Tesis düzenleme problemleri, işletmelerin üretim maliyetlerini etkileyen en önemli unsurlardan birisidir. Bu nedenle, rekabetçi gücünü korumak isteyen işletmelerin, tesis düzenleme konusuna özen göstermeleri gerekmektedir. Tek sıra tesis düzenlemesi ise, esnek üretim sistemlerinde ve hücresel imalat sistemlerinde en çok kullanılan, tesis düzenleme yöntemlerinden birisidir ve literatürde bu problemi inceleyen pek çok çalışma mevcuttur.
Tek sıra tesis düzenleme problemleri NP-zor problem sınıfında yer almaktadır ve araştırmacılar tarafından pek çok farklı sezgisel yöntemle incelenmiştir. Bu tez çalışması kapsamında, tek amaçlı tek sıra tesis düzenleme problemleri için, farklı komşuluk tarama mekanizmalarına sahip 3 farklı TB algoritması ve farklı parametre değerlerine sahip 2 GA geliştirilmiştir. Bu algoritmaların performansı, literatürde sıklıkla incelenen problemler üzerinde test edilmiş, sonuçlar ve değerlendirmeler sunulmuştur. Sonuçlar incelendiğinde, önerilen TB algoritmalarının daha uzun hesaplama sürelerine karşın, daha iyi sonuçlar verdiği görülmüştür. Önerilen genetik algoritmalar ise, kabul edilebilir hesaplama sürelerinde daha başarısız sonuçlar vermiştir. Genetik algoritmanın performansı yerel arama algoritmaları eklenmesiyle ve parametre değerlerinin iyileştirilmesiyle arttırılabilir.
Gerçek hayat problemlerinde, tesis düzenlemesini etkileyen birçok faktör vardır. Bu nedenle, tesis düzenleme problemlerine çözüm ararken, birden fazla amacın dikkate alınması daha uygundur. Literatürde tek sıra tesis düzenleme problemini, çok amaçlı olarak ele alan çok az sayıda çalışma vardır. Bu tez çalışmasının ikinci aşamasında, gerçek hayat problemlerine yaklaşmak ve literatürdeki bu alandaki eksikliğe katkıda bulunmak amacıyla, tek sıra tesis düzenleme problemleri çok amaçlı olarak da ele alınmıştır.
Problemin çözümünde, hızlı bir şekilde pareto etkin kümeyi veren NSGA II algoritması kullanılmıştır. Aynı zamanda ele alınan problemler ağırlıklı hedef programlama ile de çözülmüştür. Ele alınan problemler için ağırlıklı hedef programlama ve NSGA II ile elde edilen pareto etkin çözümler karşılaştırılmıştır. Karşılaştırma sonucunda, NSGA II algoritmasının ağırlıklı hedef programlamaya göre çok daha kısa hesaplama sürelerinde, daha iyi sonuçlar verdiği görülmüştür. Aynı zamanda NSGA II algoritması ile daha fazla
sayıda pareto etkin çözüm elde edilmiş ve karar vericinin çözümler içinden, ele alınan amaçlara verdiği önem derecesine göre seçim yapmasına imkân tanınmıştır.
