Ayrık tasarım değişkenli kafes yapıların modifiye edilmiş armoni arama algoritması ile optimum tasarımı

Abstract

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.

Keywords

• Modifiye edilmiş armoni arama, Optimum tasarım, Kafes yapılar.

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

• Modified harmony search, Optimum design, Truss structures.