This book presents adaptive solution methods for multiobjective optimization problems based on parameter dependent scalarization approaches. Readers will benefit from the new adaptive methods and ideas for solving multiobjective optimization.

Recent results on non-convex multi-objective optimization problems and methods are presented in this book, with particular attention to expensive black-box objective functions. Multi-objective optimization methods facilitate designers, engineers, and researchers to make decisions on appropriate trade-offs between various conflicting goals. A variety of deterministic and stochastic multi-objective optimization methods are developed in this book. Beginning with basic concepts and a review of non-convex single-objective optimization problems; this book moves on to cover multi-objective branch and bound algorithms, worst-case optimal algorithms (for Lipschitz functions and bi-objective problems), statistical models based algorithms, and probabilistic branch and bound approach. Detailed descriptions of new algorithms for non-convex multi-objective optimization, their theoretical substantiation, and examples for practical applications to the cell formation problem in manufacturing engineering, the process design in chemical engineering, and business process management are included to aide researchers and graduate students in mathematics, computer science, engineering, economics, and business management.

This book presents an overview of archiving strategies developed over the last years by the authors that deal with suitable approximations of the sets of optimal and nearly optimal solutions of multi-objective optimization problems by means of stochastic search algorithms. All presented archivers are analyzed with respect to the approximation qualities of the limit archives that they generate and the upper bounds of the archive sizes. The convergence analysis will be done using a very broad framework that involves all existing stochastic search algorithms and that will only use minimal assumptions on the process to generate new candidate solutions. All of the presented archivers can effortlessly be coupled with any set-based multi-objective search algorithm such as multi-objective evolutionary algorithms, and the resulting hybrid method takes over the convergence properties of the chosen archiver. This book hence targets at all algorithm designers and practitioners in the field of multi-objective optimization.

This book provides an introduction to vector optimization with variable ordering structures, i.e., to optimization problems with a vector-valued objective function where the elements in the objective space are compared based on a variable ordering structure: instead of a partial ordering defined by a convex cone, we see a whole family of convex cones, one attached to each element of the objective space. The book starts by presenting several applications that have recently sparked new interest in these optimization problems, and goes on to discuss fundamentals and important results on a wide range of topics. The theory developed includes various optimality notions, linear and nonlinear scalarization functionals, optimality conditions of Fermat and Lagrange type, existence and duality results. The book closes with a collection of numerical approaches for solving these problems in practice.

This volume encloses research articles that were presented at the EVOLVE 2014 International Conference in Beijing, China, July 1–4, 2014. The book gathers contributions that emerged from the conference tracks, ranging from probability to set oriented numerics and evolutionary computation; all complemented by the bridging purpose of the conference, e.g. Complex Networks and Landscape Analysis, or by the more application oriented perspective. The novelty of the volume, when considering the EVOLVE series, comes from targeting also the practitioner’s view. This is supported by the Machine Learning Applied to Networks and Practical Aspects of Evolutionary Algorithms tracks, providing surveys on new application areas, as in the networking area and useful insights in the development of evolutionary techniques, from a practitioner’s perspective. Complementary to these directions, the conference tracks supporting the volume, follow on the individual advancements of the subareas constituting the scope of the conference, through the Computational Game Theory, Local Search and Optimization, Genetic Programming, Evolutionary Multi-objective optimization tracks.

This volume consists of chapters written by eminent scientists and engineers from the international community and present significant advances in several theories, methods and applications of an interdisciplinary research. These contributions focus on both old and recent developments of Global Optimization Theory, Convex Analysis, Calculus of Variations, Discrete Mathematics and Geometry, as well as several applications to a large variety of concrete problems, including applications of computers to the study of smoothness and analyticity of functions, applications to epidemiological diffusion, networks, mathematical models of elastic and piezoelectric fields, optimal algorithms, stability of neutral type vector functional differential equations, sampling and rational interpolation for non-band-limited signals, recurrent neural network for convex optimization problems and experimental design. The book also contains some review works, which could prove particularly useful for a broader audience of readers in Mathematical and Engineering subjects and especially to graduate students who search for the latest information.

This book presents the latest algorithmic developments in the cell-mapping method for the global analysis of nonlinear dynamic systems, global solutions for multi-objective optimization problems, and global solutions for zeros of complex algebraic equations. It also discusses related engineering and scientific applications, including the nonlinear design of structures for better vibration resistance and reliability; multi-objective, structural-acoustic design for sound abatement; optimal multi-objective design of airfoils for better lift; and optimal multi-objective design of linear and nonlinear controls with or without time delay. The first book on the subject to include extensive Matlab and C++ codes, it presents various implementation algorithms of the cell-mapping method, enabling readers to understand how the method works and its programming aspects. A link to the codes on the Springer website will be provided to the readers.

This book features 15 chapters based on the Numerical and Evolutionary Optimization (NEO 2017) workshop, held from September 27 to 29 in the city of Tijuana, Mexico. The event gathered researchers from two complimentary fields to discuss the theory, development and application of state-of-the-art techniques to address search and optimization problems. The lively event included 7 invited talks and 64 regular talks covering a wide range of topics, from evolutionary computer vision and machine learning with evolutionary computation, to set oriented numeric and steepest descent techniques. Including research submitted by the NEO community, the book provides informative and stimulating material for future research in the field.

This book presents a collection of papers on recent advances in problems concerning dynamics, optimal control and optimization. In many chapters, computational techniques play a central role. Set-oriented techniques feature prominently throughout the book, yielding state-of-the-art algorithms for computing general invariant sets, constructing globally optimal controllers and solving multi-objective optimization problems.

This proceedings set contains 85 selected full papers presented at the 3rd International Conference on Modelling, Computation and Optimization in Information Systems and Management Sciences - MCO 2015, held on May 11–13, 2015 at Lorraine University, France. The present part I of the 2 volume set includes articles devoted to Combinatorial optimization and applications, DC programming and DCA: thirty years of Developments, Dynamic Optimization, Modelling and Optimization in financial engineering, Multiobjective programming, Numerical Optimization, Spline Approximation and Optimization, as well as Variational Principles and Applications.