Mekatronik Mühendisliği Bölümü
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Article Citation Count: Ulaş, Beldek; Leblebicioğlu, Kemal (2015). "A new systematic and exible method for developing hierarchical decision-making models", Turkish Journal of Electrical Engineering and Computer Sciences, Vol. 23, No. 1, pp. 279-297.A new systematic and exible method for developing hierarchical decision-making models(2015) Ulaş, Beldek; Leblebicioğlu, Kemal; 59950The common practice in multilevel decision-making (DM) systems is to achieve the final decision by going through afinite number of DM levels. In this study, a new multilevel DM model is proposed. This model is called the hierarchical DM (HDM) model and it is supposed to provide a exible way of interaction and information ow between the consecutive levels that allows policy changes in DM procedures if necessary. In the model, in the early levels, there are primary agents that perform DM tasks. As the levels increase, the information associated with these agents is combined through suitable processes and agents with higher complexity are formed to carry out the DM tasks more elegantly. The HDM model is applied to the case study 'Fault degree classification in a 4-tank water circulation system'. For this case study, the processes that connect the lower levels to the higher levels are agent development processes where a special decision fusion technique is its integral part. This decision fusion technique combines the previous level's decisions and their performance indicator suitably to contribute to the improvement of new agents in higher levels. Additionally, the proposed agent development process provides exibility both in the training and validation phases, and less computational effort is required in the training phase compared to a single-agent development simulation carried out for the same DM task under similar circumstances. Hence, the HDM model puts forward an enhanced performance compared to a single agent with a more sophisticated structure. Finally, model validation and eficiency in the presence of noise are also simulated. The adaptability of the agent development process due to the exible structure of the model also accounts for improved performance, as seen in the results.Conference Object Citation Count: Khalid, H.M.; Kirik, M.S.; Schmidt, K.W., "Abstraction-Based Supervisory Control for Recon-Gurable Manufacturing Systems?", Ifac Proceedings Volumes (Ifac-Papersonline), Vol. 4, No. 1, pp. 157-162, (2013).Abstraction-Based Supervisory Control for Recon-Gurable Manufacturing Systems?(2013) Khalid, Harith M.; Kırık, Mustafa Sancay; Schmidt, Klaus Werner; 271229Reconfiguration control for discrete event systems (DES) is concerned with the realization of different system configurations by modification of the supervisory control loop. In this paper, we study the reconfiguration supervisor design for reconfigurable manufacturing systems (RMS) that comprise multiple components. We construct a modular supervisor for each configuration and system component in order to realize each active configuration and to quickly change between configurations. Different from the existing literature that is focused on monolithic design, our method is abstraction-based, and, hence applicable to large-scale DES.Publication Citation Count: Turkyilmaz, S...et al. (2011). "An Electromagnetic Micro-Power Generator for Low Frequency Vibrations with Tunable Resonance", Eurosensors XXV, Vol. 25.An Electromagnetic Micro-Power Generator for Low Frequency Vibrations With Tunable Resonance(Elsevier Science BV, 2011) Türkyılmaz, S.; Zorlu, O.; Muhtaroğlu, A.; Kulah, HalukThis paper presents an electromagnetic (EM) micro-power generator with tunable resonance frequency which can harvest energy from low frequency environmental vibrations. The reported power generator up-converts low frequency environmental vibrations before mechanical-to-electrical energy conversion by utilizing two diaphragms with different resonance frequencies. Power is generated through electromagnetic induction by a magnet attached to the low frequency diaphragm, and a 50 turn, 2.1 Omega coil, and a magnetic piece on the high frequency diaphragm. Both of the diaphragms are fixed to a common frame via rubber springs, which makes the resonance frequency of