Parametric Programming Approaches to Local Approximation of the Efficient Frontier

1993 ◽  
pp. 88-100 ◽  
Author(s):  
Janusz Granat
Keyword(s):  
Efficient Frontier ◽  
Parametric Programming ◽  
Local Approximation

Local Approximation of the Efficient Frontier in Robust Design

2000 ◽  
Vol 122 (2) ◽  
pp. 232-236 ◽  
Author(s):  
Jinhuan Zhang ◽  
Margaret M. Wiecek ◽  
Wei Chen
Keyword(s):  
Robust Design ◽  
Optimization Problem ◽  
Design Procedure ◽  
Efficient Frontier ◽  
Local Approximation ◽  
Preference Structure ◽  
Design Problems ◽  
Efficient Frontiers ◽  
Computationally Expensive ◽  
Preference Structures

The problem of robust design is treated as a bi-objective optimization problem in which the performance mean and variation are optimized and minimized, respectively. A method for deriving a utility function as a local approximation of the efficient frontier is presented and investigated at different locations of candidate solutions, with different ranges of interest, and for efficient frontiers with both convex and nonconvex behaviors. As an integral part of the interactive robust design procedure earlier proposed by the authors, the method assists designers in adjusting the preference structure and exploring alternative efficient robust design solutions. It eliminates the need of solving the bi-objective problem repeatedly using new preference structures, which is often computationally expensive. Though demonstrated for robust design problems, the principle is also applicable to any bi-objective optimization problem. [S1050-0472(00)00702-9]

DEVELOPMENTS OF THE LOCAL APPROXIMATION FOR DISORDERED SYSTEMS

1972 ◽  
Vol 33 (C3) ◽  
pp. C3-135-C3-143 ◽  
Author(s):  
W. KOHN ◽  
J. OLSON
Keyword(s):  
Disordered Systems ◽  
Local Approximation

Interactive multiobjective DEA target setting using lexicographic DDF

2020 ◽  
Vol 54 (6) ◽  
pp. 1703-1722 ◽  
Author(s):  
Narges Soltani ◽  
Sebastián Lozano
Keyword(s):  
Efficient Frontier ◽  
Directional Distance Function ◽  
Fixed Number ◽  
Optimization Approach ◽  
Target Setting ◽  
Interactive Process ◽  
Decision Making Unit ◽  
Setting Approach ◽  
Promising Area ◽  
Current Region

In this paper, a new interactive multiobjective target setting approach based on lexicographic directional distance function (DDF) method is proposed. Lexicographic DDF computes efficient targets along a specified directional vector. The interactive multiobjective optimization approach consists in several iteration cycles in each of which the Decision Making Unit (DMU) is presented a fixed number of efficient targets computed corresponding to different directional vectors. If the DMU finds one of them promising, the directional vectors tried in the next iteration are generated close to the promising one, thus focusing the exploration of the efficient frontier on the promising area. In any iteration the DMU may choose to finish the exploration of the current region and restart the process to probe a new region. The interactive process ends when the DMU finds its most preferred solution (MPS).

Weighted inequalities and applications to best local approximation in Luxemburg norm

2004 ◽  
Vol 20 (3) ◽  
pp. 265-280 ◽  
Author(s):  
H. H. Cuenya ◽  
M. D. Lorenzo ◽  
C. N. Rodriguez
Keyword(s):  
Local Approximation ◽  
Weighted Inequalities ◽  
Luxemburg Norm ◽  
Best Local Approximation
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