Solution Methods For Multi Objective Robust Combinatorial Optimization

This thesis addresses combinatorial optimization problems with several objectives containing uncertain parameters. A variety of robustness concepts for multi-objective optimization problems have been developed during the last years. This thesis provides methods to find so-called robust efficient solutions with respect to several of these concepts, assuming the uncertain parameters to be given via common uncertainty sets. Several solution approaches are presented, including extensions and combinations of algorithms from both robust and multi-objective optimization, using properties of partic...

Multi-Objective Combinatorial Optimization Problems and Solution Methods discusses the results of a recent multi-objective combinatorial optimization achievement that considered metaheuristic, mathematical programming, heuristic, hyper heuristic and hybrid approaches. In other words, the book presents various multi-objective combinatorial optimization issues that may benefit from different methods in theory and practice. Combinatorial optimization problems appear in a wide range of applications in operations research, engineering, biological sciences and computer science, hence many optimization approaches have been developed that link the discrete universe to the continuous universe through geometric, analytic and algebraic techniques. This book covers this important topic as computational optimization has become increasingly popular as design optimization and its applications in engineering and industry have become ever more important due to more stringent design requirements in modern engineering practice. Presents a collection of the most up-to-date research, providing a complete overview of multi-objective combinatorial optimization problems and applications Introduces new approaches to handle different engineering and science problems, providing the field with a collection of related research not already covered in the primary literature Demonstrates the efficiency and power of the various algorithms, problems and solutions, including numerous examples that illustrate concepts and algorithms

Multiobjective optimization deals with solving problems having not only one, but multiple, often conflicting, criteria. Such problems can arise in practically every field of science, engineering and business, and the need for efficient and reliable solution methods is increasing. The task is challenging due to the fact that, instead of a single optimal solution, multiobjective optimization results in a number of solutions with different trade-offs among criteria, also known as Pareto optimal or efficient solutions. Hence, a decision maker is needed to provide additional preference information and to identify the most satisfactory solution. Depending on the paradigm used, such information may be introduced before, during, or after the optimization process. Clearly, research and application in multiobjective optimization involve expertise in optimization as well as in decision support. This state-of-the-art survey originates from the International Seminar on Practical Approaches to Multiobjective Optimization, held in Dagstuhl Castle, Germany, in December 2006, which brought together leading experts from various contemporary multiobjective optimization fields, including evolutionary multiobjective optimization (EMO), multiple criteria decision making (MCDM) and multiple criteria decision aiding (MCDA). This book gives a unique and detailed account of the current status of research and applications in the field of multiobjective optimization. It contains 16 chapters grouped in the following 5 thematic sections: Basics on Multiobjective Optimization; Recent Interactive and Preference-Based Approaches; Visualization of Solutions; Modelling, Implementation and Applications; and Quality Assessment, Learning, and Future Challenges.

This book introduces a fairly universal approach to the design and analysis of exact optimization algorithms for multi-objective combinatorial optimization problems. It proposes the circuits without repetitions representing the sets of feasible solutions along with the increasing and strictly increasing cost functions as a model for such problems. The book designs the algorithms for multi-stage and bi-criteria optimization and for counting the solutions in the framework of this model. As applications, this book studies eleven known combinatorial optimization problems: matrix chain multiplication, global sequence alignment, optimal paths in directed graphs, binary search trees, convex polygon triangulation, line breaking (text justification), one-dimensional clustering, optimal bitonic tour, segmented least squares, optimization of matchings in trees, and 0/1 knapsack problem. The results presented are useful for researchers in combinatorial optimization. This book is also useful as the basis for graduate courses.

Stochastic Local Search algorithms were shown to give state-of-the-art results for many other problems, but little is known on how to design and analyse them for Multiobjective Combinatorial Optimization Problems. This book aims to fill this gap. It defines two search models that correspond to two distinct ways of tackling MCOPs by SLS algorithms."

This book discusses the basic ideas, underlying principles, mathematical formulations, analysis and applications of the different combinatorial problems under uncertainty and attempts to provide solutions for the same. Uncertainty influences the behaviour of the market to a great extent. Global pandemics and calamities are other factors which affect and augment unpredictability in the market. The intent of this book is to develop mathematical structures for different aspects of allocation problems depicting real life scenarios. The novel methods which are incorporated in practical scenarios under uncertain circumstances include the STAR heuristic approach, Matrix geometric method, Ranking function and Pythagorean fuzzy numbers, to name a few. Distinct problems which are considered in this book under uncertainty include scheduling, cyclic bottleneck assignment problem, bilevel transportation problem, multi-index transportation problem, retrial queuing, uncertain matrix games, optimal production evaluation of cotton in different soil and water conditions, the healthcare sector, intuitionistic fuzzy quadratic programming problem, and multi-objective optimization problem. This book may serve as a valuable reference for researchers working in the domain of optimization for solving combinatorial problems under uncertainty. The contributions of this book may further help to explore new avenues leading toward multidisciplinary research discussions.

This volume constitutes the proceedings of the Fifth International Conference on Multi-Objective Programming and Goal Programming: Theory & Appli cations (MOPGP'02) held in Nara, Japan on June 4-7, 2002. Eighty-two people from 16 countries attended the conference and 78 papers (including 9 plenary talks) were presented. MOPGP is an international conference within which researchers and prac titioners can meet and learn from each other about the recent development in multi-objective programming and goal programming. The participants are from different disciplines such as Optimization, Operations Research, Math ematical Programming and Multi-Criteria Decision Aid, whose common in terest is in multi-objective analysis. The first MOPGP Conference was held at Portsmouth, United Kingdom, in 1994. The subsequent conferenes were held at Torremolinos, Spain in 1996, at Quebec City, Canada in 1998, and at Katowice, Poland in 2000. The fifth conference was held at Nara, which was the capital of Japan for more than seventy years in the eighth century. During this Nara period the basis of Japanese society, or culture established itself. Nara is a beautiful place and has a number of historic monuments in the World Heritage List. The members of the International Committee of MOPGP'02 were Dylan Jones, Pekka Korhonen, Carlos Romero, Ralph Steuer and Mehrdad Tamiz.

This text offers many multiobjective optimization methods accompanied by analytical examples, and it treats problems not only in engineering but also operations research and management. It explains how to choose the best method to solve a problem and uses three primary application examples: optimization of the numerical simulation of an industrial process; sizing of a telecommunication network; and decision-aid tools for the sorting of bids.

This volume constitutes the proceedings of the Fifth International Conference on Multi-Objective Programming and Goal programming held in Nara Japan 2002. The book is dedicated to multi-objective methods in decision making. One half of the book is devoted to theoretical aspects, covering a broad range of multi-objective methods such as multiple linear programming, fuzzy goal programming, data envelopment analysis, game theory, and dynamic programming. Readers interested in practical applications, will find in the remaining parts a variety of approaches applied in numerous fields including production planning, logistics, marketing, and finance.