each diaphragm tunable. The fabricated prototype generates 5.2 mV and 3.21 mu W RMS power by up-converting 13 Hz, 7.5 mm peak-to-peak vibrations to 200 Hz. Tunability of the resonance frequency is experimentally verified by operating the same device at 2-30 Hz external vibrations. (C) 2011 Published by Elsevier Ltd.Conference Object Citation Count: Schmidt, K...et al. (20109. "An Experimental Study of the Flexray Dynamic Segment",Ifac Proceedings Volumes (Ifac-Papersonline), Vol. 43, No. 7, pp. 413-418.An Experimental Study of the Flexray Dynamic Segment(IFAC Secretariat, 2010) Schmidt, Klaus Werner; Schmidt, Ece G.; Demirci, Ali; Yürüklü, Emrah; Karakaya, UtkuIt is expected that the time-triggered FlexRay bus will replace the event-triggered Controller Area Network (CAN) for the high-speed in-vehicle communication in future automobiles. To this end, FlexRay provides a static segment for the transmission of periodic messages and a dynamic segment that is suitable for exchanging event-based (sporadic) messages. In this paper, we experimentally evaluate the operation of the FlexRay dynamic segment. In particular, we study how the maximum and average message delays are affected if the length of the dynamic segment, the message payload, the utilization of the dynamic segment and the priority assignment changes. Our experiments are carried out on a FlexRay network with 6 nodes.Conference Object Citation Count: Özbilge, Kubilay; Ergezer, Halit. "Çekilebilir Sahte Hedef Etkinliğinin Modelleme Ve Simülasyon İle Analizi", 8. Ulusal Savunma Uygulamaları Modelleme ve Simülasyon Konferansı, Ankara 19-20 Kasım 2019, pp. 152-161.Çekilebilir Sahte Hedef Etkinliğinin Modelleme Ve Simülasyon İle Analizi(2019) Özbilge, Kubilay; Ergezer, Halit; 293396; 293396Sahte hedefler, uçağın savaş alanında hayatta kalmasını artırmak için radar güdümlü füzeden korumak için kullanılan bir savunma yöntemlerindendir. Bu çalışmada savaş uçaklarında kullanılan çekilebilir aktif sahte hedeflerin uçağın hayatta kalabilirliğine etkisi, uçağın çekilebilir sahte hedef kullandığı ve kullanmadığı durumlar için vurulma olasılıkları ve füzenin kaçırma uzaklığı değerleri hesaplanarak analiz edilmiştir. Çalışmamızda açık kaynaktan elde edilen veriler kullanılmıştır. Jenerik yapıda kurgulanan savaş uçağı modeli, çekilebilir sahte hedef modeli ve radar modeli ile elde edilen veriler sunulmuştur. Benzetim sonuçları çekilebilir aktif sahte hedef kullanımının savaş uçaklarına özellikle angajmanın son safhasında koruma sağladığını ortaya koymaktadır.Article Citation Count: Ergezer, Halit 82021). "Classification of low probability of intercept radar waveforms using gabor wavelets", Journal of the Faculty of Engineering and Architecture of Gazi University, Vol. 36, No. 4, pp. 2025-2035.Classification of low probability of intercept radar waveforms using gabor wavelets(2021) Ergezer, Halit; 29339Low Probability of Intercept (LPI Radar) is a class of radar with specific technical characteristics that make it very difficult to intercept with electronic support systems and radar warning receivers. Because of their properties as low power, variable frequency, wide bandwidth, LPI radar waveforms are difficult to intercept by ESM systems. In recent years, studies on the classification of waveforms used by these types of radar have been accelerated. In this study, Time-Frequency Images (TFI) has been obtained from the LPI radars waveforms by using Choi-Williams Distribution method. From these images, feature vectors have been generated using Gabor Wavelet transform. In contrast to many methods in the literature, waveform classification has been performed by directly comparing the feature vectors obtained without using any machine learning method. With the method we propose, classification accuracies were obtained at intervals of 2 dB between -20 dB and 10 dB and performed at reasonable classification accuracy rates up to -8 dB SNR value. Better results than the best reported in the literature were obtained for some signal types. The results obtained for all waveform types are given in comparison with the results of the existing methods in the literature.Article Citation Count: Mohammed Ali Kahya, Ardam Haseeb; Schmidt, Klaus Werner (2017). "Clothoid-based Lane Change Trajectory Computation for Self-Driving Vehicles", Çankaya