NDLI: Gradient-based multi-objective optimization with applications to waterflooding optimization

Content Provider	Springer Nature Link
Author	Liu, Xin Reylds, Albert C.
Copyright Year	2015
Abstract	We consider problems where it is desirable to maximize multiple objective functions, but it is impossible to find a single design vector (vector of optimization variables) which maximizes all objective functions. In this case, the solution of the multi-objective optimization problem is defined as the Pareto front. The defining characteristic of the Pareto front is that, given any specific point on the Pareto front, it is impossible to find another point on the Pareto front or another feasible point which yields a greater value of all objective functions. The focus of this work is on the generation of the Pareto front for bi-objective optimization problems with specific applications to waterflooding optimization.The most straightforward way to obtain the Pareto front is by application of the weighted sum method. We provide a procedure for scaling the optimization problem which makes it more straightforward to obtain points which are approximately uniformly distributed on the Pareto front when applying the weighted sum method. We also compare the performance of implementations of the weighted sum and normal boundary intersection (NBI) procedures where, with both methodologies, a gradient-based algorithm is used for optimization.The vector of objective functions maps the set of feasible design vectors onto a set Z, and it is well known that all points on the Pareto front are on the boundary of Z. The weighted sum method cannot find points which are on the concave part of the boundary of Z, whereas the NBI method can be used to find all points on the boundary of Z, even though all points on this boundary may not correspond to Pareto optimal points. We develop and implement an NBI algorithm based on the augmented Lagrange method where the maximization of the augumented Lagrangian in the inner loop of the augmented Lagrange method is accomplished by a gradient-based optimization algorithm with the necessary gradients computed by the adjoint method.Two waterflooding optimization problems are considered where we wish to optimize (maximize) two conflicting objectives. In the first, the two objectives are to maximize the life-cycle net present value (NPV) of production and to maximize the short-term NPV of production. In the second application, given an uncertain reservoir description, we wish to maximize the expected value of the NPV of life-cycle production and minimize the standard deviation of NPV over the ensemble of geological realizations.
Starting Page	677
Ending Page	693
Page Count	17
File Format	PDF
ISSN	14200597
Journal	Computational Geosciences
Volume Number	20
Issue Number	3
e-ISSN	15731499
Language	English
Publisher	Springer International Publishing
Publisher Date	2015-09-18
Publisher Place	Cham
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Multi-objective optimization Life-cycle production optimization Waterflooding optimization Weighted sum algorithm Normal boundary intersection algorithm Robust optimization Optimization under geological uncertainty Earth Sciences Geotechnical Engineering & Applied Earth Sciences Hydrogeology Mathematical Modeling and Industrial Mathematics Soil Science & Conservation
Content Type	Text
Resource Type	Article
Subject	Computers in Earth Sciences Computational Theory and Mathematics Computer Science Applications Computational Mathematics

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