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EKLER
EK-1. O verileri için elde edilen en iyi çözümler ve sapma değerleri (Obata, 1979)
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TB - araya ekleme TB - yer değiştirme TB - tekli blokGA1GA2 Sapma değerleri GA1GA2TB-araya ekleme ProblemBoyutBilinen en iyi çözümTB-yer değiştirmeTB-tekli blok
EK-2. N verileri için elde edilen en iyi çözümler ve sapma değerleri (Nugent ve Vollmann, 1968)
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Sapma değerleri GA1GA2 ProblemBoyutBilinen en iyi çözüm
TB-araya eklemeTB-yer değiştirmeTB-tekli blok
EK-3. AMR verileri için elde edilen en iyi çözümler ve sapma değerleri
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TB - araya ekleme TB - yer değiştirme TB - tekli blokGA1GA2 Sapma değerleri GA1GA2 ProblemBoyutBilinen en iyi çözüm
TB-araya eklemeTB-yer değiştirmeTB-tekli blok
EK-4. STE verileri için elde edilen en iyi çözümler ve sapma değerleri (Anjos veYen, 2009)
en büyükortalamaen küçüken büyükortalamaen küçüken büyükortalamaen küçüken büyükortalamaen küçüken büyükortalamaen küçük STE136102870,15520,09390,03450,14310,12520,02280,10660,07770,00020,54310,33490,21870,43340,35460,2473 STE2361815080,11780,06900,01780,11110,08900,00690,10040,06840,01430,36110,28880,23430,37020,27060,1780 STE336101643,50,14650,07150,00300,14470,10250,00360,14280,07940,00720,37670,32200,26110,42790,30000,2001 STE43695805,50,11660,08570,00930,12350,08850,01420,09820,04240,00070,41770,34660,28110,43320,32220,2153 STE53691651,50,13770,037400,19710,14160,01300,15480,04690,00510,46570,35520,26850,42350,34900,2415 STE136102871064210522102891253712831 STE236181508184741182762184097224039213811 STE336101643,5101948,5102013,5102374,5128179,5121984,5 STE43695805,596694,597162,595876,5122736,5116430,5 STE53691651,591651,592844,592119,5116261,5113781,5 Elde edilen en iyi çözümler ProblemBoyutBilinen en iyi çözüm
TB - araya ekleme TB - yer değiştirme TB - tekli blokGA1GA2 Sapma değerleri GA1GA2 ProblemBoyutBilinen en iyi çözüm
TB-araya eklemeTB-yer değiştirmeTB-tekli blok
EK-5. HURE verileri için elde edilen en iyi çözümler ve sapma değerleri (Hungerlander ve Rendl, 2012)
en büyükortalamaen küçüken büyükortalamaen küçüken büyükortalamaen küçüken büyükortalamaen küçüken büyükortalamaen küçük HURE140107348,50,03790,012600,03750,02000,00070,04610,03070,01300,11020,08450,04900,10750,07440,0568 HURE240976930,05090,02150,00010,06780,03240,00250,05530,02770,00250,10880,06490,02530,11500,08640,0432 HURE34078589,50,03800,008900,06180,02860,00040,07630,01960,00490,12220,08090,04980,12500,08570,0481 HURE440766690,04730,020300,04250,02420,00010,04850,03210,00110,12270,09020,05620,13270,07920,0392 HURE5401030090,05030,02720,00030,02950,01740,00030,04280,024700,11300,08640,05350,11410,08770,0625 HURE140107348,5107348,5107419,5108744,5112607,5113446,5 HURE24097693976989793997938100163101911 HURE34078589,578589,578617,578977,582501,582367,5 HURE440766697666976676767548097779671 HURE540103009103038103040103009108525109443 Elde edilen en iyi çözümler ProblemBoyutBilinen en iyi çözümTB - araya eklemeTB - yer değiştirmeTB - tekli blokGA1GA2
