Multi-Objective Optimization Problems

This book is aimed at undergraduate and graduate students in applied mathematics or computer science, as a tool for solving real-world design problems. The present work covers fundamentals in multi-objective optimization and applications in mathematical and engineering system design using a new optimization strategy, namely the Self-Adaptive Multi-objective Optimization Differential Evolution (SA-MODE) algorithm. This strategy is proposed in order to reduce the number of evaluations of the objective function through dynamic update of canonical Differential Evolution parameters (population size, crossover probability and perturbation rate). The methodology is applied to solve mathematical functions considering test cases from the literature and various engineering systems design, such as cantilevered beam design, biochemical reactor, crystallization process, machine tool spindle design, rotary dryer design, among others.

Offers an starting point to key concepts related to multi-objective optimization problems Brings a rich variety of applications in Engineering and Mathematics Presents a new optimization strategy, the Self-Adpative Multi-objective Optimization Differential Evolution (SA-MODE) algorithm in which the parameters are dynamically updated during the evolutionary process Gives a broad perspective on different solving methods based on classical and modern approaches

Autorentext

Fran Sérgio Lobato was born in Araguari, Brazil, in 1976. He received his Chemical Engineering degree, his MSc in Chemical Engineering and his PhD degree in Mechanical Engineering, all from the Federal University of Uberlândia, Brazil, in 2001, 2004 and 2008, respectively. During the year of 2009 he worked in the Federal University of São João Del Rei, Brazil. Since 2010, he has been Assistant Professor at the School of Chemical Engineering of the Federal University of Uberlândia. His current research interests include bio-inspired optimization algorithms, optimal control theory, reliability and robust optimization, and inverse problems.

Valder Steffen Jr. was born in Rio Claro, Brazil, in 1952. He received his degree on Mechanical Engineering from University of Campinas - Unicamp, Brazil, in 1976. Then, his doctorate and his Habilitation (H.D.R) were both obtained from the Franche-Comté University (Besançon, France) in 1979 and 1991, respectively. His current position is Professor of Mechanical Engineering, School of Mechanical Engineering at the Federal University of Uberlândia, Brazil. His research interests include dynamics of mechanical systems, optimization algorithms, smart structures and materials, and inverse problems in engineering sciences. Prof. Steffen is member of the following professional societies: ABCM, SEM, ABMEC and SBMAC.

Klappentext

Zusammenfassung

This book is aimed at undergraduate and graduate students in applied mathematics or computer science, as a tool for solving real-world design problems. The present work covers fundamentals in multi-objective optimization and applications in mathematical and engineering system design using a new optimization strategy, namely the Self-Adaptive Multi-objective Optimization Differential Evolution (SA-MODE) algorithm. This strategy is proposed in order to reduce the number of evaluations of the objective function through dynamic update of canonical Differential Evolution parameters (population size, crossover probability and perturbation rate). The methodology is applied to solve mathematical functions considering test cases from the literature and various engineering systems design, such as cantilevered beam design, biochemical reactor, crystallization process, machine tool spindle design, rotary dryer design, among others.

Inhalt

Chapter 1 Introduction.- Part 1 Basic Concepts.- Chapter 2 Multi-objective Optimization Problem.- Chapter 3 Treatment of multi-objective Optimization Problem.- Part 2 Methodology.- Chapter 4 Self-Adaptive Multi-objective Optimization Differential Evolution.- Part 3 Applications.- Chapter 5 Mathematical.- Chapter 6 Engineering.- Part 4 Final Considerations.- Chapter 7 Conclusions.