Decision makers in many areas, from industry to engineering and the social sector, face an increasing need to consider multiple, conflicting objectives in their decision processes. In many cases these real world decision problems can be formulated as multicriteria mathematical optimization models. The solution of such models requires appropriate techniques to compute so called efficient, or Pareto optimal, or compromise solutions that - unlike traditional mathematical programming methods - take the contradictory nature of the criteria into account. This book provides the necessary mathematical foundation of multicriteria optimization to solve nonlinear, linear and combinatorial problems with multiple criteria. Motivational examples illustrate the use of multicriteria optimization in practice. Numerous illustrations and exercises as well as an extensive bibliography are provided. In the new edition a chapter on optimality conditions has been added. The linear programming part has been extended and includes new developments. Moreover, motivational examples are now introducing the majority of chapters. Decision makers in many areas, from industry to engineering and the social sector, face an increasing need to consider multiple, conflicting objectives in their decision processes. In many cases these real world decision problems can be formulated as multicriteria mathematical optimization models. The solution of such models requires appropriate techniques to compute so called efficient, or Pareto optimal, or compromise solutions that - unlike traditional mathematical programming methods - take the contradictory nature of the criteria into account. This book provides the necessary mathematical foundation of multicriteria optimization to solve nonlinear, linear and combinatorial problems with multiple criteria. Motivational examples illustrate the use of multicriteria optimization in practice. Numerous illustrations and exercises as well as an extensive bibliography are provided. In the new editiona chapter on optimality conditions has been added. The linear programming part has been extended andincludesnew developments. Moreover,motivational examples are nowintroducing the majority ofchapters. TOC:Multicriteria Optimization:Introduction.-Efficient Solutions and Nondominated Points.- Optimality Conditions.-Weighted Sum Scalarization.-Other Scalarization Methods.-Nonscalarizing Techniques.-Multiobjective Linear Programming:Introduction.- Simplex Based Techniques.-Solving MOLPs in Objective Space.-Other Methods.- Multiobjective Combinatorial Optimization:Introduction.-General Purpose Methods.- Special Purpose Methods.-(Meta)Heuristics "This book provides the necessary mathematical foundation of multicriteria optimization to solve nonlinear, linear and combinatorial problems with multiple criteria. Motivational examples, illustrate the use of multicriteria optimization in practice. Numerous illustrations and exercises as well as an extensive bibliography are provided." "In the new edition a section on optimality conditions has been added. Additional scalarization techniques have been introduced and the chapters on multiobjective linear programming and multiobjective combinatorial optimization have been extended and spread over several chapters. A "Notes" section has been added to each chapter for further links to relevant literature and recent developments. The bibliography has more than doubled."--BOOK JACKET Content: Efficiency and nondominance -- The weighted sum method and related topics -- Scalarization techniques -- Other definitions of opimality : nonscalarizating methods -- Introduction to multicriteria linear programming -- A multiobjective simplex method -- Multiobjective combinatorial optimization -- Multiobjective versions of polynomially solvable problems -- Multiobjective versions of some NP-hard problems.
- Collection Of Results Of Multicriteria Optimization, Including Nonlinear, Linear And Combinatorial Optimization Problems
- Includes Numerous Illustrations, Examples And Problems
