خوارزمية القطع والتفريع الجديدة لحل مسائل البرمجة الخطية الصحيحة
Abstract
يتناول هذا البحث طريقة جديدة لحل مسائل البرمجة الخطية الصحيحة بالاعتماد على طرق سابقة لحل مثل هذه المسائل, نذكر منها طريقة التفريع والعقد (الحدود) وطريقة قطع المستويات (خوارزمية الاقتطاع لغوماري) المعروفتين. وطريقتنا الجديدة تعتمد على عملية تركيب وربط بين الطريقتين المذكورتين وقد اقترحنا تسميتها بطريقة القطع والتفريع الجديدة.
الأسباب التي أدت إلى الربط بين طريقة التفريع والعقد وطريقة قطع المستويات, هي للتغلب على بعض مساوئ الطريقتين وخاصة عند التكرارات الكبيرة والوقت المستغرق الكبير في الحل, والحصول على نتائج تنحصر بين نتائج كل من الطريقتين, ويمكن القول إن طريقة القطع والتفريع الجديدة أخذت الصفات الجيدة واستبعدت الكثير من الصفات السيئة للطريقتين المذكورتين.
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 them 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.
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