Geology Reference
In-Depth Information
fitness in the problem environment, 2) selection of
a new individual to fill new population based on the
fitness values, 3) interchanging gene information
between strings (i.e. individuals) by using genetic
operators such as crossover and mutation. The
cycle of these four steps, which is called genetic
loop, is repeated until the population converges
or pre-defined criteria are satisfied. Although the
SGA has significant problem solving performance
for the single objective problem domain, it shows
limitation for solving multi-objective problems by
formulating a composite, weighted single fitness
function. The objectives conflict each other in
most cases, i.e., if performance of an objective
is improved, the performance of other objectives
may be degraded. The optimization of control
device and sensor layout with best efficiency and
minimum control cost as defined in this research
effort is a typical conflicting objective problem:
minimum distributions of both control devices and
sensors installed and minimum interstory drift of
controlled structure, which is the set of equally
optimal solutions, called Pareto-optimal solutions.
To investigate more robust Pareto-optimal set
for the two conflict objectives, this research studies
three multi-objective genetic algorithms (MOGA):
The first MOGA is developed through the integra-
tion of Implicit redundant representation (IRR)
genetic algorithm (GA) and Non-dominated sort-
ing GA 2 (NSGA2): NS2-IRR GA. The second
one is proposed by combining the best features of
both IRR GA and Strength Pareto Evolutionary
Algorithm (SPEA2): SP2-IRR GA. Lastly, Gene
Manipulation GA (GMGA) is developed based
on novel recombination and mutation mechanism.
The main difference among these MOGA lies in
the ranking mechanism at the selection step in the
genetic loop. Diverse ranking processes have been
developed to assign reasonable relative fitness
values among individuals. Another difference lies
in sharing or strength measures used to promote
diversity across the Pareto-optimal front. The
other difference lies in storing non-dominated
individuals found during the genetic loop. How-
ever the other steps are very similar in information
exchange step. In order to find and keep Pareto
fronts which are evenly and equally considering
conflicting objectives, two advanced MOGA are
used in this research effort: NSGA-II and SPEA2.
These methods are explained in greater detail in
the following section.
NS2-IRR GA
Implict Redundant Representation
(IRR) Genetic Algorithm (GA)
The SGA which uses binary or real-coded encoding
policies is fairly good to represent single objec-
tive problem. To solve multi-objective problems,
new appropriate encoding policy is required to
consider highly complex optimization problems,
in particular, requiring high-cost computation. To
consider high nonlinear solution domain, a novel
encoding policy, which is implicit redundant repre-
sentation genetic algorithm (IRR GA), is proposed
by Raich and Ghaboussi (1998). The IRR GA is
composed of gene locator (GL) which indicates
starting points of the gene instance which has
design variables and redundant segments which
do not use for design variables at current genera-
tion but it may be used at other generations by
becoming gene instances by genetic operators as
shown in Figure 1. This redundant segment can
keep useful design information and can dynami-
cally trip during the binary strings. This implicit
coding policy can solve complex multi-objective
problems. The IRR GA is integrated with non-
dominated sorting genetic algorithms and strength
Pareto evolutionary algorithms.
Non-Dominated Sorting GA
In most cases, the optimal solution for each
objective for the design problem in numerous
engineering areas may usually be different to
each other (Hans 1988). For example, if drivers
want to drive fast, the vehicle consumes more
Search WWH ::
Custom Search