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Solving Urban Bus Terminal Location Problem Using Genetic Algorithm S.M. Seyed-Hosseini*, R. Heydari & T. Heydari S.M. Seyed-Hosseini,Department of Industrial Engineering, Iran University of Science & Technology, Tehran, Iran R. Heydari, Department of Industrial Engineering, Shahed University T. Heydari, Department of Industrial Engineering, Iran University of Science & Technology, Tehran, Iran Keywords ABSTRACT Bus network design is an important problem in public transportation. The main step to this design, is determining the number of required terminals and their locations. This is an especial type of facility location problem, a large scale combinatorial optimization problem that requires a long time to be solved. Branch & bound and simulated annealing methods have already been used for solving Urban Bus Terminal Location Problem(UBTLP) that first method requires much time and second method doesnt reach desired solution. In this paper, a Genetic Algorithm is suggested for solving the problem. The main advantages of proposed algorithm are reaching better solution and taking less time. The demonstrated results have shown that proposed Genetic Algorithm can be an efficient and confident approach for solving UBTLP. For verification of proposed methodology, two illustrative practical examples are solved and obtained outcomes are reported. ' Ŷǀƫƺţ ŢƿźƿŶƯ ƹ ƖƿŚƴƇ ƾſŶƴƸƯ ƾƬƬưƫř Ʋǀŝ ƶƿźƄƳ ƵŹŚưƃ è ŶƬū çå æèíí ƱŚƨƯ ƶƫŚƀƯ ƪů ƱŚƨƯ ƶƫŚƀƯ ƪů ƶƳŚƿŚě ƾŝŚƿ ƶƳŚƿŚě ƾŝŚƿ Žƺŝƺţř ƶƨŞƃ ƽŚƷ Žƺŝƺţř ƶƨŞƃ ƽŚƷ ƱƹŹŵ ƾƳřŹ ƱƹŹŵ ƾƳřŹ Śŝ ƽźƸƃ Śŝ ƽźƸƃ ƦǀŤƳĥ ƮŤƿŹƺĮƫř Żř ƵŵŚƠŤſř ƦǀŤƳĥ ƮŤƿŹƺĮƫř Żř ƵŵŚƠŤſř ƾƴǀƀůŶǀſ ŶưŰƯŶǀſ ƾƴǀƀůŶǀſ ŶưŰƯŶǀſ ŭƹŹ ŭƹŹ ƽŹŶǀů ƶƫř ƽŹŶǀů ƶƫř ƹ ƽŹŶǀů ƵźƷŚƏ ƽŹŶǀů ƵźƷŚƏ ŶǀƬĩ šŚưƬĩ ƽ ƵŶǀĪģ Î ƶƨŞƃ ƾůřźƏ Žƺŝƺţř ƽŚƷ Ţſř ƾƯƺưƗ ƪƤƳ ƹ ƪưů Źŵ ƮƸƯ ƶƫŚƀƯ Ʀƿ ƾƳřŹ ƭŚĭ Żř ƾƨƿ ƮƸƯ ƽŚƷ ƶŞſŚŰƯ ŚŤſřŹ Ʋƿř Źŵ ƱŚƨƯ ƹ ŵřŶƘţ ƽ ƶƴǀƸŝ ƽŚƷ ƶƳŚƿŚě ƽ Ţſř ŻŚǀƳ ŵŹƺƯ ƽŚƷ ƶŝ ƶƫŚƀƯ Ʋƿř Ɩƣřƹ Źŵ ƱŚƨƯ ƶƫŚƀƯ Żř ƾƇŚų ŢƫŚů ƱřƺƴƗ ƶƫŚƀƯ Ʀƿ ƶĩ šLjǀƸƀţ ƾŝŚƿ Śŝ ƾţŚǀŞǀƧźţ ƽŻŚſ ƶƴǀƸŝ ƽ ŵŹřŵ ƪů ƽřźŝ ƽŵŚƿŻ ƱŚƯŻ ƶŝ ŻŚǀƳ Ţſř īŹżŝ ŽŚǀƤƯ ƩƺƇƹ ŲƿŹŚţ ƩƺƇƹ ŲƿŹŚţ çç çç æå æå íë íë Ŝƿƺƈţ ŲƿŹŚţ Ŝƿƺƈţ ŲƿŹŚţ æê æê í íì íì ƾƴǀƀůŶǀſ ŶưŰƯ Ŷǀſ źŤƧŵ ƬƗ ƵŚĮƄƳřŵ ƖƿŚƴƇ ƾſŶƴƸƯ ƵŶƨƄƳřŵ Ʊřźƿř ŢƘƴƇ ƹ Ʈ [email protected] ŭƹŹ ƽŹŶǀů ƶƫř ƱřźƸţ ŶƷŚƃ ƵŚĮƄƳřŵ ƾſŶƴƸƯ ƹ ƾƴƟ ƵŶƨƄƳřŵ [email protected] ƽŹŶǀů ƵźƷŚƏ ƱŚƜƯřŵ ŹƺƳ ƭŚǀě ƵŚĮƄƳřŵ šŚƗLjƏř įŹƹŚƴƟ Ƶƹźĭ [email protected] Bus Networks, Location Problem, Genetic Algorithm (GA), Mixed Integer Programming (MIP) ƶƨŞƃ Žƺŝƺţř ƽ ƾƳřŹ ƶƫŚƀƯ ƱŚƨƯ ƽ ƾŝŚƿ ƦǀŤƳĥ ƮŤƿŹƺĮƫř Ƴźŝ ƎƬŤŴƯ ŮǀŰƇ ŵŶƗ ƽżƿŹ ƶƯŚ ưƃ ưƃ ºº ºº ƵŹŚ ƵŹŚ è è Ƭū Ƭū ºº ºº Ŷ Ŷ çå çå żǀƿŚě żǀƿŚě æèíí æèíí Journal Website: http://IJIEPM.iust.ac.ir/ ISSN: 2008-4870 Downloaded from ijiepm.iust.ac.ir at 4:55 IRST on Friday January 24th 2020