University Journal of Science and Engineering, Vol. 14, no. 2, pp. 152-179.Clothoid-based Lane Change Trajectory Computation for Self-Driving Vehicles(2017) Mohammed Ali Kahya, Ardam Haseeb; Schmidt, Klaus WernerThe subject of this paper is the efficient computation of lane change trajectories for self-driving vehicles. The paper first identifies that a certain type of clothoid-based bi-elementary paths can be used to represent lane change trajectories for vehicles. It is further highlighted that the curvature of such trajectories must be adjusted to the driving situation in order to obtain feasible lane change trajectories. Accordingly, the paper establishes an analytical relation between the maximum admissible curvature of the lane change trajectory and the velocity profile during a lane change. Using this relation, the paper proposes an efficient Newton iteration for computing the parameters of bi-elementary paths for lane changes. The resulting lane change trajectories are as short as possible, while meeting the constraint on the maximum curvature. Simulation experiments for various driving situations show that the computed bi-elementary paths can be computed efficiently and constitute suitable lane change trajectories.Article Citation Count: Can, S.E.; Leblebicioğlu, M.k.; Ergezer, H. (2022). "Çoklu ˙IHA Kullanımı ile Kabloya Asılı Yük TaşınımıTransportation of Cable Suspended Slung Load System Using Multiple UAVs", Fırat Üniversitesi Uzay ve Savunma Teknolojileri Dergisi , Vol.1, No.1, pp.435-440.Çoklu ˙IHA Kullanımı ile Kabloya Asılı Yük Ta¸sınımı Transportation of Cable Suspended Slung Load System Using Multiple UAVs(2022) Can, Süleyman Emre; Leblebicioğlu, M. Kemal; Ergezer, Halit; 293396Bu çalı¸smada, kablolar ile asılı esnemeyen bir yükün ortakla¸sa ta¸sınımı için kontrolcü tasarımı tanıtılmı¸stır. Yük, birden çok insansız hava aracına (˙IHA) yükün kablo ile baglanması ˘ ile ta¸sınmakta olup, istenen üç boyutlu rota üzerinde hareket etmesi saglanmaktadır. Sistemde yük lider olarak alınmaktadır. ˘ Hiyerar¸sik ve merkezcil bir yapıda kontrol edilmektedir. Ta¸sıma görevi, bir optimizasyon problemi olarak ele alınmı¸stır. Sistemi istenen rotada hareket ettirebilmek için bir otopilot algoritması tasarlanmı¸s olup PD yapıları kullanılarak olu¸sturulmu¸stur. Pozisyon kontrolcüsünün çıktısı kontrol atama matrisi tarafından ele alınmaktadır ve uygun kuvvet dagılımını sistemin istenen ˘ davranı¸slarına uygun olacak ¸sekilde türetmektedir. Kontrolcü performansları, takip edilmesi istenen bir rota üzerinde test edilmektedir.Conference Object Citation Count: Sülek, A.N., Schmidt, K.W.,"Computation of Supervisors for Fault-Recovery and Repair for Discrete Event Systems",Advances in the Astronautical Sciences, Vol. 9, No. 3, pp. 428-433, (2014).Computation of Supervisors for Fault-Recovery and Repair for Discrete Event Systems(IFAC Secretariat, 2014) Sülek, Ayşe Nur; Schmidt, Klaus Werner; 17337; 107424In this paper, we study the fault-recovery and repair of discrete event systems (DES). To this end, we first develop a new method for the fault-recovery of DES. In particular, we compute a fault-recovery supervisor that follows the specified nominal system behavior until a fault-occurrence, that continues its operation according to a degraded specification after a fault and that finally converges to a desired behavior after fault. We next show that our method is also applicable to system repair and we propose an iterative procedure that determines a supervisor for an arbitrary number of fault occurrences and system repairs. We demonstrate our method with a manufacturing system example.Article Citation Count: Erdoğan, S.; Bektaş, a.; Ergezer, H. (2022). "Development of air-to-ground engagement analysis model of fighter aircrafts", Journal of the Faculty of Engineering and Architecture of Gazi University, Vol.37, No.4, pp.2225-2239.Development of air-to-ground engagement analysis model of fighter aircrafts(2022) Erdoğan, Sinem; Bektaş, Almila; Ergezer, Halit; 293396In operational analysis studies; it is possible to model and simulate at an engineering level, engagement level, task level and campaign forces level. In this study, modelling and simulation studies are performed in engagement-level allowing the analysis of air-to-ground engagement effectiveness of fighter