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Internet Engineering Internet Engineering Czesław Smutnicki Czesław Smutnicki Discrete Mathematics Discrete Mathematics – Discrete – Discrete Optimization Optimization
Internet Engineering Czesław Smutnicki Discrete Mathematics – Discrete Optimization
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Internet Engineering Czesław Smutnicki Discrete Mathematics – Discrete Optimization. CONTENT S. Numerical troubles Packages Tools Useful methods. 2D. 1D. OPTIMIZATION TROUBLES. NICE BEGINNINGS OF BAD NEWS. FIND EXTREMES OF THE FUNCTION. DE JONG TEST FUNCTION. 2D. - PowerPoint PPT Presentation
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Internet Engineering
Czesaw Smutnicki
Discrete Mathematics Discrete Optimization
CONTENTSNumerical troublesPackagesToolsUseful methods
FIND EXTREMES OF THE FUNCTIONDE JONG TEST FUNCTIONOPTIMIZATION
TROUBLES. NICE BEGINNINGS OF BAD NEWS
GRIEWANGK TEST FUNCTION
FIND EXTREMES OF THE FUNCTIONOPTIMIZATION TROUBLES. MULTIPLE
EXTREMES
LANGERMANN TEST FUNCTION
FIND EXTREMES OF THE FUNCTIONOPTIMIZATION TROUBLES. EXPONENTAL
NUMBER OF EXTREMES
FOX HOLES TEST FUNCTION
FIND EXTREMES OF THE FUNCTIONOPTIMIZATION TROUBLES. DECEPTION
POINTS
Please wait. Calculations will last 3 289 yearsINSTANCE FROM
PRACTICE! ! ?NONLINEAR FUNCTION OF 1980 VARIABLES !!!CURSE OF
DIMENSIONALITYOPTIMIZATION TROUBLES. TIME OF CALCULATIONS/COST OF
CALCULATIONSLAB INSTANCE
5..20 VARIABLESNP-HARDNESS
SOLUTION SPACEThe smallest practical instance FT10 of the
job-shop scheduling problem (waited 25 years for the solving),
consists of 10 jobs, 10 machines, 100 operations; solution space
contains 1048 discrete feasible solutions; each solution has
dimension 90; the greatest currently used benchmarks have dimension
1980dimension and sizeFT 10 corresponds to printed area of 1032 km2
(Jupiter has 1010 km2) if single solution is a dot 0.01 x 0.01
mmOPTIMIZATION TROUBLES. SIZE OF THE SOLUTION SPACE
Example: job-shop scheduling problem; relative Hamming distances
DIST between a feasible solution and the best solution are
distributed normally in the solution space
Goal function values are distributed normally in the solution
space; OPTIMIZATION TROUBLES. DISTRIBUTION OF THE GOAL FUNCTION
VALUES
Wykres1
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00
00
00.0002
00
00
00
00
00
00
00
00.0002
00.0002
00.0002
00.0002
00.0004
00.0002
00
00
00.0002
00
00
00.0004
00.0012
00.0008
00.0004
00.0008
00.0008
00.001
00.0006
00.001
00.0016
00.0008
00.0024
00.0022
00.0034
00.0018
00.0016
00.0028
00.0024
00.0056
00.005
00.003
00.0062
00.0054
00.0064
00.0062
00.0062
00.0056
00.0108
00.0094
00.01
00.0126
00.0144
00.0142
00.0142
00.0174
00.018
00.0164
00.0226
00.0196
00.0272
00.0268
00.0266
00.0296
00.0354
00.0348
00.0404
00.0408
00.0454
00.0446
00.0486
00.0548
00.0556
00.0616
00.058
00.0676
00.0706
00.0736
00.0814
00.0864
00.0926
00.098
00.0982
00.1066
00.113
00.1216
00.1286
00.1422
00.1434
00.152
00.1594
00.172
00.1704
00.1796
00.177
00.192
00.1998
00.2008
00.228
00.2424
00.2578
00.2536
00.2696
