حداقلسازی توابع هدف غیرنزولی برای مسئله زمانبندی واحد زمان کارگاه باز با الگوریتم ژنتیک
محورهای موضوعی :
مدیریت صنعتی
Ghorbanali Mohammadi
1
,
Taher Daali Matoorian
2
1 - Associate Professor, Industrial Engineering Department, College of Engineering, Qom University of Technology, Qom, Iran
2 - Master of Science, Industrial Engineering Department, College of Industrial Engineering, Islamic Azad University, Khalij Fars International Branch, Khormashahr, Iran
تاریخ دریافت : 1395/12/14
تاریخ پذیرش : 1395/04/28
تاریخ انتشار : 1395/06/04
کلید واژه:
Genetic Algorithm,
الگوریتم ژنتیک,
کارگاه باز,
روش تقاطع PMX,
جهش جابجایی,
تابع هدف تفکیک پذیر,
Open shop,
partially matched crossover,
Displacement mutation,
Separable objective functions,
چکیده مقاله :
در عصر حاضر، برنامه ریزی فعالیتی ضروری و اجتناب ناپذیر در تمام امور فردی، اجتماعی و سازمانی محسوب میشود. به نحوی که بدون توجه به آن هیچ فعالیتی به صورت کارآمد و موثر تحقق نخواهد گرفت. یکی از مسائل مهم مورد بحث در علم تحقیق در عملیات راجع به موضوع زمانبندی است. این مطالعه به مسئله کارگاه باز میپردازد، زیرا در سالهای اخیر، کاربرد مدل‌های ریاضیاتی برای حل بهینه ای مسائل زمانبندی توجه بسیاری از محققین را به خود جلب کرده است. در این راستا، بسیاری از تحقیقات درباره مدلسازی کار کارگاهی و جریان کارگاهی بوده و روی فرمول‌بندی مسئله زمانبندی کارگاه باز انجام شده است. هدف این تحقیق یافتن راه حلی ساده و بهینه برای مسئله زمانبندی کارگاه باز با تابع هدف تفکیکپذیر با استفاده از روش فراابتکاری الگوریتم ژنتیک می باشد. در الگوریتم این مسئله، عملگر تقاطع PMX و عملگر جهش جابهجایی استفاده شد. در ادامه نیز مقایسهای میان جوابهای به دست آمده به سه روش انتخاب متفاوت در کدبندی الگوریتم ژنتیک شامل روشهای انتخاب برتر، انتخاب تورنمنتی و انتخاب چرخ رولت صورت می گیرد. اطلاعات مورد نیاز برای این پژوهش بهصورت کتابخانهای و مراجعه به اسناد، مدارک و سایتهای معتبر جمع آوری شد. نتایج پژوهش حاضر حاکی از آن بود که مسئله زمانبندی کارگاه باز با استفاده از الگوریتم فراابتکاری ژنتیک راحت تر و سریعتر به جواب می رسد و روش انتخاب برتر جواب بهتری را نسبت به دو روش دیگر نشان میدهد.
چکیده انگلیسی:
Planning is currently considered as an important element for the whole personal, societal and organizational affairs, whereby every activity would be performed effectively. Scheduling is of high significance in operations research. Recently, scholars have drawn much attention to the application of mathematical modeling as an optimization approach in solving the complex scheduling problems. However, only a few have addressed the open-shop scheduling problem. This study was intended to investigate the effectiveness of meta-heuristic genetic algorithm in order to minimize non-decreasing separable objective functions for such problem. In this genetic algorithm, displacement mutation and partially matched crossover were adopted as two operators. Moreover, the obtained solutions were compared based on how to select the best chromosome by using methods of tournament selection, rank selection, and roulette wheel selection. The data were collected through literature review. It was exhibited that meta-heuristic genetic algorithm can rapidly find the optimal solution. Furthermore, rank selection resulted in more optimal solutions instead of the other two.
منابع و مأخذ:
Adiri, I. (1989). Open‐shop scheduling problems with dominated machines. Naval Research Logistics, 36(3), 273-281.
Alam-Tabriz, A., & Mohmmadrahimi A. (2013). Meta-heuristic algorithms in combinatorial optimization. Tehran: Safar Publication.
Alharkan, I. M. (2005). Algorithms for sequencing and scheduling. King Saud University, Riyadh, Saudi Arabia.
Baker, K. R. (1995). Elements of sequencing and scheduling. New York: Wiley.
Cheng, T. E., & Shakhlevich, N. V. (2005). Minimizing non-decreasing separable objective functions for the unit-time open shop scheduling problem. European Journal of Operational Research, 165(2), 444-456.
Conway, R. W., Maxwell, W. L., & Miller, L. W. (2012). Theory of scheduling. New York: Dover Publications, Incs.
Deb, K. (1995). Optimization for engineering design: algorithms and examples. New Delhi: Prentice Hall.
Fang, H. L. (1994). Genetic algorithms in timetabling and scheduling (Doctoral dissertation). University of Edinburgh, Scotland.
