Items related to Multicriteria Optimization
Synopsis
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
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