scholarly journals Gradient-Based Multiobjective Optimization with Uncertainties

2017 ◽  
pp. 159-182 ◽  
Author(s):  
Sebastian Peitz ◽  
Michael Dellnitz
Keyword(s):  
Multiobjective Optimization ◽  
Gradient Based

Multiobjective optimization using an aggregative gradient-based method

2014 ◽  
Vol 51 (1) ◽  
pp. 173-182 ◽  
Author(s):  
Kazuhiro Izui ◽  
Takayuki Yamada ◽  
Shinji Nishiwaki ◽  
Kazuto Tanaka
Keyword(s):  
Multiobjective Optimization ◽  
Gradient Based

Gradient-based multiobjective optimization using a distance constraint technique and point replacement

2015 ◽  
Vol 48 (7) ◽  
pp. 1226-1250 ◽  
Author(s):  
Yuki Sato ◽  
Kazuhiro Izui ◽  
Takayuki Yamada ◽  
Shinji Nishiwaki
Keyword(s):  
Multiobjective Optimization ◽  
Distance Constraint ◽  
Gradient Based

Gradient-Based Multiobjective Optimization for Maximizing Expectation and Minimizing Uncertainty or Risk With Application to Optimal Well-Control Problem With Only Bound Constraints

SPE Journal ◽  
2016 ◽  
Vol 21 (05) ◽  
pp. 1813-1829 ◽  
Author(s):  
Xin Liu ◽  
Albert C. Reynolds
Keyword(s):  
Life Cycle ◽  
Multiobjective Optimization ◽  
Pareto Front ◽  
Net Present Value ◽  
Bound Constraints ◽  
Geological Uncertainty ◽  
Well Control ◽  
Gradient Based ◽  
Normal Boundary ◽  
Nbi Method

Summary We consider two procedures for multiobjective optimization, the classical weighted-sum (WS) method and the normal-boundary-intersection (NBI) method. To enhance computational efficiency, the methods use gradients calculated with the adjoint method. Our objective is to develop implementations that one can apply for waterflooding optimization under geological uncertainty when we wish to develop well controls that satisfy two objectives: The first is to maximize the expectation of life-cycle net present value (NPV) (commonly referred to as robust optimization), and the second is either to minimize the standard deviation of NPV over that set of plausible reservoir descriptions or to minimize the risk when risk means downside risk. Specifically, minimizing risk refers to maximizing the minimum value of the life-cycle NPV (i.e., is equivalent to a maximum/minimum (max/min) problem). To avoid nondifferentiability issues, we recast the max/min problem as a constrained optimization problem and apply a gradient-based version of either WS or NBI to construct a point on the Pareto front. To deal with the constraints introduced, we derive an augmented-Lagrange algorithm to find points on the Pareto front. To the best of our knowledge, the resulting versions of “constrained” WS and “constrained” NBI were not presented previously in the scientific literature. The methodology is demonstrated for two synthetic reservoirs. We only consider bound constraints in this paper.

J0110203 A gradient-based multiobjective optimization considering diversity of solutions

2014 ◽  
Vol 2014 (0) ◽  
pp. _J0110203--_J0110203-
Author(s):  
Yuki SATO ◽  
Kazuhiro IZUI ◽  
Takayuki YAMADA ◽  
Shinji NISHIWAKI
Keyword(s):  
Multiobjective Optimization ◽  
Gradient Based

scholarly journals ROM-Based Inexact Subdivision Methods for PDE-Constrained Multiobjective Optimization

2021 ◽  
Vol 26 (2) ◽  
pp. 32
Author(s):  
Stefan Banholzer ◽  
Bennet Gebken ◽  
Lena Reichle ◽  
Stefan Volkwein
Keyword(s):  
Multiobjective Optimization ◽  
Elliptic Partial Differential Equation ◽  
Computational Effort ◽  
Reduced Basis ◽  
Solution Approach ◽  
Gradient Based ◽  
Descent Condition ◽  
Basis Method ◽  
Parameter Dependent ◽  
Constrained Multiobjective Optimization

The goal in multiobjective optimization is to determine the so-called Pareto set. Our optimization problem is governed by a parameter-dependent semi-linear elliptic partial differential equation (PDE). To solve it, we use a gradient-based set-oriented numerical method. The numerical solution of the PDE by standard discretization methods usually leads to high computational effort. To overcome this difficulty, reduced-order modeling (ROM) is developed utilizing the reduced basis method. These model simplifications cause inexactness in the gradients. For that reason, an additional descent condition is proposed. Applying a modified subdivision algorithm, numerical experiments illustrate the efficiency of our solution approach.

Gradient based system-level diagnosis

2007 ◽  
Vol 51 (1-2) ◽  
pp. 43
Author(s):  
Balázs Polgár ◽  
Endre Selényi
Keyword(s):  
System Level ◽  
Gradient Based
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