França, P. M., Gupta, J. N., Mendes, A. S., Moscato, P., Veltink, K. J. (2005). Evolutionary algorithms for scheduling a flowshop manufacturing cell with sequence dependent family setups. Computers & Industrial Engineering, 48(3), 491-506.
Karuno, Y., & Nagamochi, H. (2004). An approximability result of the multi-vehicle scheduling problem on a path with release and handling times. Theoretical Computer Science, 312(2), 267-280.
Lawler, E. L., Lenstra, J. K., Rinnooy Kan, A. H. G., & Shmoys, D. B. (1993). Sequencing and scheduling: algorithms and complexity. P27-130, In: Graves, S.C., A.H.G. Rinnooy Kan and P.H. Zipkin (eds.), Handbooks in operations research and management science.Amsterdam: Elsevier Science Publishers.
Lee, C.-Y., and Herrmann, J. W. (1993). A Three-Machine Scheduling Problem with Look-Behind Characteristics. Research Reports, 93-11.
Mohammadi, G. (2015). Multi-objective flow shop production scheduling via robust genetic algorithms optimization technique. International Journal of Service Science, Management and Engineering, 2(1), 1-8.
Mohammadi, G. (2011). Metaheuristic algorithms. Kerman: Jahad Daneshgahi Publication.
Morton, T., & Pentico, D. W. (1993). Heuristic scheduling systems: with applications to production systems and project management. New York: John Wiley & Sons.
Pinedo, M. L. (2008). Scheduling: theory, algorithms and systems. New York: Springer.
Seraj, O., & Tavakkoli-Moghaddam, R. (2009). A tabu search method for a new bi-objective open shop scheduling problem by a fuzzy multi-objective decision making approach (research note). International Journal of Engineering-Transactions B: Applications, 22(3), 1-14.
Zobolas, G. I., Tarantilis, C. D., & Ioannou, G. (2009). Solving the open shop scheduling problem via a hybrid genetic-variable neighborhood search algorithm. Cybernetics and Systems, 40(4), 259-285.
_||_
Adiri, I. (1989). Open‐shop scheduling problems with dominated machines. Naval Research Logistics, 36(3), 273-281.
Alam-Tabriz, A., & Mohmmadrahimi A. (2013). Meta-heuristic algorithms in combinatorial optimization. Tehran: Safar Publication.
Alharkan, I. M. (2005). Algorithms for sequencing and scheduling. King Saud University, Riyadh, Saudi Arabia.
Baker, K. R. (1995). Elements of sequencing and scheduling. New York: Wiley.
Cheng, T. E., & Shakhlevich, N. V. (2005). Minimizing non-decreasing separable objective functions for the unit-time open shop scheduling problem. European Journal of Operational Research, 165(2), 444-456.
Conway, R. W., Maxwell, W. L., & Miller, L. W. (2012). Theory of scheduling. New York: Dover Publications, Incs.
Deb, K. (1995). Optimization for engineering design: algorithms and examples. New Delhi: Prentice Hall.
Fang, H. L. (1994). Genetic algorithms in timetabling and scheduling (Doctoral dissertation). University of Edinburgh, Scotland.
França, P. M., Gupta, J. N., Mendes, A. S., Moscato, P., Veltink, K. J. (2005). Evolutionary algorithms for scheduling a flowshop manufacturing cell with sequence dependent family setups. Computers & Industrial Engineering, 48(3), 491-506.
Karuno, Y., & Nagamochi, H. (2004). An approximability result of the multi-vehicle scheduling problem on a path with release and handling times. Theoretical Computer Science, 312(2), 267-280.
Lawler, E. L., Lenstra, J. K., Rinnooy Kan, A. H. G., & Shmoys, D. B. (1993). Sequencing and scheduling: algorithms and complexity. P27-130, In: Graves, S.C., A.H.G. Rinnooy Kan and P.H. Zipkin (eds.), Handbooks in operations research and management science.Amsterdam: Elsevier Science Publishers.
Lee, C.-Y., and Herrmann, J. W. (1993). A Three-Machine Scheduling Problem with Look-Behind Characteristics. Research Reports, 93-11.
Mohammadi, G. (2015). Multi-objective flow shop production scheduling via robust genetic algorithms optimization technique. International Journal of Service Science, Management and Engineering, 2(1), 1-8.
Mohammadi, G. (2011). Metaheuristic algorithms. Kerman: Jahad Daneshgahi Publication.
Morton, T., & Pentico, D. W. (1993). Heuristic scheduling systems: with applications to production systems and project management. New York: John Wiley & Sons.
Pinedo, M. L. (2008). Scheduling: theory, algorithms and systems. New York: Springer.
Seraj, O., & Tavakkoli-Moghaddam, R. (2009). A tabu search method for a new bi-objective open shop scheduling problem by a fuzzy multi-objective decision making approach (research note). International Journal of Engineering-Transactions B: Applications, 22(3), 1-14.
Zobolas, G. I., Tarantilis, C. D., & Ioannou, G. (2009). Solving the open shop scheduling problem via a hybrid genetic-variable neighborhood search algorithm. Cybernetics and Systems, 40(4), 259-285.