Sapma değerleri GA2 ProblemBoyutBilinen en iyi çözüm
TB-araya eklemeTB-yer değiştirmeTB-tekli blokGA1
EK-6. S verileri için elde edilen en iyi çözümler ve sapma değerleri (Sarker, 1989)
en büyükortalamaen küçüken büyükortalamaen küçüken büyükortalamaen küçüken büyükortalamaen küçüken büyükortalamaen küçük S11244310,10180,011400,08670,009900,03770,003800,01760,011500,03020,01400 S21358970,07770,010900,03730,007000,04950,008000,01630,01080,00470,01760,01290,0039 S31473160,08110,008400,07850,014000,05400,006300,02300,01490,00450,02100,00980,0023 S41589420,01930,001900,04100,008900,01720,003300,02450,01430,00180,02250,01270,0057 S516110190,02150,004200,02430,007800,00860,001000,02500,01510,00850,02760,01560,0050 S617131720,01490,004200,00820,003700,01180,003300,02460,01410,00350,02840,01530,0040 S718156990,01500,003100,01320,002700,01500,003600,02960,01230,00340,02540,01170,0044 S819187000,00910,00420,00020,01340,005100,00710,001900,02760,01260,00240,02390,01450,0063 S920218250,00620,002200,00960,004800,01260,004200,01750,01050,00420,02110,01100,0042 S1021248910,01230,002200,01560,00970,00030,01520,00480,00030,01650,00820,00290,02010,01030,0023 S1122286070,01150,00250,00020,01610,00570,00010,00240,00130,00020,02380,01220,00480,01500,01020,0055 S1223330460,01410,003200,00960,00270,00030,01430,00480,00060,01490,00880,00400,02000,00940,0045 S1324374980,01850,004100,01000,005100,00600,00120,00030,02050,01440,00530,01980,01350,0078 S1425423490,01450,003300,01290,005800,00810,00160,00020,01700,01010,00460,01620,01220,0061
Sapma değerleri GA1GA2 ProblemBoyutBilinen en iyi çözüm
TB-araya eklemeTB-yer değiştirmeTB-tekli blok
EK-6. (devam) S verileri için elde edilen en iyi çözümler ve sapma değerleri (Sarker, 1989)
S1 12 4431 4431 4431 4431 4431 4431
S2 13 5897 5897 5897 5897 5925 5920
S3 14 7316 7316 7316 7316 7349 7333
S4 15 8942 8942 8942 8942 8958 8993
S5 16 11019 11019 11019 11019 11113 11074
S6 17 13172 13172 13172 13172 13218 13225
S7 18 15699 15699 15699 15699 15753 15768
S8 19 18700 18704 18700 18700 18744 18817
S9 20 21825 21825 21825 21825 21916 21916
S10 21 24891 24891 24899 24899 24964 24948
S11 22 28607 28613 28611 28614 28745 28763
S12 23 33046 33046 33055 33067 33178 33195
S13 24 37498 37498 37498 37509 37695 37789
S14 25 42349 42349 42349 42356 42542 42608
Elde edilen en iyi çözümler
Problem Boyut Bilinen en iyi çözüm
TB - araya ekleme
TB - yer
değiştirme TB - tekli blok GA1 GA2
EK-7. Y verileri için elde edilen en iyi çözümler ve sapma değerleri (Yu ve Sarker, 2003)
en büyükortalamaen küçüken büyükortalamaen küçüken büyükortalamaen küçüken büyükortalamaen küçüken büyükortalamaen küçük Y1613720,04300,006900,01460,002800,01240,002400,00510,000500,00290,00050 Y2718010,02720,005400,04440,006100,06500,02670,01110,01390,003200,01280,00510 Y3823020,09210,010800,07300,007800,05300,00840,00350,01260,004600,01040,00500,0017 Y4928080,09050,020900,11180,018000,08440,008400,02170,007300,02670,00880 Y51035080,05500,008600,12940,016700,09610,02400,01480,01450,00790,00060,01510,00660 Y61140220,06810,011900,06740,008200,06660,02830,02310,02490,00850,00250,02810,01390,0027 