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206 Intelligent Digital Oil and Gas Fields

Parameter 2 Feasible

Pareto region
front

Max
Pareto
solution set

Min

Infeasible
region

Min Max Parameter 1
Fig. 6.3 Illustration of the concept of Dominance and Pareto optimality in objective
space. (Modified from Schulze-Riegert, R.W., Krosche, M., Fahimuddin, A., Ghedan, S.G.,
2007. Multi-Objective Optimization with Application to Model Validation and Uncertainty
Quantification. SPE-105313-MS. https://doi.org/10.2118/105313-MS.)

objectives (direct, min-max, and nonparametric) and propose a nonpara-
metric, conflict-based objective grouping to obtain faster and more robust
history matches with better quality.

6.2.2 Local vs. Global Optimization

Specifically when solving multiobjective optimization problems, the selec-
tion of optimization technologies based on the nature of search for an
optimal cost function value becomes highly relevant and sets the distinc-
tion between the local and global optimization. Note that the literature
frequently prefers the term “global search” over “global optimization.”
The reason for this preference is that “…finding the global optimum in
practical situations where the cost function is relatively time demanding
and the number of optimization variables is larger than few tens is an
extremely arduous (and virtually impossible in most cases) task. Hence,
at most we can aspire is to search globally…”(Echeverria Ciaurri
et al., 2012).