Linear multiobjective programming

TL;DR: The Origin of the Multiobjective Problem and a Short Historical Review are reviewed and a method for Generating Adjacent Extreme Points - A Second Approach (Multicriteria Simplex Method).

Abstract: 1. Introduction.- 1.1 The Origin of the Multiobjective Problem and a Short Historical Review.- 1.2. Linear Multiobjective Programming.- 1.3. Comment on Notation.- Linear Multibojective Programming I.- 2. Basic Theory and Decomposition of the Parametric Space.- 2.1. Basic Theory - Linear Case.- 2.2. Reduction of the Dimensionality of the Parametric Space.- 2.3. Decomposition of the Parametric Space as a Method to Find Nondominated Extreme Points of X.- 2.4. Algorithmic Possibilities.- 2.5. Discussion of Difficulties connected with the Decomposition Method.- 2.5.1. Some Numerical Examples of the Difficulties.- Linear Multiobjective Programming II.- 3. Finding Nondominated Extreme Points - A Second Approach (Multicriteria Simplex Method).- 3.1. Basic Theorems.- 3.2. Methods for Generating Adjacent Extreme Points.- 3.3 Computerized Procedure - An Example.- 3.4. Computer Analysis.- Linear Multiobjective Programming III.- 4. A Method for Generating All Nondominated Solutions of X..- 4.1. Some Basic Theorems on Properties of N.- 4.2. An Algorithm for Generating N from Known Nex.- 4.3. Numerical Examples.- 4.3.1. An Example of Matrix Reduction.- 4.3.2. An Example of Nondominance Subroutine.- 5. Additional Topics and Extensions.- 5.1. Alternative Approach to Finding Nex.- 5.1.1. The Concept of Cutting Hyperplane.- 5.1.2. Nondominance in Lower Dimensions.- 5.2. Some Notes on Nonlinearity.- 5.3. A Selection of the Final Solution.- 5.3.1. Direct Assessment of Weights.- 5.3.2. The Ideal Solution.- 5.3.3. Entropy as a Measure of Importance.- 5.3.4. A Method of Displaced Ideal.- Appendix:.- A1. A Note on Elimination of Redundant Constraints.- A.2. Examples of Output Printouts.- A.3. The Program Description and FORTRAN Printout.