Y71247930,11180,012300,11430,012500,05650,00780,00020,01420,00810,00100,02300,01200,0021 Y81354710,09910,009900,01770,001800,05850,02360,01720,02390,00800,00050,02470,01390,0009 Y91464450,07430,009000,05660,006700,01660,00380,00140,02020,01180,00110,02020,00970,0054 Y101573590,01710,006300,06130,009000,01770,00670,00160,01980,01110,00530,02550,01470,0043 Y1120121850,02880,007100,01060,001500,01110,002700,03740,01760,00470,04340,02180,0070 Y1225203570,00990,004000,00560,003000,01290,00720,00410,02230,01570,00860,03010,01800,0086 Y1330276730,01400,002100,00180,000700,00960,00390,00040,02610,01510,00740,03140,01920,0109 Y1435381940,01260,003200,01200,003400,02320,00900,00690,02980,01800,00670,04040,02380,0116 Y1540475610,01570,00670,00080,00710,003000,00830,00430,00200,03320,02010,01170,02900,01790,0099 Y1645624090,01890,01190,00820,01340,01000,00790,01850,01170,00840,03710,02730,01670,04020,02890,0170 Y1750830860,01310,00730,00110,01460,00770,00260,01160,00770,00280,02720,01740,00660,02340,01890,0116 Y18601118840,01050,00610,00160,00810,00590,00180,01550,00880,00230,02620,01820,01190,02590,02180,0164 Sapma değerleri GA1GA2 ProblemBoyutBilinen en iyi çözüm
TB-araya eklemeTB-yer değiştirmeTB-tekli blok
EK-7.(devam) Y verileri için elde edilen en iyi çözümler ve sapma değerleri (Yu ve Sarker, 2003)
Y1 6 1372 1372 1372 1372 1372 1372
Y2 7 1801 1801 1801 1821 1801 1801
Y3 8 2302 2302 2302 2310 2302 2306
Y4 9 2808 2808 2808 2808 2808 2808
Y5 10 3508 3508 3508 3560 3510 3508
Y6 11 4022 4022 4022 4115 4032 4033
Y7 12 4793 4793 4793 4794 4798 4803
Y8 13 5471 5471 5471 5565 5474 5476
Y9 14 6445 6445 6445 6454 6452 6480
Y10 15 7359 7359 7359 7371 7398 7391
Y11 20 12185 12185 12185 12185 12242 12270
Y12 25 20357 20357 20357 20440 20532 20532
Y13 30 27673 27673 27673 27683 27877 27976
Y14 35 38194 38194 38194 38457 38450 38638
Y15 40 47561 47597 47561 47658 48118 48034
Y16 45 62409 62918 62903 62935 63449 63467
Y17 50 83086 83181 83298 83318 83633 84048
Y18 60 111884 112066 112089 112146 113217 113722
Elde edilen en iyi çözümler
değiştirme TB - tekli blok GA1 GA2
EK-8. AKV verileri için elde edilen en iyi çözümler ve sapma değerleri (Anjos ve diğerleri, 2003)
en büyükortalamaen küçüken büyükortalamaen küçüken büyükortalamaen küçüken büyükortalamaen küçüken büyükortalamaen küçük AKV16014772950,02430,00420,00040,00940,00500,00040,01790,00430,00180,08060,06300,03910,07570,06120,0251 AKV2608415590,00940,00270,00030,02170,00730,00030,02200,00930,00060,08070,06400,03760,07650,05910,0383 AKV360647283,50,01650,00750,00290,01450,00690,00270,01910,00850,00490,08440,07480,06540,06600,05830,0508 AKV4603980950,03030,00950,00080,04040,01210,00530,05430,03380,02700,12030,09460,06220,10460,08230,0424 AKV5603188010,04480,013500,01750,00900,00340,04460,02980,01700,11660,09460,06790,10050,08240,0535 AKV67015263590,00850,00450,00140,01090,00590,00270,02310,00620,00310,09370,08310,06650,07950,07190,0616 AKV77014391220,00580,00370,00270,02590,01210,00320,01610,00850,00670,09850,08600,06570,09180,07510,0635 AKV8701517803,50,01330,00440,00080,01350,00580,00160,03190,01260,00810,07980,06870,05350,06630,04810,0341 