A regression study of the number of efficient extreme points in multiple objective linear programming

A regression study of the number of efficient extreme points in multiple objective linear programming

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Article ID: iaor2006365
Country: Netherlands
Volume: 162
Issue: 2
Start Page Number: 484
End Page Number: 496
Publication Date: Apr 2005
Journal: European Journal of Operational Research
Authors: ,
Keywords: programming: linear, statistics: regression
Abstract:

In this paper we employ regression analysis to construct relationships for predicting the number of efficient extreme points in MOLPs (multiple objective linear programs) with up to 120,000 efficient extreme points, and the CPU time to compute them. Principal among the factors affecting the number of efficient extreme points and CPU time are the number of objectives, criterion cone size, number of constraints, number of variables, and nonzero density of the constraint matrix. The regression equations show the degree to which interactions are present among the factors and provide a more formal basis for understanding how the complexity of the efficient set, an indicator of the difficulty involved in solving a multiple criteria problem, increases with problem size.

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