Life is about decisions. Decisions, no matter if made by a group or an indi­ vidual, involve several conflicting objectives. The observation that real world problems have to be solved optimally according to criteria, which prohibit an "ideal" solution - optimal for each decision-maker under each of the criteria considered - has led to the development of multicriteria optimization. From its first roots, which where laid by Pareto at the end of the 19th century the discipline has prospered and grown, especially during the last three decades. Today, many decision support systems incorporate methods to deal with conflicting objectives. The foundation for such systems is a mathematical theory of optimization under multiple objectives. Fully aware of the fact that there have been excellent textbooks on the topic before, I do not claim that this is better text, but it has a has a consid­ erably different focus. Some of the available books develop the mathematical background in great depth, such as [SNT85, GN90, Jah86). Others focus on a specific structure of the problems covered as [Zel74, Ste85, Mie99) or on methodology [Yu85, CH83a, HM79). Finally there is the area of multicriteria decision aiding [Roy96, Vin92, KR93), the main goal of which is to help deci­ sion makers find the final solution (among many "optimal" ones) eventually to be implemented.

Introduction.- Optimization with Multiple Criteria.-Decision Space and Objective (Criterion) Space.- Notions of Optimality.- Orders and Cones.- Classification of Multicriteria Optimization Problems.- Exercises.- Pareto Optimality and Efficiency.- Pareto Optimal Solutions and Efficient Points.- Weakly and Strictly Pareto Optimal Solutions.- Proper Pareto Optimality and Proper Efficiency.- Exercises.- Weighted Sum Scalarization.- Scalarization and Efficiency.- Scalarization and Weak Efficiency.- Scalarization and Proper Efficiency.- Connectedness of Yeff and XPar.- Exercises.- Other Methods for Pareto Optimality.- Bounds of the Efficient Set.- The E(Epsilon)-Constraint Method.- Benson's Method.- Compromise Solutions - Approximation of the Ideal Point.- Exercises.- Multicriteria Linear Programming.- Introduction.- Theory of Multicriteria Linear Programming.- A Multicriteria Simplex Algorithm.- Identifying Scalarizing Vectors and Pareto Faces.- Exercises.- Other Optimality Concepts.-Lexicographic Optimization.- Max-Ordering Optimization.- Lexicographic Max-Ordering Optimization.- Exercises.- Combinatorial Problems with Multiple Objectives.- Introduction.- Finite Problems: The Case X = E.- The Shortest Path Problem.- The Minimum Spanning Tree Problem and Matroids.- The Assignment Problem.- The Knapsack Problem.- The Travelling Salesperson Problem.- Exercises