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 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 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 book constitutes the refereed proceedings of the 9th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2017 held in Münster, Germany in March 2017. The 33 revised full papers presented together with 13 poster presentations were carefully reviewed and selected from 72 submissions. The EMO 2017 aims to discuss all aspects of EMO development and deployment, including theoretical foundations; constraint handling techniques; preference handling techniques; handling of continuous, combinatorial or mixed-integer problems; local search techniques; hybrid approaches; stopping criteria; parallel EMO models; performance evaluation; test functions and benchmark problems; algorithm selection approaches; many-objective optimization; large scale optimization; real-world applications; EMO algorithm implementations.