more generally in acquainting themselves with this method of vector-based optimization.

The fourth book of a four-part series, Design Theory and Methods using CAD/CAE integrates discussion of modern engineering design principles, advanced design tools, and industrial design practices throughout the design process. This is the first book to integrate discussion of computer design tools throughout the design process. Through this book series, the reader will: Understand basic design principles and all digital modern engineering design paradigms Understand CAD/CAE/CAM tools available for various design related tasks Understand how to put an integrated system together to conduct All Digital Design (ADD) product design using the paradigms and tools Understand industrial practices in employing ADD virtual engineering design and tools for product development The first book to integrate discussion of computer design tools throughout the design process Demonstrates how to define a meaningful design problem and conduct systematic design using computer-based tools that will lead to a better, improved design Fosters confidence and competency to compete in industry, especially in high-tech companies and design departments

In this genuinely ground-breaking book the authors argue against the orthodox conception that Descartes had no method. Through a rigorous and thorough examination they unearth and explain the role of the method of analysis in Meditiations.