00.2664
00.2934
00.2966
00.303
00.3054
00.3234
00.3448
00.3444
00.3674
00.3682
00.395
00.4108
00.4128
00.4336
00.4346
00.4436
00.4672
00.4874
00.505
00.5178
00.5166
00.5466
00.5594
00.5696
00.5566
00.5766
00.607
00.6134
00.6396
00.629
00.6424
00.6498
00.6728
00.6624
00.7116
00.7102
00.7366
00.7288
00.7388
00.7526
00.7512
00.7876
00.8086
00.7882
00.8006
00.8182
00.8226
00.847
00.8566
00.8414
00.861
00.8668
00.8682
00.87
00.868
00.8878
00.9054
00.8998
00.8878
00.88
00.8934
00.8794
00.9078
00.9248
00.9184
00.93
00.932
00.9098
00.889
00.9132
00.8976
00.9028
00.8914
00.8812
00.8782
00.893
00.898
00.8498
00.8754
00.876
00.8638
00.8692
00.85
00.8392
00.8394
00.8222
00.8132
00.8138
00.786
00.7796
00.7952
00.7692
00.751
00.741
00.7426
00.7338
00.6902
00.7194
00.6774
00.694
00.6914
00.6508
00.6668
00.638
00.6422
00.603
00.6174
00.5902
00.594
00.5772
00.5626
00.5426
00.5276
00.5278
00.4994
00.5112
00.4932
00.4744
00.466
00.4548
00.438
00.4452
00.4262
00.3968
00.404
00.3792
00.372
00.3572
00.3578
00.3498
00.3402
00.3266
00.3116
00.3066
00.3046
00.2846
00.266
00.2634
00.2608
00.2488
00.2458
00.2242
00.2186
00.2246
00.203
00.198
00.1958
00.197
00.1826
00.164
00.1622
00.1606
00.1568
00.1454
00.155
00.1328
00.1362
00.1232
00.1254
00.1286
00.1028
00.1098
00.1014
00.094
00.0964
00.0904
00.0796
00.078
00.0766
00.0746
00.0714
00.0646
00.0632
00.0594
00.0552
00.0566
00.0494
00.051
00.0478
00.046
00.0456
00.0354
00.037
00.0372
00.032
00.032
00.034
00.0258
00.0304
00.0238
00.0228
00.0234
00.018
00.022
00.0214
00.0252
00.0158
00.0142
00.013
00.0148
00.0142
00.0098
00.0128
00.0102
00.0098
00.0082
00.0108
00.0066
00.0076
00.0082
00.006
00.0066
00.0058
00.0062
00.0072
00.0044
00.0042
00.0036
00.0038
00.0058
00.0046
00.0024
00.003
00.0024
00.0028
00.0026
00.0038
00.0018
00.0034
00.001
00.0022
00.0008
00.0018
00.0004
00.001
00.0018
00.001
00.0014
00.0012
00.0012
00.0008
00.0014
00.0008
00.0002
00.0004
00.001
00.0008
00.0004
00.0006
00.0004
00.0004
00.001
00
00.0002
00
00
00.0002
00
00.0004
00.0002
00
00.0002
00.0002
00
00
00
00
00.0002
00
00
00
00
00
00
00.0002
00
00
00
00
00
00
00.0002
00.0002
00
00.0002
00.0002
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00.0002
00
00
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0.00020
0.00020
00
00
00
00
0.00020
0.00020
00
0.00020
00
00
00
00
00
00
00
0.00020
00
0.00020
0.0010
0.00040
00
00
0.00020
0.00060
0.00080
0.00020
0.00080
0.0010
0.00060
0.00080
0.00140
0.00060
0.00120
0.00140
0.00160
0.00180
0.00120
0.0020
0.00340
0.00160
0.00160
0.0020
0.00220
0.00440
0.00340
0.00380
0.0030
0.00380
0.00440
0.00420
0.00480
0.0060
0.0060
0.00620
0.0080
0.00920
0.00980
0.0070
0.0120
0.01360
0.0110
0.01120
0.01080
0.0160
0.0170
0.0190
0.01660
0.02020
0.01920
0.02160
0.0250
0.02520
0.02420
0.02840
0.03280
0.03460
0.04220
0.04060
0.04340
0.04720
0.04440
0.05520
0.05120
0.05740
0.0620
0.0640
0.07240
0.07260
0.08020
0.08540
0.09140
0.09040
0.09940
0.0990
0.1040
0.1150
0.1210
0.13220
0.15060
0.1420
0.15080
0.1580
0.16620
0.1740
0.1920
0.19340
0.1990
0.2080
0.22420
0.23920
0.24440
0.24820
0.26420
0.2750
0.2940