AKV9709673160,03140,01410,00220,02500,01230,00330,03630,01170,00230,08640,06650,04700,09070,06680,0401 AKV10704213774,50,00430,00200,00100,00800,00380,00130,00690,00420,00310,06730,05640,04680,06070,05070,0413 AKV11752387590,50,00980,00580,00250,01300,01090,00790,03540,03150,02660,07820,06490,04820,06450,05310,0402 AKV127543091850,00830,00510,00280,01220,00550,00320,02010,01520,01080,06770,06070,05030,05860,05200,0410 AKV137512431360,01810,01080,00440,01380,00940,00440,03630,02520,02100,09280,08030,06230,08740,07050,0563 AKV14753936460,50,00850,00520,00210,00980,00560,00190,00830,00490,00220,07090,06090,04860,06340,05150,0402 AKV157517861540,01450,00850,00340,01400,00650,00330,01610,00960,00420,07790,06180,04440,06120,04850,0401 AKV16802063346,50,00660,00470,00280,02450,00760,00390,01720,00650,00410,08860,07410,04540,08150,06340,0499 AKV178019189450,00680,00190,00110,01340,00460,00120,01360,00780,00640,08790,07160,05730,08180,06490,0525 AKV188032452540,01610,00660,00190,00870,00620,00400,01340,00690,00230,08540,06790,05760,06440,05860,0462 AKV198037396570,00990,00360,00180,01690,00960,00510,01180,00670,00380,07700,06460,05630,06420,05510,0485 AKV208015854910,02970,01260,00240,03600,01260,00390,02650,00640,00250,10820,07770,05490,07890,06140,0455
Sapma değerleri GA1GA2 ProblemBoyutBilinen en iyi çözüm
TB-araya eklemeTB-yer değiştirmeTB-tekli blok
EK-8. (devam) AKV verileri için elde edilen en iyi çözümler ve sapma değerleri (Anjos ve diğerleri, 2003)
AKV1 60 1477295 1477834 1477840 1479978 1535049 1514436
AKV2 60 841559 841776 841778 842032 873210 873803
AKV3 60 647283,5 649145,5 649056,5 650440,5 689598,5 680179,5
AKV4 60 398095 398406 400188 408853 422861 414984
AKV5 60 318801 318805 319895 324233 340459 335868
AKV6 70 1526359 1528537 1530470 1531052 1627901 1620407
AKV7 70 1439122 1443040 1443709 1448829 1533690 1530476
AKV8 70 1517803,5 1518993,5 1520263,5 1530022,5 1599000,5 1569487,5
AKV9 70 967316 969474 970546 969565 1012820 1006111
AKV10 70 4213774,5 4218002,5 4219044,5 4226917,5 4411067,5 4387680,5 AKV11 75 2387590,5 2393456,5 2406380,5 2451107,5 2502690,5 2483617,5
AKV12 75 4309185 4321310 4322842 4355643 4525769 4485663
AKV13 75 1243136 1248607 1248593 1269287 1320602 1313113
AKV14 75 3936460,5 3944796,5 3944028,5 3945164,5 4127581,5 4094675,5
AKV15 75 1786154 1792222 1792024 1793696 1865472 1857749
AKV16 80 2063346,5 2069124,5 2071328,5 2071738,5 2157118,5 2166265,5
AKV17 80 1918945 1921136 1921232 1931178 2028966 2019632
AKV18 80 3245254 3251368 3258248 3252810 3432118 3395113
AKV19 80 3739657 3746515 3758599 3753882 3950143 3920941
AKV20 80 1585491 1589253 1591640 1589524 1672604 1657680
Elde edilen en iyi çözümler
değiştirme TB - tekli blok GA1 GA2
EK-9. SKO verileri için elde edilen en iyi çözümler ve sapma değerleri (Anjos ve Yen, 2009)
