Risk assessment and management of civil infrastructure networks: a systems approach - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 446

number of variables or constraints, respectively. There also exist powerful
heuristics for many different types of problems, within which evolutionary
and other bio-inspired techniques have gained momentum in the last
decade (Reeves, 1993; Bonabeau et al. , 1999; Lee and El-Sharkawi, 2008).
In particular, Chang (2010) has used evolutionary algorithms for global
level optimization of supply chains.
Most practical problems have several (usually) confl icting objectives.
Multi-objective optimization (Coello et al. , 2006) deals with such kinds of
problems by fi nding a Pareto front, which defi nes a region in which neither
of the objectives can be improved without degrading another. An alterna-
tive option is to fi x one of the objectives as a constraint, i.e., attend at least
P people or spend at most D dollars and then perform sensitivity analyses
on P and/or D to unravel and evaluate tradeoffs. This way, stakeholders
get to know a set of equivalent choices and their consequences on the
objective.
Researchers have defi ned several archetype problems that encapsulate
common features that appear in most applications (e.g., the travelling sales-
man problem). The capacitated facility location problem (CFLP; Levi et al. ,
2012) is a specifi c case, in which a set of facilities/service-providers is to be
installed to satisfy the demand from a set of users/clients, under a restricted
capacity. The basic assignment problem is proved to be NP-hard (Khan,
2003), and the decision about the number of alternatives to assign is highly
combinatorial. Therefore, formal methods of optimization may not suffi ce
for practical applications.
17.5.2 Hierarchy-based optimization
The hierarchical model provides information about cluster structures of a
network at several levels of abstraction. Nodes within these clusters are
characterized for being relatively close to each other, and having high con-
nectivity with respect to the whole network. Additionally, cluster centroids
can be thought of as hubs, with enhanced centrality and connectivity within
their corresponding clusters. This suggests that resources can be assigned
to fi ctitious nodes instead of actual nodes, reducing complexity. Then, if a
certain resource is to be allocated at a fi ctitious node, it can be located at
the centroid, which can provide the whole cluster with access to the service
more effectively than any other node in the cluster. In this sense, a variety
of resources of different characteristics (cost, capacity, and accessibility) can
be assigned coherently with the multi-scale intrinsic structure of the network.
This strategy seeks to simplify the optimization process of resource allo-
cation. This is achieved by using the hierarchical model instead of the origi-
nal network. The underlying principle is that a more complete data structure
simplifi es the algorithm due to a pre-processing of the network topology.