aircraft according to the operational environment. The operating environment of the combat aircraft, which provides survivability analysis based on low visibility and electronic mixing capabilities, is created. The search radar and tracking radar models for ground-to-air threats have been designed in accordance with the engagement level. The dynamic model of the fighter aircraft and the ground-to-air missile have been modelled using pseudo 5 degree-of-freedom. Modelling has been carried out to allow the use of changes in the Radar Crosssectional Area (RCS), which is one of the most important factors affecting the survivability of the aircraft, with respect to azimuth and elevation angles. The Radio Frequency (RF) jamming capability of the fighter aircraft has also been modelled in accordance with the engagement level. The results of the generic scenarios for the analysis of the effect of these models' parameters on the survivability of fighter aircraft have been presented.Article Citation Count: Schmidt, K.W., Schmidt, E.G. (2012). Distributed real-time protocols for industrial control systems: framework and examples. IEEE Transactions on Parallel And Distributed Systems, 23(10), 1856-1866. http://dx.doi.org/ 10.1109/TPDS.2011.300Distributed real-time protocols for industrial control systems: framework and examples(IEEE-Computer Soc, 2012) Schmidt, Klaus Werner; Schmidt, Ece Güran; 17337The automation of today's large-scale industrial systems relies on the operation of distributed controller devices that perform local computations and exchange information via communication networks. The subject of this paper is the development of a family of shared-medium industrial communication protocols that support the transmission of real-time (RT) and nonreal-time (nRT) data among distributed controller devices. Different from existing protocols, we suggest to incorporate information that is available from the control application in the protocol definition. As a result, our protocols dynamically change the bandwidth allocation on the shared medium according to the instantaneous communication requirements while ensuring hard RT guarantees. Following the recent developments in industrial automation, our protocols can be realized as software layers on top of low-cost conventional EthernetArticle Citation Count: Erdem, Oğuz; Çoğun, Can; Uslan, İ. (2019). "Effect of Machining on Workpiece Surface Characteristics in Electric Discharge Drilling (EDD)", International journal of advances in engineering and pure sciences (Online), Vol.31, No.1, pp.11-16.Effect of Machining on Workpiece Surface Characteristics in Electric Discharge Drilling (EDD)(2019) Erdem, Oğuz; Çoğun, Can; Uslan, İbrahim; 3837In electric discharge drilling (EDD), rapid local heating and cooling of the workpiece surface by means of electric discharges results insurface layers (recast, heat affected and base material). In this study, the main workpiece surface texture measures, namely the recast layerthickness (RLT) and average surface roughness (Ra) characteristics were investigated for varying machining parameters (discharge currentand pulse on time). The conducted experiments revealed the strong dependence of surface characteristics on machining parameters.Article Citation Count: Özerkan, Hacı Bekir; Çoğun, Can (2020). "ELECTROCHEMICAL SMALL DIAMETER DEEP HOLE DRILLING OF POWDER METAL STEEL", Transactions of Famena, Vol. 44, No. 4, pp. 47-58.ELECTROCHEMICAL SMALL DIAMETER DEEP HOLE DRILLING OF POWDER METAL STEEL(2020) Özerkan, Hacı Bekir; Çoğun, Can; 3837In this study, a new hybrid electrochemical drilling (ECD) method is proposed. The method makes use of a tubular tool capable of rotating and an electrolyte flushing through the inner hole at the same time. The designed and manufactured small size ECD machine's most important features are the regulation of the tool feed rate via current feedback control and the use of a rotating tubular tool with internal electrolyte flushing. The powder metal (PM) FLN2 4405 steel was drilled by using a brass tubular tool with various combinations of machining parameters such as machining voltage, electrolyte concentration and flushing pressure, and tool rotation speed. The machining performance outputs, namely, material removal rate (MRR), average radial overcut (RADOC), conicity (CO) and hole geometries were calculated and compared in different machining conditions. The results have shown that the aforementioned variables had a direct impact on the machining performance outputs in ECD. In all experiments, MRR increased with an in increase in machining voltage, tool rotational speed, electrolyte concentration and flushing pressure. RADOC values decreased with the rotational speed of the tool. The present study shows that deep holes with precise geometries and dimensions can be drilled successfully by employing the proposed hybrid ECD method. The method is economical and environmentally friendly since it requires low machining current values (0.1 to 0.7A) and a small amount of non-hazardous halide salt solutions instead of acidic solutions throughout the drilling process.Article Citation Count: Gülcan, Orhan;...et.al. (2015). "Elektro Erozyon İle İşlemede Cu-Cr T/M Elektrot Kullanımının İşleme Performansına Etkisi", Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, Vol.30, No.3, pp.381-394.Elektro Erozyon İle İşlemede Cu-Cr T/M Elektrot Kullanımının İşleme Performansına Etkisi(2015) Gülcan, Orhan; Uslan, İbrahim; Usta, Yusuf; Çoğun, Can; 3837Bu çalışmada, Cu-Cr toz metal (T/M) elektrot kullanımının elektro erozyon ile işleme (EEİ) performans çıktılarından işparçası işleme hızı (İİH), elektrot aşınma hızı (EAH), işlenmiş yüzeyin ortalama ve azami yüzey pürüzlülükleri (Ra ve Rz) ve işparçası yüzey katman kalınlıklarına etkileri deneysel olarak incelenmiştir. Farklı toz karıştırma oranları, sıkıştırma basınçları ve sinterleme sıcaklıklarında elde edilen Cu-Cr T/M elektrotlar SAE 1040 çeliğinin işlenmesinde kullanılmıştır. Analizler, elektrot malzemesinin işparçası yüzeyinde katman halinde alaşımlandığını ve karıştırma oranı, sıkıştırma basıncı ve sinterleme sıcaklığının EEİ performans çıktılarını etkilediğini göstermiştir.Article Citation Count: Ayhan, Emre; Yurdakul, Mustafa; Çoğun, Can. (2021). "Elektrokimyasal Jet İşleme (EJİ) Parametrelerinin İşlenen Kanal Geometrilerine Etkisi", Gazi Mühendislik Bilimleri Dergisi, Vol.7, No.3, pp.213-221.Elektrokimyasal Jet İşleme (EJİ) Parametrelerinin İşlenen Kanal Geometrilerine Etkisi(2021) Ayhan, Emre; Yurdakul, Mustafa; Çoğun, Can; 3837Bu çalışmada alışılmamış imal usullerinden elektrokimyasal jet işleme yöntemi (EJİ) kullanılarak YHÇ malzeme üzerine kanallar oluşturularak, işleme parametrelerinin kanal kesit geometrisine etkileri incelenmiştir. Çalışmada, işleme parametreleri olarak takım ilerleme hızı, işleme gerilimi, elektrolit sıvı basıncı ve elektrolit tuz derişimi ele alınmıştır. Her deneye ait kanal kesit geometrileri için profil tamlık değerleri, ortalama kanal derinliği ve genel uyum değerleri hesaplanmıştır. Hesaplanan genel uyum değerlerinde en iyi sonuçların işleme geriliminin 20 V olduğu deneylerde elde edildiği görülmüştür. Takım ilerleme hızının 0,5 mm/dak olduğu deneylerde genel uyum değerlerinin daha yüksek olduğu görülmüştür.Article Citation Count: Bingöl, Hilal; Çankaya, Erkam; Schmıdt, Klaus W. (2016). "Eyleyici doyumu altında dizi kararlı kooperatif otomatik seyir kontrolü", Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi, Vol.22, No.8, pp.636-642.Eyleyici doyumu altında dizi kararlı kooperatif otomatik seyir kontrolü(2016) Bingöl, Hilal; Çankaya, Erkam; Schmıdt, Klaus Werner; 218795Kooperatif otomatik seyir kontrolü (CACC), araçtan araca haberleşme yöntemiyle veri iletilmesini ve uzaklık ölçümlerine göre yoğun trafikte güvenilir araç takibinin yapılmasını sağlar. Kullanılan CACC dizaynları dizi kararlılığının temel özelliklerini sorunsuz bir şekilde yerine getirirken doğrusal araç modelleri için sınırlıdır. Bu makalede ise, doğrusal olmayan araç modeli kullanıldığında ve lider araca uygulanan giriş sinyali doyuma uğramadığında dizi kararlılığının korunabildiği gösterilmiştir.Article Citation Count: Özgedik, Ali; Çoğun, C. (2014). "Farklı İşleme Derinliklerinde Uygulanan Titreşimlerin Elektro-Erozyon ile İşleme Performansına Etkisi", Makine Teknolojileri Elektronik Dergisi (elektronik), Vol.11, No.3Farklı İşleme Derinliklerinde Uygulanan Titreşimlerin Elektro-Erozyon ile İşleme Performansına Etkisi(2014) Özgedik, Ali; Çoğun, Can; 3837Bu çalışmada, Elektro-Erozyon ile İşleme (EEİ) tekniğinin performans çıktılarını iyileştirmek amacı ile işparçasına farklı