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.
Efficiency and Nondominance.- The Weighted Sum Method and Related Topics.- Scalarization Techniques.- Other Definitions of Optimality - Nonscalarizing Methods.- Introdcution to Multicriteria Linear Programming.- A Multiobjective Simplex Method.- Multiobjective Combinatorial Optimization.- Multiobjective Versions of Polynomially Solvable Problems.- Multiobjective Versions of Some NP-Hard Problems. The second edition of 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 this new edition, a chapter on optimality conditions has been added. The linear programming part has been extended and includes new developments. And motivational examples have been added to the majority of chapters.
