Ehrgott M. Multicriteria optimization

Contents.
Introduction.
Optimization with Multiple Criteria.
Decision Space and Objective (Criterion) Space.
Notions of Optimality.
Orders and Cones.
Classification of Multicriteria Optimization Problems.
Efficiency and Nondominance.
Efficient Solutions and Nondominated Points.
Bounds on the Nondominated Set.
Weakly and Strictly Efficient Solutions.
Proper Efficiency and Proper Nondominance.
The Weighted Sum Method and Related Topics.
Weighted Sum Scalarization and (Weak) Efficiency.
Weighted Sum Scalarization and Proper Efficiency.
Optimality Conditions.
Connectedness of Efficient and Nondominated Sets.
Scalarization Techniques.
The ?-Constraint Method.
The Hybrid Method.
The Elastic Constraint Method.
Benson’s Method.
Compromise Solutions – Approximation of the Ideal Point.
The Achievement Function Method.
Other Definitions of Optimality – Nonscalarizing Methods.
Lexicographic Optimality.
Max-Ordering Optimality.
Lexicographic Max-Ordering Optimization.
ntrodcution to Multicriteria Linear Programming.
Notation and Definitions.
The Simplex Method and Biobjective Linear Programs.
A Multiobjective Simplex Method.
Algebra of Multiobjective Linear Programming.
The Geometry of Multiobjective Linear Programming.
Multiobjective Combinatorial Optimization.
Basics.
Problems with Explicitely Given Feasible Set.
Scalarization of Multiobjective Integer Programs.
Multiobjective Versions of Polynomially Solvable Problems.
Algorithms for the Shortest Path Problem.
The Minimum Spanning Tree Problem.
Matroids.
The Assignment Problem and the Two Phase Method.
Multiobjective Versions of Some NP-Hard Problems.
The Knapsack Problem and Branch and Bound.
The Travelling Salesperson Problem and Heuristics.