Weak Subdifferential in Nonsmooth Analysis and Optimization

Some properties of the weak subdifferential are considered in this paper. By using the definition and properties of the weak subdifferential which are described in the papers (Azimov and Gasimov, 1999; Kasimbeyli and Mammadov, 2009; Kasimbeyli and Inceoglu, 2010), the author proves some theorems connecting weak subdifferential in nonsmooth and nonconvex analysis. It is also obtained necessary optimality condition by using the weak subdifferential in this paper

Optimality conditions for nonsmooth optimization problems via generalised derivatives

Aquatic plants are integral components of freshwater ecosystems and provide essential ecosystem services. However, when invasive species establish in new aquatic environments, there are few natural checks and balances to inhibit their growth and spread. Overabundant aquatic vegetation can harm aquatic systems if left unchecked and negatively impact on agricultural productivity, social amenity and biodiversity values. Prevention and early intervention are recognised as the most cost effective means to manage invasive species that pose a biosecurity risk. This thesis contributes to the development of effective management strategies for one of the world’s most invasive aquatic plant species, known as alligator weed (Alternanthera philoxeroides (Mart.) Griseb.). It focusses on developing management strategies in an early stage of invasion, in order to achieve extirpation of this species from catchments and waterways. Developing effective detection and surveillance strategies are required for invasive aquatic plants, as a key impediment to achieving extirpation is the ability to detect infestations, so that control strategies can be enacted. This thesis investigates the effectiveness of aerial surveillance for detection of alligator weed at different spatial scales, using high altitude aerial imagery (orthophotos) and unmanned aerial vehicle (UAV) technology. An examination of the growth rate of alligator weed in Victoria, Australia, over a five year period, demonstrates the effective use of orthophotos to detect and monitor large infestations of aquatic alligator weed. The efficacy of unmanned aerial vehicle technology, including the use of automated algorithms, to detect patches of alligator weed growing in waterways is evaluated against current detection techniques. Effective management of invasive aquatic plants targeted for extirpation requires the coupling of effective detection and control efforts to prevent reproduction. To date, development of control strategies for aquatic alligator weed has been limited to evaluating the efficacy of short-term control at a local scale without regard to the effects of management strategies on dispersal of propagules throughout catchments. This thesis determines that viable alligator weed stem fragments are produced following herbicide application, which comprises extirpation efforts. This thesis has gone further than current practice in that it has evaluated the efficacy of current and novel control techniques, in both laboratory and field trials and has developed methods to manage viable fragment production post-herbicide application, to limit dispersal throughout catchments. In this respect, the application of the herbicides glyphosate, metsulfuron-methyl and imazapyr, and their effectiveness when incorporating surfactant systems and plant growth regulators, have been evaluated in field and laboratory studies to optimise control techniques for aquatic alligator weed. Results have shown that our approaches, when used in an early stage of invasion, are capable of eliminating patches of alligator weed in two to three years. Integral to the research is an experiment to determine the effect of herbicide treatments on the production of alligator weed stem fragments and their subsequent viability. Further investigation to determine the usefulness of commercially available plant growth regulators (PGRs) to reduce the number of viable propagules produced by alligator weed post-herbicide application was found to be ineffective. This thesis also evaluates the impact of herbicides and surfactant systems, on all key alligator weed response metrics in aquatic environments including; above ground biomass, below ground biomass and viable stem fragmentation. No previous studies have looked simultaneously at these three important measures for determining the efficacy of a particular control regime, and we have determined that this is essential for effective management of aquatic alligator weed in an early stage of invasion. The thesis has underscored the notion that development of more effective management strategies, based upon experimental trials, will result in an increased likelihood of eradicating invasive aquatic plants that pose a biosecurity risk, and thus move toward the mitigation of the threat that high-risk species pose to aquatic ecosystems. PLEASE NOTE: Portions of the full text have been removed due to copyright restrictions.Doctor of Philosoph

Esnek atölye tipi hücre çizelgeleme problemleri için çok amaçlı matematiksel model ve genetik algoritma ile çözüm önerisi