en büyükortalamaen küçüken büyükortalamaen küçüken büyükortalamaen küçüken büyükortalamaen küçüken büyükortalamaen küçük SKO142255210,02800,01520,00120,04180,02200,00170,03650,01050,00020,06240,04760,02610,08150,05830,0416 SKO242216099,50,03240,01480,00120,03090,02050,00050,04150,02390,01120,08510,05800,03260,06670,04930,0313 SKO342173245,50,02410,01100,00260,03930,01790,00780,03870,02120,00710,06300,04590,02770,07640,06070,0462 SKO4421373790,01360,00770,00180,03040,01580,00460,03220,01270,00370,06960,04910,02970,06270,05240,0349 SKO542248238,50,03870,01480,00030,02820,010900,02500,011300,09660,05160,03120,08200,05450,0381 SKO649408950,02840,01120,00220,04060,02320,00440,04140,01880,00210,08600,04970,03390,06440,04850,0276 SKO7494161420,04150,01630,00060,03400,01650,00280,03820,01170,00500,07700,04770,02950,05930,04530,0275 SKO8493244640,02650,01170,00030,05010,01600,00100,05260,02410,00930,07460,04700,02880,06120,04660,0221 SKO949236718,50,03690,02020,00240,02690,01110,00280,04300,01350,00020,07000,05450,04130,06810,04310,0218 SKO10496661300,03070,013500,04260,01640,00020,02900,01150,00020,08550,06580,04390,07640,05520,0284 SKO1156639710,03920,01680,00200,04110,01630,00390,03900,02070,00240,06650,04190,01690,07230,05370,0136 SKO12564964820,03690,01790,00040,04360,01990,00740,02930,01500,00300,07040,05340,04200,07540,05300,0347 SKO13561696440,02010,01170,00540,01860,01340,00730,02010,01550,00980,06220,04800,03620,06310,04880,0432 SKO14563126560,02820,01250,00230,02850,01680,00360,03040,01950,01050,06410,04870,03810,07020,04520,0277 SKO1556591915,50,02880,01730,00550,03330,01700,00570,02610,01790,00470,06620,04850,03100,07170,05520,0421 SKO1664966070,03320,01480,00510,04660,02300,00690,02870,01730,00680,05970,04020,02800,05720,04440,0328 SKO1764633694,50,02080,01140,00140,03850,02350,00950,02290,01350,00250,05930,04810,03420,05890,04700,0307 SKO1864413079,50,02680,01560,00750,03250,01610,00300,01850,01070,00430,07200,05090,02730,06320,04350,0304 SKO19642954230,03160,01910,00940,02620,02010,01650,02530,01710,00730,05530,03940,03190,07830,04670,0297 SKO2064501342,50,02660,01640,00140,04020,02090,00330,03460,01940,00540,05930,04780,01940,05430,04400,0304 SKO21721388850,04220,01490,00220,04230,02210,00460,03350,01910,00740,06890,04690,02630,06320,05000,0341 SKO22727076430,02660,01430,01020,02630,01600,00830,02720,01580,00620,07090,05020,03120,06470,04660,0323 SKO23721048930,50,01730,01130,00530,03190,01860,00670,02070,01430,00730,06280,05050,03760,05370,04390,0330 SKO2472916229,50,02430,01350,00370,02220,01450,00720,02310,01650,01200,07170,05270,02040,05580,05120,0439 SKO2572426224,50,03420,01390,00740,02440,01680,00920,02920,02080,00970,05500,04240,02170,06210,03750,0284 SKO26812034240,02710,01970,01070,02400,01800,00840,02770,01900,01100,04800,04000,02760,05370,03970,0264 SKO2781518711,50,01950,01120,00530,02980,01980,00930,02500,01500,00540,06080,04680,03040,05680,04150,0326 SKO28819628860,02920,01610,00830,02300,01700,01170,02490,01900,01410,06900,05030,03570,05530,04610,0305 SKO298120190580,03150,01700,01070,03030,01650,00670,03080,02010,01160,05870,04820,02340,06420,04300,0279 SKO308112939050,02120,01750,01040,02620,01830,00910,02600,01830,01060,05590,04730,04030,05420,04430,0342 SKO311003759990,03010,02040,00650,03150,02210,00820,03880,01950,00730,06040,04580,03340,05110,04460,0389 SKO321002056997,50,02880,01920,00930,03910,02240,01160,03040,01900,00930,06680,04860,03440,05830,04660,0321 SKO33100159878410,02540,01840,01130,02810,02110,01300,02300,01810,01130,07230,05070,03840,05620,04840,0358 SKO3410032006430,02200,01730,01000,03820,02090,01560,02300,01880,01460,07000,05770,04340,06560,05160,0379 SKO351001021584,50,02600,02040,01320,02970,02140,01300,02320,01800,01400,06220,04680,03710,05920,04250,0324
