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Integrated Asset Management and Optimization Workflows 209

6.2.2.1 Stochastic or (Meta) Heuristic Optimization
The majority of global search/optimization methods in one way or another
leverage stochastic/(meta)heuristic algorithms (Ombach, 2014) to explore
large-scale optimization space, to reduce the probability of being trapped
in the local solution that does not satisfy the global cost function, and to
quantify the uncertainty of parameters in the sampled domain (Mohamed
et al., 2010a). Many global search/optimization algorithms belong to the
group of population-based methods described in great detail in Hajizadeh
(2011) for improved history matching and uncertainty quantification in
petroleum reservoirs. Echeverria Ciaurri et al. (2012) provide a condensed
list of the main characteristics of population-based methods:
• Multiple points [i.e., solutions (see Fig. 6.4 for MOGA application)] are
evaluated in every global search iteration.
• Unlike in pattern-search methods, these points are not clearly structured
and can be, from iteration to iteration, rearranged with a much larger
degree of flexibility.
• There are no theoretical results or empirical rules of thumb that recom-
mend the population size for a given optimization problem, but it can be
anticipated that the larger the size, the more globally the search space is
explored. This is of course under the assumption that the space of opti-
mization variables has been parameterized with sufficient degree of var-
iability to allow a robust uncertainty quantification.
• Consistent with the above observation, if the population size is very
small (compared to the number of optimization variables) the impact
of these population-based methods will be locally confined.
A variety of stochastic/(meta)heuristic global search methods have recently
emerged in applications to reservoir characterization (Compan et al., 2016)
or production optimization, which are summarized in Table 6.1. The table
lists a selected number of (meta)heuristic optimization methods with asso-
ciated engineering application and relevant references.
6.2.3 Optimization Under Uncertainty

The process of optimizing reservoir performance under the assumption that
all the system variables are deterministically known is relatively straightfor-
ward. However, with the presence of physical and financial uncertainties the
problem is elevated to optimization with risk-managed, decision-making
focus. According to McVay and Dossary (2014), the value of “reliably quan-
tifying uncertainty is reducing or eliminating both expected disappointment
(ED), when realizing an NPV is substantially less than estimated NPV, and