With the high demand and the critical situation of solving hard optimization problems we are facing in social, environment, bioinformatics, traffic, and indus-trial systems, the development of more efficient novel optimization solutions has been a serious challenge to academic and practical societies in an information-rich era. In addition to the traditional math-programming-inspired optimiza-tion solutions, computational intelligence has been playing an important role in developing novel optimization solutions for practical applications. On the basis of the features of system complexity, a new general-purpose heuristic for finding high-quality solutions to NP-hard (nondeterministic polynomial-time) optimi-zation problems, the so-called “extremal optimization (EO),” was proposed by Boettcher and Percus. In principle, this method is inspired by the Bak–Sneppen model of self-organized criticality describing “far-from-equilibrium phenomena,” from statistical physics, a key concept describing the complexity in physical sys-tems. In comparison with other modern heuristics, such as simulated anneal-ing, genetic algorithm (GA), through testing on some popular benchmarks (TSP [traveling salesman problem], coloring, K-SAT, spin glass, etc.) of large-scale combinatory-constrained optimization problems, EO shows superior performance in the convergence and capability of dealing with computational complexity, for example, the phase transition in search dynamics and having much fewer tuning parameters.
The aim of this book is to introduce the state-of-the-art EO solutions from fun-damentals, methodologies, and algorithms to applications based on numerous clas-sic publications and the authors’ recent original research results, and to make EO more popular with multidisciplinary aspects, such as operations research, software, systems control, and manufacturing. Hopefully, this book will promote the move-ment of EO from academic study to practical applications. It should be noted that EO has a strong basic science foundation in statistical physics and bioevolution, but from the application point of view, compared with many other metaheuristics, the application of EO is much simpler, easier, and straightforward. With more studies in EO search dynamics, the hybrid solutions with the marriage of EO and other metaheuristics, and the real-world application, EO will be an additional weapon to deal with hard optimization problems. The contents of this book cover the follow-ing four aspects:
1. General review for real-world optimization problems and popular solutions with a focus on computational complexity, such as “NP-hard” and the “phase transitions” occurring on the search landscape.
2. General introduction to computational extremal dynamics and its applica-tions in EO from principles, mechanisms, and algorithms to the experiments on some benchmark problems such as TSP, spin glass, Max-SAT (maximum satisfiability), and graph partition. In addition, the comparisons of EO with some popular heuristics, for example, simulated annealing and GA, are given through analytical and simulation studies.
3. The studies on the fundamental features of search dynamics and mechanisms in EO with a focus on self-organized optimization, evolutionary probability distribution, and structure features (e.g., backbones) are based on the authors’ recent research results. Moreover, modified extremal optimization (MEO) solutions and memetic algorithms are presented.
4. On the basis of the authors’ research results, the applications of EO and MEO in multiobjective optimization, systems modeling, intelligent control, and production scheduling are presented.
The authors have made great efforts to focus on the development of MEO and its applications, and also present the advanced features of EO in solving NP-hard problems through problem formulation, algorithms, and simulation studies on popular benchmarks and industrial applications. This book can be used as a refer-ence for graduate students, research developers, and practical engineers when they work on developing optimization solutions for those complex systems with hard-ness that cannot be solved with mathematical optimization or other computational intelligence, such as evolutionary computations. This book is divided into the fol-lowing three parts.
Section I: Chapter 1 provides the general introduction to optimization with a focus on computational complexity, computational intelligence, the highlights of EO, and the organization of the book; Chapter 2 introduces the fundamental and numerical examples of extremal dynamics-inspired EO; and Chapter 3 presents the extremal dynamics–inspired self-organizing optimization.
Section II: Chapter 4 covers the development of modified EO, such as pop-ulation-based EO, multistage EO, and modified EO with an extended evolu-tionary probability distribution. Chapter 5 presents the development of memetic algorithms, the integration of EO with other computational intelligence, such as GA, particle swarm optimization (PSO), and artificial bee colony (ABC). Chapter 6 presents the development of multiobjective optimization with extremal dynamics.
Section III includes the applications of EO in nonlinear modeling and predic-tive control, and production planning and scheduling, covered in Chapters 7 and 8, respectively.