Trade-off rates in the hyperplane method for multiobjective optimization problems
type: Item
instance of: scholarly article
title: Trade-off rates in the hyperplane method for multiobjective optimization problems
zbMATH Open document ID: 0696.90064
DOI: 10.1016/0377-2217(90)90319-7
author: Masatoshi Sakawa
author: Hitoshi Yano
published in: European Journal of Operational Research
publication date: 1990-01-01T00:00:00Z
review text: In a recent paper [ibid. 39, No.1, 61-70 (1989; Zbl 0677.90069)] the authors proposed a fully integrated scalarizing method, called hyperplane method. In this paper they develop a meaningful formula which relates the trade-off rates within the Pareto optimal solution set to the Lagrange multipliers of the hyperplane method. It is shown that such a formula can be regarded as a generalized version of the trade-off rate formulae for all of the well-known scalarizing problems. A numerical example illustrates the various aspects of the results developed in this paper.
Mathematics Subject Classification ID: 90C31
zbMATH DE Number: 4141813
zbMATH Keywords: scalarizing method
zbMATH Keywords: hyperplane method
zbMATH Keywords: Pareto optimal solution set
zbMATH Keywords: Lagrange multipliers
reviewed by: I. M. Stancu-Minasian
MaRDI profile type: Publication
full work available at URL: 0377-2217(90)90319-7
OpenAlex ID: W2042600086
cites work: Q4139985
cites work: Q3039055
cites work: Introduction to sensitivity and stability analysis in nonlinear programming
cites work: Kuhn-Tucker multipliers as trade-offs in multiobjective decision-making analysis
cites work: An interactive fuzzy satisficing method using augmented minimax problems and its application to environmental systems
cites work: Multiple criteria decision analysis in regional planning. Concepts, methods and applications
cites work: Q3804472
cites work: A unified approach for characterizing Pareto optimal solutions of multiobjective optimization problems: The hyperplane method
Recommended article: Generalized hyperplane methods for characterizing \(\Lambda\)-extreme points and trade-off rates for multiobjective optimization problems
Recommended article: Trade-off ratio functions for linear and piecewise linear multi-objective optimization problems
Recommended article: Tradeoff directions in multiobjective optimization problems
Recommended article: Trade-off in multiobjective optimization
Recommended article: Q3337207
Recommended article: Generalized trade-off directions in multiobjective optimization problems
Recommended article: Q4322781
Recommended article: Q3483094
Recommended article: Tradeoff oriented solutions in multicriteria optimization
Recommended article: A unified approach for characterizing Pareto optimal solutions of multiobjective optimization problems: The hyperplane method
description: scientific article; zbMATH DE number 4141813