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Proven effectiveness in solving complex problems that cannot be readily solved
with other optimization methods. The mapping of the objective function for a day
lighting design problem showed the existence of local minima that would
potentially trap a gradient-based method (Chutarat
2001
). Building optimization
problems may include a mixture of a large number of integer and continuous
variables, non-linear inequality and equality constraints, a discontinuous objec-
tive function and variables embedded in constraints. Such characteristics make
gradient-based optimization methods inappropriate and restrict the applicability
of direct-search methods (Wright and Farmani
2001
). The calculation time of
mixed integer programming (MIP), which was used to optimize the operation of a
district heating and cooling plant, increases exponentially with the number of
integer variables. It was shown that it takes about two times longer than a genetic
algorithm for a 14 h optimization window and 12 times longer for a 24 h period
(Sakamoto et al.
1999
), although the time required byMIP was suf
ciently fast for
a relatively simple plant to make on-line use feasible.
Methods to allow genetic algorithms to handle constraints that would make
some solutions unattractive or entirely infeasible.
Performing on a set of solutions instead of one solution is one of notable abilities
of stochastic algorithms. Thus, at
first, initial population consisting of a random set
of solutions is generated by the genetic algorithm. Each solution in a population is
named an individual or a chromosome. The size of population (N) is the number of
chromosomes in a population. The genetic algorithm has the capability of per-
forming with coded variables. In fact, the binary coding is the most popular
approach of encoding the genetic algorithm. When the initial population is gener-
ated, the genetic algorithm has to encode the whole parameters as binary digits.
Hence, while performing over a set of binary solutions, the genetic algorithm must
decode all the solutions to report the optimal solutions. To this end, a real-coded
genetic algorithm is utilized in this study (Mahmoodabadi et al.
2013
). In the real
coded genetic algorithm, the solutions are applied as real values. Thus, the genetic
algorithm does not have to devote a great deal of time to coding and decoding the
values (Arumugam et al.
2005
). Fitness which is a value assigned to each chro-
mosome is used in the genetic algorithm to provide the ability of evaluating the new
population with respect to the previous population at any iteration. To gain the
fitness value of each chromosome, the same chromosome is used to obtain the value
of the function which must be optimized. This function is the objective function.
Three operators, that is, reproduction, crossover and mutation are employed in the
genetic algorithm to generate a new population in comparison to the previous
population. Each chromosome in new and previous populations is named offspring
and parent, correspondingly. This process of the genetic algorithm is iterated until
the stopping criterion is satis
fitness in the
last generation is proposed as the optimal solution. In the present study, crossover
and mutation are hybridized with the formula of particle swarm optimization
(Mahmoodabadi et al.
2013
). The details of these genetic operators are elaborated in
the following sections.
ed and the chromosome with the best
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