frekansta titreşimlerin uygulandığı boşalım akımı ve işleme derinliği gibi farklı işleme koşullarında deneyler yapılmıştır. Deneylerde titreşimsiz koşullara göre elektrot aşınma hızı (EAH) ve bağıl aşınma (BA) değerlerinde belirgin azalma elde edilmiştir. Titreşimli deneylerde işparçası işleme hızı (İİH) ve ortalama yüzey pürüzlülüğü (Ra) değerlerinde EAH ve BA değerlerine göre daha küçük değişimler tespit edilmiştir.Conference Object Citation Count: Moor, Thomas; Schmidt, Klaus Werner (2015). "Fault-tolerant control of discrete-event systems with lower-bound specifications", IFAC-PapersOnLine, Vol. 28, No. 7, pp. 161-166.Fault-tolerant control of discrete-event systems with lower-bound specifications(2015) Moor, Thomas; Schmidt, Klaus WernerFault-tolerant control addresses the control of dynamical systems such that they remain functional after the occurrence of a fault. To allow the controller to compensate for a fault, the system must exhibit certain redundancies. Alternatively, one may relax performance requirements for the closedloop behaviour after the occurrence of a fault. To achieve fault tolerance for a hierarchical control architecture, a combination of both options appears to be advisable: on each individual level of the hierarchy, the controller may compensate the fault as far as possible, and then pass on responsibility to the next upper level. This approach, when further elaborated for discrete-event systems represented by formal languages, turns out to impose a hard lower-bound inclusion specification on the closed-loop behaviour. The present paper discusses the corresponding synthesis problem and presents a solution. © 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.Article Citation Count: Ghanbarpour Asl, Habib; Han, Kerim Youde, "Investigition on the Influence of Parameter Uncertainties in the Position Tracking of Robot Manipulators", Tehnicki Glasnik-Technical Journal, Vol. 13, No. 1, pp. 16-24, (March 2019).Investigition on the Influence of Parameter Uncertainties in the Position Tracking of Robot Manipulators(Univ North, 2019) Ghanbarpour Asl, Habib; Han, Kerim YoudeThis paper presents a novel trajectory tracking method for robot arms with uncertainties in parameters. The new controller applies the robust output feedback linearization method and is designed so that it is robust to the variation of parameters. Robustness of the algorithm is evaluated when the parameters of the system are floating over 10 percent up and down. An Unscented Kalman Filter (UKF) is applied for state and parameter estimation purposes. As the considered system has 8 unknown parameters while only 5 of them are independent parameters, UKF is applied only to the augmented system with independent parameters. Three types of simulations are applied depending on sensor groups - first with both position and joint sensors, second with only position sensors and third with only joint sensors. The observation of parameters in these groups is discussed. Simulation results show that when both position sensors and joint sensors are used, all the parameters and states are observable and good tracking performances are obtained. When only position sensors are used, the accuracy of the estimated parameters is reduced, and low tracking performances are revealed. Finally, when only joint sensors are applied, the lengths of robot arms are unobservable, but other parameters related to the dynamic system are observable, and poor tracking performances are given.Article Citation Count: BELDEK, U., ÖNAL. T., (2013). Kromozom seçim metriğinin yinelemeli iki-aşamalı evrimsel programlamada performansa katkısı. Çankaya University Journal of Science and Engineering Volume 10 (2013), No.1, pp.79–90Kromozom seçim metriğinin yinelemeli iki-aşamalı evrimsel programlamada performansa katkısı(Çankaya Üniversitesi, 2013) Önal, Turgut; Beldek, Ulaş; 59950Bu çalışmada yeni bir evrimsel eniyileştirme algoritması olan yinelemeli iki-aşamalı evrimsel programlama algoritmasında kromozom seçmek için kullanılan metriğin farklılaştırlmasının eniyileştirme problemlerinin çözümlemedeki katkısı incelenmiştir. Gerçekleştirlen metrik değişikliği , önceden uygulanan metriğe göre test edilen eniyileştirme problemlerinde karşılaştırılabilecek sonuçlar sunmaktadır. Elde edilen sonuçlar bu çalışmada gösterilmektedir.