Sapma değerleri GA1GA2 ProblemBoyutBilinen en iyi çözüm
TB-araya eklemeTB-yer değiştirmeTB-tekli blok
EK-9. (devam) SKO verileri için elde edilen en iyi çözümler ve sapma değerleri (Anjos ve Yen, 2009)
SKO1 42 25521 25551 25564 25526 26188 26583
SKO2 42 216099,5 216358,5 216209,5 218518,5 223134,5 222873,5 SKO3 42 173245,5 173693,5 174590,5 174478,5 178041,5 181242,5
SKO4 42 137379 137626 138006 137887 141464 142169
SKO5 42 248238,5 248301,5 248238,5 248238,5 255990,5 257690,5
SKO6 49 40895 40987 41076 40980 42280 42022
SKO7 49 416142 416404 417311 418221 428427 427571
SKO8 49 324464 324556 324782 327480 333794 331633
SKO9 49 236718,5 237279,5 237372,5 236755,5 246491,5 241881,5
SKO10 49 666130 666143 666232 666264 695341 685037
SKO11 56 63971 64101 64218 64122 65050 64839
SKO12 56 496482 496673 500159 497956 517351 513701
SKO13 56 169644 170566 170878 171301 175777 176972
SKO14 56 312656 313388 313792 315954 324553 321320
SKO15 56 591915,5 595180,5 595275,5 594712,5 610286,5 616815,5
SKO16 64 96607 97098 97274 97263 99313 99774
SKO17 64 633694,5 634567,5 639726,5 635293,5 655337,5 653147,5 SKO18 64 413079,5 416186,5 414338,5 414859,5 424340,5 425630,5
SKO19 64 295423 298197 300303 297574 304844 304194
SKO20 64 501342,5 502061,5 503016,5 504066,5 511056,5 516583,5
SKO21 72 138885 139194 139517 139915 142543 143615
SKO22 72 707643 714829 713545 712015 729722 730508
SKO23 72 1048930,5 1054539,5 1055940,5 1056588,5 1088341,5 1083556,5 SKO24 72 916229,5 919630,5 922824,5 927237,5 934913,5 956459,5 SKO25 72 426224,5 429367,5 430135,5 430342,5 435453,5 438329,5
SKO26 81 203424 205606 205142 205664 209044 208793
SKO27 81 518711,5 521475,5 523543,5 521521,5 534498,5 535614,5
SKO28 81 962886 970856 974178 976504 997296 992233
SKO29 81 2019058 2040658 2032622 2042453 2066237 2075384 SKO30 81 1293905 1307315 1305738 1307604 1345993 1338143
SKO31 100 375999 378448 379071 378737 388553 390642
SKO32 100 2056997,5 2076222,5 2080841,5 2076130,5 2127714,5 2123062,5 SKO33 100 15987840,5 16167994 16196266,5 16168114 16601041,5 16560486,5 SKO34 100 3200643 3232565 3250420 3247453 3339516 3322025 SKO35 100 1021584,5 1035117,5 1034887,5 1035839,5 1059531,5 1054678,5
Elde edilen en iyi çözümler
EK-10. 6 bölüm için hedef programlama ve NSGA II sonuçları ve Pareto diyagramı karşılaştırması (Dutta ve Sahu, 1982)
w1 w2 f1 f2 süre (saniye) f1 f2 süre (saniye)
0,05 0,95 138 89 1 120 100 0,89
0,1 0,9 138 89 1 124 96
0,15 0,85 138 89 1 134 93
0,2 0,8 138 89 1 138 89
0,25 0,75 138 89 1
0,3 0,7 138 89 1
0,35 0,65 138 89 1
0,4 0,6 138 89 1
0,45 0,55 138 89 1
0,5 0,5 124 96 1
0,55 0,45 124 96 1
0,6 0,4 124 96 1
0,65 0,35 120 100 1
0,7 0,3 120 100 1
0,75 0,25 120 100 1
0,8 0,2 120 100 1
0,85 0,15 120 100 1
0,9 0,1 120 100 1
0,95 0,05 120 100 1
Hedef Programlama NSGAII
EK-11. 8 bölüm için hedef programlama ve NSGA II sonuçları ve Pareto diyagramı karşılaştırması (Dutta ve Sahu, 1982)
