تحليل الخوارزميات Big-Oh notation
This work deals with a new method for solving Integer Linear Programming Problems depending on a previous methods for solving these problems, such that Branch and Bound method and Cutting Planes method where this new method is a combination between t
hem and we called it Cut and Branch method. The reasons which led to this combination between Cutting Planes method and Branch and Bound method are to defeat from the drawbacks of both methods and especially the big number of iterations and the long time for the solving and getting of a results between the results of these methods where the Cut and Branch method took the good properties from the both methods. And this work deals with solving a one problem of Integer Linear Programming Problems by Branch and Bound method and Cutting Planes method and the new method, and we made a programs on the computer for solving ten problems of Integer Linear Programming Problems by these methods then we got a good results and by that, the new method (Cut and Branch) became a good method for solving Integer Linear Programming Problems. The combination method which we doing in this research opened a big and wide field in solving Integer Linear Programming Problems and finding the best solutions for them where we did the combination method again between the new method (Cut and Branch) and the Cutting Planes method then we got a new method with a very good results and solutions.
In this paper we consider the properties of linear systems by means of
directed graphs and numerical structures. We also state efficient algorithms
for determining an approximate number of the non-zero terms within
determinants' expressions of the
ir matrices. The stated algorithms make use of
trees representing numerical structures which contains the indices of the nonzero
terms.
This paper yields interesting results used in practical engineering
applications which include linear systems with sparse matrices, for example:
networks, electronic circuits, earth velocities boxes (gearboxes), multi-works
systems ...etc.
In this paper we present mathematical models for
transportation problems, primal problem and dual. First, we show
how is the formulation of dual transportation problem models.
Finally, As a solution to the two models lead to a solution other
model, we have to dissolve the Dual transportation problem, so we
relied on the least cost method in resolving the primal
transportation problem.
في المشكلة التي نعالجها, تحتاج شركة اتصالات إلى بناء مجموعة من الأبراج الخلوية لتوفير خدمة الاتصالات الخليوية للسكان في منطقة جغرافية. تم تحديد عدد من المواقع المحتملة لبناء الأبراج. يعتم اختيار هذه المواقع على عدة عوامل ، بما في ذلك مدى اتساق البرج
مع البيئة المحيطة وارتفاع التضاريس, تتمتع الأبراج بمدى تغطية ثابت ، وبسبب قيود الميزانية ، لا يمكن بناء سوى عدد محدود منها . بالنظر إلى هذه القيود ، ترغب الشركة في توفير تغطية لأكبر قدر ممكن من السكان, والهدف هو اختيار في أي من المواقع المحتملة يجب أن تقوم الشركة ببناء الأبراج.
إن المشكلة التي شرحناها يمكن نمذجتها لتصبح أحد أمثلة مشكلة 0/1 knapsack الشهيرة لذلك شرحنا في الحلقة مفهوم مشكلة 0/1 Knapsack والطرق المستخدمة في الحل, وتوسعنا في الشرح عن خوارزمية Branch and Bound كونها تعتبر أفضلها.