حل مساله مکانیابی پایانههای شبکه اتوبوسرانی درونشهری ...ijiepm.iust.ac.ir/article-1-156-fa.pdfS olv ingUrbaBu sT emLct P! Genetic Algorithm

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Solving Urban Bus Terminal Location Problem Using

Genetic Algorithm S.M. Seyed-Hosseini*, R. Heydari & T. Heydari

S.M. Seyed-Hosseini,Department of Industrial Engineering, Iran University of Science & Technology, Tehran, Iran R. Heydari, Department of Industrial Engineering, Shahed University T. Heydari, Department of Industrial Engineering, Iran University of Science & Technology, Tehran, Iran

Keywords ABSTRACT

Bus network design is an important problem in public transportation. The main step to this design, is determining the number of required terminals and their locations. This is an especial type of facility location problem, a large scale combinatorial optimization problem that requires a long time to be solved.�Branch & bound and simulated annealing methods have already been used for solving Urban Bus Terminal Location Problem(UBTLP) that first method requires much time and second method doesn�t reach desired solution. In this paper, a Genetic Algorithm is suggested for solving the problem. The main advantages of proposed algorithm are reaching better solution and taking less time. The demonstrated results have shown that proposed Genetic Algorithm can be an efficient and confident approach for solving UBTLP. For verification of proposed methodology, two illustrative practical examples are solved and obtained outcomes are reported.

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ƾƴǀƀůŶǀſ�ŶưŰƯ�Ŷǀſ�źŤƧŵ��ƬƗ�ƵŚĮƄƳřŵ��ƖƿŚƴƇ�ƾſŶƴƸƯ�ƵŶƨƄƳřŵƱřźƿř�ŢƘƴƇ�ƹ�Ʈ�[email protected]� ��ŭƹŹƽŹŶǀů�ƶƫř�ƱřźƸţ��ŶƷŚƃ�ƵŚĮƄƳřŵ��ƾſŶƴƸƯ�ƹ�ƾƴƟ�ƵŶƨƄƳřŵ���[email protected]���

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Bus Networks, Location Problem, Genetic Algorithm (GA), Mixed Integer Programming (MIP)

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ŶǀŝŚǀŝ� řŹ�ƦǀŤƳĥ�ƮŤƿŹƺĮƫř�ƽŚƷźŤƯřŹŚě� �� źƿŵŚƤƯxƹ�yƱŚƄƳ� ƶĩ� ��ƵŶƴƷŵƵźĭ�ƉźƗ�ƹ�ƩƺƏƾƯ�šŚƈŤŴƯ�ƵŚĮŤſŵ�Źŵ�ƶĪŞƃ�ƽŚƷ�Ŝƀů�źŝ��ŶƴƃŚŝ

æåå�źƿŵŚƤƯ�ƹ�źŤƯ�dŢſř�ƵŶƃ�Ƶŵřŵ�ŢƗŚſ�Źŵ�źƠƳ�Ŝƀů�źŝ����J�=�{1,2,�,60}

I={2,3,5,11,15,17,18,20,21,23,27,28,35,43,44,49,50,52,56,59} k�=�5 r�=�5

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Y = {24/74, 40/09, 50/39, 15/43, 33/47, 57/08, 13/35, 0/42, 44/30, 24/02, 15/10, 36/13, 17/61, 2/73, 30/79, 2/13, 29/85, 48/19, 30/16, 14/29, 5/32, 54/21, 37/89, 22/74, 18/88, 32/11, 52/50, 53/12,37/63, 50/87, 48/44, 57/70, 57/22, 38/79, 10/48, 58/21, 15/06, 40/59, 30/73, 13/61, 51/68, 29/15, 46/37, 31/35, 35/47,6/58,59/83,10/56,18/56,22/57,43/16,37/06,45/38,35/97,10/32,4/16,19/04,45/60,42/92, 50/75}

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D = {24, 44, 41, 32, 40, 33, 17, 14, 17, 26, 36, 15, 41, 28, 18, 35, 27, 22, 34, 31, 20, 14, 40, 23, 13, 30, 15, 14, 11, 23, 40, 13, 41, 21, 12, 12, 33, 30, 51, 36, 28, 40, 45, 23, 58, 51, 17, 38, 41, 21, 33, 45, 40, 29, 8, 55, 23, 37, 15, 19}

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