0.29660
0.31640
0.3380
0.33020
0.36180
0.37060
0.35560
0.38440
0.40920
0.42460
0.44860
0.44520
0.44720
0.45760
0.49260
0.50860
0.53140
0.53740
0.55040
0.56040
0.57420
0.58340
0.60740
0.63120
0.67220
0.67220
0.68520
0.70280
0.71960
0.70440
0.7360
0.76460
0.75540
0.7870
0.79120
0.80560
0.82640
0.81460
0.85880
0.86040
0.86440
0.88960
0.9090
0.91480
0.9250
0.92740
0.93860
0.96640
0.96160
0.97460
0.96820
0.97860
1.00560
0.99340
0.98480
0.9840
0.98720
0.99660
0.99160
1.02780
1.00040
1.01420
0.99180
1.02180
0.99660
1.02120
1.00120
0.99280
1.01640
1.00060
1.01280
10
0.96480
0.97340
1.0070
0.99920
0.9480
0.9170
0.90980
0.93220
0.91280
0.90060
0.87380
0.8910
0.87560
0.85140
0.8270
0.82460
0.80580
0.78580
0.79160
0.75740
0.73940
0.7420
0.7320
0.7070
0.67920
0.66740
0.65860
0.62920
0.63140
0.61280
0.5920
0.59340
0.55920
0.54780
0.53460
0.53460
0.50120
0.49660
0.47540
0.4670
0.43780
0.42960
0.42760
0.39520
0.37540
0.3550
0.37080
0.34040
0.33940
0.33280
0.30740
0.3070
0.28620
0.27540
0.270
0.25240
0.23540
0.22920
0.22840
0.220
0.20360
0.18960
0.18940
0.1690
0.16020
0.15260
0.15140
0.14660
0.13620
0.1320
0.13380
0.11160
0.11140
0.10720
0.10180
0.09780
0.09080
0.0810
0.0850
0.07420
0.07160
0.07320
0.06220
0.05220
0.05540
0.05160
0.04460
0.04640
0.04340
0.0430
0.03580
0.03820
0.03160
0.0290
0.02960
0.0260
0.02660
0.02480
0.01960
0.01740
0.01680
0.02020
0.01380
0.01520
0.01360
0.01340
0.01220
0.01120
0.0090
0.01060
0.00860
0.00720
0.00680
0.0080
0.00680
0.00440
0.00560
0.00480
0.00460
0.00460
0.00360
0.00280
0.0030
0.00260
0.00260
0.0040
0.00260
0.00260
0.00240
0.00220
0.00160
0.00080
0.0010
0.00260
0.00120
0.00060
0.00080
0.00080
0.00080
0.00040
0.00080
0.00080
0.00040
0.00060
0.00060
0.00080
0.00020
00
0.00060
00
00
0.00020
0.00020
00
00
0.00020
0.00040
00
00
0.00040
0.00020
0.00020
00
00
00
00
00
00
00
0.00020
00
00
00
00
00
00
00
00
00
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FEAS
ALL
los_all
los_dop
DIST [%]
frequence [%]
CMAX
CmaxCmaxlos_dop
11750.0000.0000
11760.0900.0000
11770.1700.0000
11780.2600.0000
11790.3400.0000
11800.4300.0000
11810.5100.0000
11820.6000.0000
11830.6800.0000
11840.7700.0000
11850.8500.0000
11860.9400.0000
11871.0200.0000
11881.1100.0000
11891.1900.0000
11901.2800.0000
11911.3600.0000
11921.4500.0000
11931.5300.0000
11941.6200.0000
11951.7000.0000
11961.7900.0000
11971.8700.0000
11981.9600.0000
11992.0400.0000
12002.1300.0000
12012.2100.0000
12022.3000.0000
12032.3800.0000
12042.4700.0000
12052.5500.0000
12062.6400.0000
12072.7200.0000
12082.8100.0000
12092.8900.0000
12102.9800.0000
12113.0600.0000
12123.1500.0000
12133.2300.0000
12143.3200.0000
12153.4000.0000
12163.4900.0000
12173.5700.0000
12183.6600.0000
12193.7400.0000
12203.8300.0000
12213.9100.0000
12224.0000.0000
12234.0900.0000
12244.1700.0000
12254.2600.0000
12264.3400.0000
12274.4300.0000
12284.5100.0000
12294.6000.0000
12304.6800.0000
12314.7700.0000
12324.8500.0000
12334.9400.0000
12345.0200.0000
12355.1100.0000
12365.1900.0000
12375.2800.0000
12385.3600.0000
12395.4500.0000
12405.5300.0000
12415.6200.0000
12425.7000.0000
12435.7900.0000