w1 w2 f1 f2 süre (saniye) f1 f2 süre (saniye)
0,05 0,95 346 253 20 269 299 1,08
0,1 0,9 346 253 25 277 298
0,15 0,85 346 253 28 309 297
0,2 0,8 346 253 74 310 294
0,25 0,75 346 253 45 320 290
0,3 0,7 346 253 37 330 285
0,35 0,65 346 253 100 331 280
0,4 0,6 346 253 85 333 274
0,45 0,55 346 253 24 341 268
0,5 0,5 346 253 46 346 259
0,55 0,45 269 299 27
0,6 0,4 269 299 42
0,65 0,35 269 299 30
0,7 0,3 269 299 29
0,75 0,25 269 299 63
0,8 0,2 269 299 61
0,85 0,15 269 299 19
0,9 0,1 269 299 25
0,95 0,05 269 299 18
Hedef Programlama NSGAII
EK-12. 6 bölüm için hedef programlama ve NSGA II sonuçları ve Pareto diyagramı karşılaştırması (Fortenberry ve Cox, 1985)
w1 w2 f1 f2 süre (saniye) f1 f2 süre (saniye)
0,05 0,95 138 45 1 120 57 0,64
0,1 0,9 138 45 1 124 53
0,15 0,85 138 45 1 134 49
0,2 0,8 138 45 1 138 45
0,25 0,75 138 45 1
0,3 0,7 138 45 1
0,35 0,65 138 45 1
0,4 0,6 138 45 1
0,45 0,55 138 45 1
0,5 0,5 124 53 1
0,55 0,45 124 53 1
0,6 0,4 124 53 1
0,65 0,35 120 57 1
0,7 0,3 120 57 1
0,75 0,25 120 57 1
0,8 0,2 120 57 1
0,85 0,15 120 57 1
0,9 0,1 120 57 1
0,95 0,05 120 57 1
Hedef Programlama NSGAII
EK-13. 8 bölüm için hedef programlama ve NSGA II sonuçları ve Pareto diyagramı karşılaştırması (Fortenberry ve Cox, 1985)
w1 w2 f1 f2 süre (saniye) f1 f2 süre (saniye)
0,05 0,95 346 157 141 270 213 1,03
0,1 0,9 346 157 95 278 212
0,15 0,85 346 157 89 303 207
0,2 0,8 346 157 107 305 204
0,25 0,75 346 157 108 309 202
0,3 0,7 346 157 92 311 200
0,35 0,65 343 160 254 322 198
0,4 0,6 343 160 230 336 197
0,45 0,55 343 160 127 339 194
0,5 0,5 343 160 198 340 188
0,55 0,45 269 211 158 344 162
0,6 0,4 269 211 153 347 159
0,65 0,35 269 211 219
0,7 0,3 269 211 142
0,75 0,25 269 211 136
0,8 0,2 269 211 167
0,85 0,15 269 211 151
0,9 0,1 269 211 88
0,95 0,05 269 211 103
Hedef Programlama NSGAII
EK-14. 6 bölüm için hedef programlama ve NSGA II sonuçları ve Pareto diyagramı karşılaştırması (Urban, 1987)
w1 w2 f1 f2 süre (saniye) f1 f2 süre (saniye)
0,05 0,95 150 36 1 110 55 0,58
0,1 0,9 150 36 1 117 51
0,15 0,85 150 36 1 125 47
0,2 0,8 150 36 1 128 43
0,25 0,75 150 36 1 135 39
0,3 0,7 143 37 1 142 38
0,35 0,65 143 37 1 143 37
0,4 0,6 143 37 1 150 36
0,45 0,55 135 39 1
0,5 0,5 135 39 1
0,55 0,45 135 39 1
0,6 0,4 135 39 1
0,65 0,35 128 43 1
0,7 0,3 110 55 1
0,75 0,25 110 55 1
0,8 0,2 110 55 1
0,85 0,15 110 55 1
0,9 0,1 110 55 1
0,95 0,05 110 55 1
Hedef Programlama NSGAII
EK-15. 6 bölüm için hedef programlama ve NSGA II sonuçları ve Pareto diyagramı karşılaştırması (Urban, 1987)
w1 w2 f1 f2 süre (saniye) f1 f2 süre (saniye)
0,05 0,95 114 47 1 86 63 0,5
0,1 0,9 100 48 1 90 55
0,15 0,85 100 48 1 95 50
0,2 0,8 100 48 1 100 48
0,25 0,75 100 48 1 114 47
0,3 0,7 100 48 1
0,35 0,65 100 48 1
0,4 0,6 95 50 1
0,45 0,55 95 50 1
0,5 0,5 95 50 1
0,55 0,45 95 50 1
0,6 0,4 90 55 1
0,65 0,35 90 55 1
0,7 0,3 90 55 1
0,75 0,25 84 67 1
0,8 0,2 84 67 1
0,85 0,15 84 67 1
0,9 0,1 84 67 1
0,95 0,05 84 67 1
Hedef Programlama NSGAII
EK-16. 12 bölüm için hedef programlama ve NSGA II sonuçları ve Pareto diyagramı
EK-16. 12 bölüm için hedef programlama ve NSGA II sonuçları ve Pareto diyagramı