On compromise solutions in multiple objective programming

2018 ◽  
Vol 52 (2) ◽  
pp. 383-390 ◽  
Author(s):  
Majid Soleimani–Damaneh ◽  
Moslem Zamani
Keyword(s):  
General Setting ◽  
Multiple Objective Programming ◽  
Multiple Objective ◽  
Properly Efficient Solution ◽  
Compromise Solutions ◽  
Image Set ◽  
Objective Programming ◽  
Feasible Points ◽  
Utopia Point ◽  
The Ideal

Compromise solutions, as feasible points as close as possible to the ideal (utopia) point, are important solutions in multiple objective programming. It is known in the literature that each compromise solution is a properly efficient solution if the sum of the image set and conical ordering cone is closed. In this paper, we prove the same result in a general setting without any assumption.

FUZZY MULTIPLE OBJECTIVE PROGRAMMING IN AN INTERVAL PIECEWISE REGRESSION MODEL

2009 ◽  
Vol 17 (03) ◽  
pp. 365-376 ◽  
Author(s):  
JING-RUNG YU ◽  
GWO-HSHIUNG TZENG
Keyword(s):  
Regression Model ◽  
Regression Models ◽  
Heuristic Approach ◽  
Multiple Objective Programming ◽  
Change Points ◽  
Multiple Objective ◽  
Compromise Solution ◽  
Numerical Examples ◽  
Piecewise Regression ◽  
Objective Programming

This study proposes fuzzy multiple objective programming to determine the measure of fitness and the number of change-points in an interval piecewise regression model. To increase the measure of fitness, Tanaka and Lee proposed a conceptual procedure, which is a heuristic approach and becomes complicated for determining the proper polynomial. Therefore, a multiple objective approach is adopted to obtain a compromise solution among three objectives — maximizing the measure of fitness, minimizing the number of change-points and minimizing the width to obtain the interval regression models. By using the proposed method, a better measure of fitness can be obtained. Two numerical examples are used as demonstrations to illustrate our approach in more detail.

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