Doğrusal parametrik ve doğrusal olmayan gerçek sistemlerin yapay arı kolonisi algoritması kullanılarak modellenmesi

Abstract

Araştırmacılar, klasik optimizasyon tekniklerinin kullanılmasının yetersiz olduğu problemler için farklı çözüm arayışlarına girmiş, çalışmalarını bu yönde devam ettirmişlerdir. Yapay zeka optimizasyon teknikleri ise bu çalışmaların bir sonucu olarak ortaya çıkmıştır. Yapay zeka optimizasyon teknikleri, karmaşık optimizasyon problemlerinin çözümünde sık sık kullanılmaya başlanmış ve olumlu sonuçlar verdiği görülmüştür. Doğadan esinlenen algoritmaların yeni bir dalı olan sürü zekâsı yaklaşımı, böceklerin içgüdüsel problem çözme becerilerini kullanan etkili metasezgisel yöntemler geliştirebilmek için böcek davranışlarının modellenmesine odaklanmıştır. Yapay Arı Kolonisi (YAK) Algoritması da sürü zekasına sahip olan arıların davranışlarını esas alıp geliştirilmiş ve karmaşık problemlerin çözümünde kullanılmaya başlanmıştır. Bu çalışmada da, doğrusal olan parametrik ve doğrusal olmayan gerçek sistemlerin sürü zekası yaklaşımına örnek olan yapay zeka optimizasyon tekniklerinden Yapay Arı Kolonisi (YAK) Algoritması ile modellenmesi gerçekleştirilmiş olup, Genetik algoritma (GA) ve Klonal Seçme Algoritması (KSA) ile başarımı karşılaştırılmıştır. Benzetim çalışmalarında literatürde kıyaslama problemlerinde sıklıkla kullanılan bir adet doğrusal parametrik ve bir adet doğrusal olmayan gerçek sistem bu algoritmalar yardımıyla modellendirilmiştir. Benzetim sonuçlarına göre doğrusal parametrik sistemlerin modellenmesinde YAK algoritması, GA’ya çok yakın bir sürede parametre tahmini yapmış, farklı koloni sayılarında ise hem GA’dan hemde KSA’dan daha düşük modelleme hatası ile sonuç alındığı görülmüştür. Doğrusal olmayan gerçek sistem modellemelerde ise aynı durum söz konusu olup, koloni sayılarındaki değişime bağlı olarak YAK algoritması, GA ve KSA’na göre daha düşük hata ve daha erken sürede sistemi modelleyebildiği görülmüştür.

Keywords

• Yapay arı kolonisi algoritması, doğrusal sistem modelleme, doğrusal olmayan gerçek sistem modelleme

Modelling of linear parametric and non-linear real systems by using artificial bee colony algorithm

Abstract

A system can be define as in accordance with a specific purpose in response to inputs producing outputs that have a reciprocal interaction between one element to another and the relation between external world and within its elements. The main purpose of using the term of the system is to investigate the structure of the systems in order to attain desired outcomes, to determine the basic principles concerning with the system and to regulate the system based on purposes if possible. However, it is not always possible to investigate the actual system and to determine its principles. Therefore, a tool is needed to represent all the features of the actual system. This tool will provide the best way to understand the system and its process . This representation tool, which will be used for this purpose, is called model. In other words, the model refers to simplified structures that can usually be either mathematical or computable. The purpose of modelling is to determine the relation between input and output of an unknown system. In other words, modelling aims to find parameters of the transfer function that is characterized by the system. Modelling should be based on well defining for determination of complex parameters. By all means, if a model is established with chosen correct relationships, the solution would lead to more accurate and better results. A trend towards the use of the natural simulations is increasing in order for modelling and solving complex optimization problem as day goes on because classical optimization algorithms are not sufficient to solve the problems that oversized, linear and non-linear mathematical or real system. Modelling of real systems that suits a particular solution method is often not easy. Nature-inspired heuristic optimization algorithms, which are independent from the problem and model, are suggested to overcome deficiencies of conventional optimization techniques. New ways of searching have brought along in cases where the use of classical optimization techniques is insufficient. Artificial intelligence optimization techniques have been proposed as a result of this search. Swarm intelligence approach, which is a new branch of algorithms inspired by nature, is used instinctively problem solving skills of the insects. This approach has focused on the modeling of insects' behavior to develop effective meta-heuristics methods. An example of swarm intelligence approach is ABC algorithm developed by Karaboga. As a result of the interaction between insects, one of the most important parts of collective intelligence is to share information among insects individually. Oscillation dance of honey bees can be given as an example of types of interactive behaviors in which honey bees share information regarding the source and the quality of the discovered foods. By performing the dance, honey bees give messages to other bees in respect to quality of food supply, the direction of the food, the distance and the amount of the nectar. Through this successful mechanism, the colony can be directed to the region where good quality of food resources is available. This study aims to determine the parameters estimation by using Artificial Bee Colony (ABC) Algorithm, Genetic Algorithm (GA) and Clonal Selection Algorithm (CSA). The obtained results have been compared with one algorithm to another. Furthermore, Artificial Bee Colony (ABC) Algorithm, which have been introduced into the literature newly, has been given as a good example of swarm intelligence approach. In the literature, for comparison problems in the modelling studies, one linear parametric and one non-linear real system are often modelled by using these algorithms. The results of modelling have demonstrated that in the modelling of linear parametric system, ABC algorithm estimated parameter in a time very close to GA and indicated less modelling error in the number of different colonies than both GA and CSA. Same case also occurs in the modeling of non-linear parametric real system and depending on changes in the number of colonies, ABC algorithm modelled the system with less error in a shorter time compare to GA and CSA.

Keywords

• Artificial Bee Colony Algorithm, linear system modelling, non-linear real system modelling