On degeneracy and collapsing in the construction of the set of objective values in a multiple objective linear program

DOI10.1007/BF02023100zbMath0796.90046MaRDI QIDQ1312767

Jerald P. Dauer

Publication date: 26 September 1994

Published in: Annals of Operations Research (Search for Journal in Brave)

zbMATH Keywords

convex polytopecollapsingmultiple objective linear programdegeneracy graph

Mathematics Subject Classification ID

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

Related Items (8)

A geometrical analysis of the efficient outcome set in multiple objective convex programs with linear criterion functions ⋮ Unnamed Item ⋮ Outcome-based algorithm for optimizing over the efficient set of a bicriteria linear programming problem ⋮ Reducing wall-clock time for the computation of all efficient extreme points in multiple objective linear programming ⋮ Primal and dual algorithms for optimization over the efficient set ⋮ 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 ⋮ A weight set decomposition algorithm for finding all efficient extreme points in the outcome set of a multiple objective linear program

Cites Work

• Unnamed Item
• Solving multiple objective linear programs in objective space
• On the structure of the set bases of a degenerate point
• Constructing the set of efficient objective values in multiple objective linear programs
• Degeneracy graphs and the neighbourhood problem
• Analysis of the objective space in multiple objective linear programming
• Survey of solved and open problems in the degeneracy phenomenon
• A representation of an efficiency equivalent polyhedron for the objective set of a multiple objective linear program
• A multiobjective optimization model for water resources planning
• An all-linear programming relaxation algorithm for optimizing over the efficient set
• A new pivoting rule for solving various degeneracy problems
• A general method for determining the set of all efficient solutions to a linear vectormaximum problem
• Towards an algebraic characterization of convex polyhedral cones
• Optimization over the efficient set using an active constraint approach
• Algorithms for frames and lineality spaces of cones
• Optimization over the efficient set

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