Techniques of finding lower bounds in multi objective functions
Joint Authors
Jabbar, Adil K.
Ramadan, Iyad M.
Source
al- Rafidain Journal of Computer Sciences and Mathematics
Issue
Vol. 3, Issue 2 (31 Dec. 2006), pp.23-29, 7 p.
Publisher
University of Mosul College of Computer Science and Mathematics
Publication Date
2006-12-31
Country of Publication
Iraq
No. of Pages
7
Main Subjects
Topics
Abstract AR
تناولنا في هذا البحث جدولة n من النتاجات على ماكنة واحدة مع دالة الهدف المركبة.
مسألتان تمت دراستهما و هما مجموع الإتمام الكلي مضافا إليها أكبر تأخير(Tmax ∑_ieN▒〖C1+ 〗) و مجموع الإتمام الكلي مع أكبر تأخير (Tmax ∑_ieN▒〖c1 and〗).
المسألة الأولى لها حل أمثل عن طريق تقنية التفرع و التقيد أما المسألة الثانية فلها حلول كفؤة وجدت بطريقة خوارزمية فان وازنهوف.
قدمت نظرية تبين العلاقة بين الحلول الكفؤة، القيد و الحل الأمثل.
هذه النظرية تحدد مدى القيد الأدنى الذي يعتبر العامل الرئيسي لإيجاد الحل الأمثل، كذلك تقد مفاهيم و عمليات جبرية لإيجاد قيود دنيا جديدة.
Abstract EN
In this paper, the problm of sequencing n jobs on one machine is considered with a multi objective function.Two problems have been studied sum of completion times added with the maximum tardiness ∑_█(i∈N@ )▒〖Ci+ (T max) 〗 and sum of completion times with the maximum tardiness ∑_█(i∈N@ )▒〖Ci+ (T max) 〗 the first one has optimal solution solved by Branch and bound technique, the second has efficient solutions founded by Van Wassen hove algorithm.
A theorem is presented to show a relation between the number of efficient solutions, lower bound (LB) and optimal solution.
This theorem restricts the range of the lower bound, which is the main factor to find the optimal solution.
Also the theorem opens algebraic operations and concepts to find new lower bounds.
American Psychological Association (APA)
Ramadan, Iyad M.& Jabbar, Adil K.. 2006. Techniques of finding lower bounds in multi objective functions. al- Rafidain Journal of Computer Sciences and Mathematics،Vol. 3, no. 2, pp.23-29.
https://search.emarefa.net/detail/BIM-348848
Modern Language Association (MLA)
Ramadan, Iyad M.& Jabbar, Adil K.. Techniques of finding lower bounds in multi objective functions. al- Rafidain Journal of Computer Sciences and Mathematics Vol. 3, no. 2 (2006), pp.23-29.
https://search.emarefa.net/detail/BIM-348848
American Medical Association (AMA)
Ramadan, Iyad M.& Jabbar, Adil K.. Techniques of finding lower bounds in multi objective functions. al- Rafidain Journal of Computer Sciences and Mathematics. 2006. Vol. 3, no. 2, pp.23-29.
https://search.emarefa.net/detail/BIM-348848
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references : p. 29
Record ID
BIM-348848