06.03.2018 tarihli ve 30352 sayılı Resmi Gazetede yayımlanan “Yükseköğretim Kanunu İle Bazı Kanun Ve Kanun Hükmünde Kararnamelerde Değişiklik Yapılması Hakkında Kanun” ile 18.06.2018 tarihli “Lisansüstü Tezlerin Elektronik Ortamda Toplanması, Düzenlenmesi ve Erişime Açılmasına İlişkin Yönerge” gereğince tam metin erişime açılmıştır.Günümüz rekabetçi iş ortamında, müşteriler daha düşük maliyetle daha yüksek kalitede çeşitli ürünleri satın almak istemektedir. İmalat firmaları, talep çeşitliliğini karşılamak için yüksek derecede ürün çeşitliliğine ve küçük imalat parti büyüklüğüne ihtiyaç duymaktadır. Üretimdeki ürün çeşitlilikleri uzun hazırlık ve taşıma süreleri, karmaşık çizelgeleme problemleri gibi birçok probleme neden olmaktadır. Geleneksel imalat sistemleri, bu tip değişikliklere cevap vermede yeterince esnek değilken Hücresel Üretim Sistemleri üreticilerin bu ihtiyaçlarına cevap verebilecek özelliklere sahiptir. Ayrıca gerçek hayat problemlerinin çoğunda, bir parçanın bazı ya da bütün operasyonları birden fazla makinede işlem görebilmekte ve bazen de bu operasyonlar bir makineyi ya da iş merkezini birden fazla kez ziyaret etmektedir. Bu seçenek sisteme esneklik kazandırırken bu kadar karmaşık bir üretim sisteminin başarılı ve doğru bir şekilde işletilebilmesi kaynakların etkin kullanılmasını da gerektirmektedir. Bu çalışma, istisnai parçaları, hücrelerarası hareketleri, hücrelerarası taşıma sürelerini, sıra bağımlı parça ailesi hazırlık sürelerini ve yeniden işlem gören parçaları dikkate alarak hücresel imalat ortamında esnek atölye tipi çizelgeleme probleminin çözümüne dair bir matematiksel model ve çözüm yöntemi sunmaktadır. Mevcut bilgilerimiz ışığında yapılan bu çalışma Esnek Atölye Tipi Hücre Çizelgeleme Probleminde (EATHÇP) çok amaçlı matematiksel model ve meta-sezgiselinin kullanımı için ilk girişimdir. Bununla birlikte gerçek hayat uygulamaları için EATHÇP süreci, birçok çelişen amacı dikkate almayı gerektirdiği için ele alınan skalerleştirme metodu pratik uygulama ve teorik araştırma açısından oldukça önemlidir. Önerilen karma tamsayılı doğrusal olmayan matematiksel modelle küçük ve orta boyutlu problemler çözülebilmektedir. Büyük boyutlu problemlerin çözümü, doğrusal olmayan modellerle makul zamanlarda olamayacağı ya da çok uzun süreceği için konik skalerleştirmeli çok amaçlı matematiksel modeli kullanan bir Genetik Algoritma (GA) meta-sezgisel çözüm yöntemi önerilmiştir. GA yaklaşımının en iyi veya en iyiye yakın çözüme ulaşmasına etki eden parametrelerin en iyi kombinasyonu belirlemek amacı ile bir deney tasarımı gerçekleştirilmiştir. Bu tez çalışması için Eskişehir Tülomsaş Motor Fabrikası'nda bir uygulama çalışması yürütülmüştür. Yürütülen bu çalışma, altı farklı amaç ağırlık değerleri kullanılarak hem konik skalerleştirmeli GA yaklaşımı ile hem de ağırlıklı toplam skalerleştirmeli GA yaklaşımı ile çözülmüştür. Amaç ağırlıklarının beşinde çok amaçlı konik skalerleştirme GA yaklaşımının daha baskın sonuçlara ulaşabildiği vurgulanmıştır. Ayrıca, önerilen çok amaçlı modelin gerçek hayat problemleri için de makul zamanda uygun çözümler üretebildiği gösterilmiştir.In today's highly competitive business environment, customers desire to buy various products with higher quality at lower costs. Manufacturing firms require a high degree of product variety and small manufacturing lot sizes to meet the demand variability. The product variations in manufacturing cause many problems such as lengthy setup and transportation times, complex scheduling. Cellular Manufacturing Systems contain the characteristics, which will respond to the needs of manufacturers, even though Conventional Manufacturing Systems are not flexible enough to respond to changes. In addition, in most real life manufacturing problems, some or all operations of a part can be processed on more than one machine, and sometimes operations may visit a machine or work center more than once. It is necessary to use resources effectively in order to run such a complex production system successfully. In this study, a mathematical model and a solution approach that deals with a flexible job shop scheduling problem in cellular manufacturing environment is proposed by taking into consideration exceptional parts, intercellular moves, intercellular transportation times, sequence-dependent family setup times, and recirculation. To the best of our knowledge, this is the first attempt to use multi-objective mathematical model and meta-heuristic approach for a Flexible Job Shop Cell Scheduling Problem (FJCSP). However, in the real-life applications, the scalarization method considered is highly important in terms of theoretical research and practical application because the FJCSP process is not easy because of many conflicting objectives. The proposed mixed integer non-linear model can be used for solving small and middle scaled problems. Solution of large scaled problems is not possible in reasonable time or takes too long time, so a Genetic Algorithm (GA) meta-heuristic approach that uses a multi-objective mathematical model with conic scalarization has been presented. An experimental design was used to determine the best combination of parameters which are affected performance of genetic algorithm to achieve optimum or sub-optimum solution. In this thesis study, a case study was conducted in Tülomsaş Locomotive and Engine Factory in Eskişehir. This study was solved by using both conic scalarization GA approach and weighted sum scalarization GA approach with six different weights of objective. It is emphasized that the multi-objective conic scalarization GA approach has better quality than other approach for five different weights of objective. In addition, it has been shown that the multi-objective model could also obtain optimum results in reasonable time for the real-world problems