Ayrık tasarım değişkenli kafes yapıların modifiye edilmiş armoni arama algoritması ile optimum tasarımı
Öz
Bu çalışma ile ayrık tasarım değişkenli kafes yapıların optimizasyonunda modifiye edilmiş armoni arama
algoritması (MHS) kullanılmıştır. Armoni arama; müzisyenlerin beste yaparken en iyi armoniyi bulmak için
izledikleri yol ile optimizasyon problemlerinin çözümünde izlenen yol arasında benzerlik kuran bir
yöntemdir. Optimum tasarımda amaç; gerilme ve deplasman sınırlayıcıları altında minimum ağırlıklı kafes
yapıların elde edilmesidir.
Bu çalışmada sunulan modifiye edilmiş armoni arama yöntemiyle, klasik armoni arama yöntemine göre
daha güçlü bir yöntem elde edilmesi amaçlanmıştır. Önerilen yöntemin etkinliğini test etmek için literatürde
daha önce klasik armoni arama, sezgisel parçacık sürü optimizasyonu, mayın patlatma algoritması, modifiye
edilmiş ateş böceği algoritması ve öğretme-öğrenme esaslı optimizasyon yöntemleri kullanılarak optimum
tasarımı yapılmış olan 25 elemanlı uzay kafes yapı kullanılmıştır. Modifiye edilmiş armoni arama
yönteminin stokastik (olasılığa dayalı) yapısından dolayı tasarım örneği 10 kez icra edilmiş ve bu farklı
icralardan elde edilen tasarımlardan en hafif olanı ile literatürden alınan sonuçlarla kıyaslanmıştır. Bu
kıyaslamalar sonucunda, modifiye edilmiş armoni arama algoritması ile daha hafif kafes yapı tasarımının
elde edildiği tespit edilmiştir.
Anahtar Kelimeler
Optimum design of truss structures with discrete variables using modified harmony search algorithm
Abstract
In this study, modified harmony search algorithm
(MHS) was used for the optimization of truss
structures with discrete variables. The objective of
optimum design is to obtain the minimum weight
truss structures under the stress and displacement
constraints. The modified harmony search method
was developed to increase the classical harmony
search method. In recent years, a number of
metaheuristic optimization methods were proposed
for solving different problems. The metaheuristic
optimization called as genetic algorithms, simulated
annealing, harmony search (HS), particle swarm
optimization, artificial bee colony algorithm and
teaching-learning based optimization were used for
solving optimization problems. The main philosophy
of metaheuristic optimization methods is to make an
analogy between the optimization problems and a
process in the nature. The harmony search makes an
analogy between the path musicians follow to find
the best harmonies while composing and the path
followed in solving optimization problems.
Design variables used in optimization can be divided
into two groups such as discrete and constant
variables. The discrete variables can take only a
certain value within a specified range whereas the
constant variables can receive any values. In this
study, the discrete design variable will be used. The
modified objective function is used in this study. HS
algorithm in this study consists of following steps:
assignment of harmony search parameters,
executing the harmony memory and obtaining of the
new harmony, updating of the harmony memory and
termination of the search process. The tuning
parameters, pitch adjusting ratio (PAR) ratio and
neighbouring index (bw), used in classical HS
remain constant throughout the search process
However, the parameters should be modified during
the search in order to increase the efficiency of
standard HS method. The search space at the
beginning of the optimization is quite extensive while
it is gradually shrunk at the end of the search and
approximately same designs are obtained. Based on
this rationale, pitch adjusting ratio (PAR) and
neighbouring index (bw) were decreased during the
search.
In this study, modified harmony search algorithm
was developed for optimum design of truss
structures. The proposed algorithm was coded in
FORTRAN programming language and executed on
the computer with 2.20GHz microprocessor. The
efficiency of the proposed method was tested on the
25-member space truss structure. The computer
program was executed ten times for 25-member
space truss structure because of stochastic nature of
the algorithm. Moreover, average weight and
standard deviation of 10 different designs and
constraint violation tolerance was presented The
results obtained by modified harmony search
method were compared to the other optimization
methods like harmony search algorithm, heuristic
particle swarm optimization, mine blast algorithm,
the enhanced accelerated firefly algorithm and
teaching-learning based optimization. The
comparisons showed that modified harmony search
algorithm could obtain lighter truss structure design
than the other methods.
The average weight derived from 10 different
desings is too close the optimum design and
standard deviation for these designs are quite little
value comparing to average weight. These results
proved that the modified harmony search algorithm
could converge to global or near global optimum
designs.
Keywords
