A representation of an efficiency equivalent polyhedron for the objective set of a multiple objective linear program

DOI10.1016/0377-2217(93)E0247-UzbMath0928.90080OpenAlexW2095537371MaRDI QIDQ1129976

Ossama A. Saleh, Richard J. Gallagher

Publication date: 9 January 2000

Published in: European Journal of Operational Research (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0377-2217(93)e0247-u

zbMATH Keywords

multiple objective linear programminglinear \(k\)-objective minimizationobjective space analysis

Mathematics Subject Classification ID

Multi-objective and goal programming (90C29) Linear programming (90C05)

Related Items (10)

Efficient solution generation for multiple objective linear programming based on extreme ray generation method ⋮ ON THE PROJECTION OF THE EFFICIENT SET AND POTENTIAL APPLICATIONS ⋮ Unnamed Item ⋮ Outcome-based algorithm for optimizing over the efficient set of a bicriteria linear programming problem ⋮ Constructing efficient solutions structure of multiobjective linear programming ⋮ Hybrid approach for solving multiple-objective linear programs in outcome space ⋮ A combined constraint-space, objective-space approach for determining high-dimensional maximal efficient faces of multiple objective linear programs ⋮ Outcome space partition of the weight set in multiobjective linear programming ⋮ Branch-and-bound variant of an outcome-based algorithm for optimizing over the efficient set of a bicriteria linear programming problem ⋮ On degeneracy and collapsing in the construction of the set of objective values in a multiple objective linear program

Uses Software

• ADBASE
• EFFACET

Cites Work

• A characterisation of the feasible set of objective function vectors in linear multiple objective problems
• Constructing the set of efficient objective values in multiple objective linear programs
• Analysis of the objective space in multiple objective linear programming
• An analytical comparison of different formulations of the travelling salesman problem
• A representation of the set of feasible objectives in multiple objective linear programs
• The set of all nondominated solutions in linear cases and a multicriteria simplex method
• A general method for determining the set of all efficient solutions to a linear vectormaximum problem
• Generating all maximal efficient faces for multiple objective linear programs
• Determination of the efficient set in multiobjective linear programming
• Constructing the set of efficient objective values in linear multiple objective transportation problems
• A new algorithm to find all vertices of a polytope
• The Complexity of Vertex Enumeration Methods
• Polarities Given by Systems of Bilinear Inequalities
• Computational results on an algorithm for finding all vertices of a polytope
• A Survey and Comparison of Methods for Finding All Vertices of Convex Polyhedral Sets
• Identifying Efficient Vectors: Some Theory and Computational Results
• Polyhedral polarity defined by a general bilinear inequality
• The Enumeration of the Set of All Efficient Solutions for a Linear Multiple Objective Program
• Finding all efficient extreme points for multiple objective linear programs
• Blocking and Antiblocking Polyhedra
• A revised simplex method for linear multiple objective programs
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