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Article
Solving Four Cost Multi-Objective Scheduling Problem Simultaneously
حل أربعة دوال في مسألة جدولة متعددة الأهداف سويتا

Authors: Tariq S . Abdul – Razaq --- Hafed M . Motair2
Journal: journal of kerbala university مجلة جامعة كربلاء ISSN: 18130410 Year: 2018 Volume: 16 Issue: 1 Pages: 77-88
Publisher: Kerbala University جامعة كربلاء

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Abstract

In this paper, we consider single machine scheduling problem (P) to minimize four cost functions, total completion times, total tardiness, maximum tardiness, and maximum earliness. The minimization besed on two types, in the first one we study some special cases including lexigraphical minimization of problem (P). In the second type we minimize four cost functions simultaneously and propose CTTE algorithm ( total completion time, total tardiness, maximum tardiness and maximum earliness) to find the set of "non-dominated solutions" of problem (P), also improve this algorithm by using intensification procedure (IMCTTE) (Imoroved CTTE). Also we propose MOVNS (Multiobjective variable neighborhood search) algorithm based on the variable neighborhood and Intensification Procedure ideas .We compare the proposed algorithms with NSGA2 algorithm. The performance of the proposed algorithms is evaluated on a large set of test problems and the results are compared. The compu- tational results show that IMCTTE algorithm is more efficient than CTTE algorithm in both, number of "non-dominated solutions" and the controbution of "non-dominated solutions" that belong to reference set. Also we find that MOVNS algorithm give better performance than CTTE and IMCTTE algorithms for all problem instancs, and better than NSGA2 specially for small size problems .

تم في البحث دراسة مسأله الجدولة لماكنة واحدة (P) لتصغير أربعة دوال: مجموع زمن إتمام النتاجات , مجموع أزمان التبكير, أكبر زمن تبكير, وأكبر زمن تأخير. تم تناول نوعين من مسائل التصغير: الأول التصغير حسب الأهمية(lexigraphical) والثاني تصغير الدوال سويتا (simultaneously). اقترحنا خوارزميه (CTTE) ثم تحسينها بخوارزمية (IMCTTE). وتم في البحث اقتراح خوارزميه البحث المحلي متعددة الأهداف (MOVNS) ومقارنه جميع الخوارزميات المقترحه مع الخوارزمية الجينية متعددة الأهداف (NSGA2). أداء الخوارزميات المقترحة تم اختباره مع مجموعه واسعه من مسائل الاختبار وبمقارنة النتائج ظهر أداء خوارزمية (IMCTTE) أفضل من خوارزمية (CTTE) وذلك حسب معياري المقارنة, وكذلك وجدنا أن أداء خوارزمية (MOVNS) أفضل من الخوارزميات المقترحة (CTTE, IMCTTE) في جميع المسائل المدروسة, وأنها أفضل من خوارزمية (NSGA2) عندما n صغيرة.


Article
Solving Composite Multi objective Single Machine Scheduling Problem Using Branch and Bound and Local Search Algorithms

Author: Tariq S. Abdul – Razaq1
Journal: Al-Mustansiriyah Journal of Science مجلة علوم المستنصرية ISSN: 1814635X Year: 2017 Volume: 28 Issue: 3 Pages: 200-208
Publisher: Al-Mustansyriah University الجامعة المستنصرية

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Abstract

This paper present algorithm for solving a single machine scheduling problem to minimize the sum of total completion times, total tardiness, maximum tardiness, and maximum earliness. The single machine total tardiness problem is already NP-hard, so they consider problem is strongly NP-hard, and several algorithms are used to solve it. Branch and bound algorithm with dominance rule and local search algorithms are proposed for the problem. For the Branch and bound algorithm results- show that using dominance rule improve the performance of the algorithm in both computation times and optimal values, but it needs longer times. Thus we tackle the problem of large sizes with local search algorithms descent method, simulated annealing and tabu search. The performance of these algorithms is evaluated on a large set of test problems and the results are compared. The computational results show that simulated annealing algorithm and Tabu search algorithm are better than descent method with preference to simulated annealing algorithm, and show that the three algorithms find optimal or near optimal solutions in reasonable times.

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