12445.8700.0000
12455.9600.0000
12466.0400.0000
12476.1300.0000
12486.2100.0000
12496.3000.0000
12506.3800.0000
12516.4700.0000
12526.5500.0000
12536.6400.0000
12546.7200.0000
12556.8100.0000
12566.8900.0000
12576.9800.0000
12587.0600.0000
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3602206.5510.0002
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3632209.1100.0000
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3769220.7700.0000
3770220.850.0000
3771220.940.0000
3772221.020.0000
3773221.110.0000
500,000.00100.00
ODL
ODL_swapODL_swaplos_alllos_dop
00.0000.000000.0000
10.0600.000000.0000
20.1300.000000.0000
30.1900.000000.0000
40.2500.000000.0000
50.3200.000000.0000
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150.9500.000000.0000
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171.0800.000000.0000
181.1400.000000.000015750.14171.5
191.2100.000000.00000.27330.75
201.2700.000000.0000
211.3300.000000.0000
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231.4600.000000.0000
241.5200.000000.0000
251.5900.000000.0000
261.6500.000000.0000
271.7100.000000.0000
281.7800.000000.0000
291.8400.000000.0000
301.9000.000000.0000
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322.0300.000000.0000
332.1000.000000.0000
342.1600.000000.0000
352.2200.000000.0000
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372.3500.000000.0000
382.4100.000000.0000
392.4800.000000.0000
402.5400.000000.0000
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432.7300.000000.0000
442.7900.000000.0000
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533.3700.000000.0000
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553.4900.000000.0000
563.5600.000000.0000
573.6200.000000.0000
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593.7500.000000.0000
603.8100.000000.0000
613.8700.000000.0000
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634.0000.000000.0000
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1519.5900.000010.0002
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15810.0300.000000.0000
15910.1000.000010.0002
16010.1600.000010.0002
16110.2200.000010.0002
16210.2900.000010.0002
16310.3500.000020.0004
16410.4100.000010.0002
16510.4800.000000.0000
16610.5400.000000.0000
16710.6000.000010.0002
16810.6700.000000.0000
16910.7300.000000.0000
17010.7900.000020.0004
17110.8600.000060.0012
17210.9200.000040.0008
17310.9800.000020.0004
17411.0500.000040.0008
17511.1100.000040.0008
17611.1700.000050.0010
17711.2400.000030.0006
17811.3000.000050.0010
17911.3700.000080.0016
18011.4300.000040.0008
18111.4900.0000120.0024
18211.5600.0000110.0022
18311.6200.0000170.0034
18411.6800.000090.0018
18511.7500.000080.0016
18611.8100.0000140.0028
18711.8700.0000120.0024
18811.9400.0000280.0056
18912.0000.0000250.0050
19012.0600.0000150.0030
19112.1300.0000310.0062
19212.1900.0000270.0054
19312.2500.0000320.0064
19412.3200.0000310.0062
19512.3800.0000310.0062
19612.4400.0000280.0056
19712.5100.0000540.0108
19812.5700.0000470.0094
19912.6300.0000500.0100
20012.7000.0000630.0126
20112.7600.0000720.0144
20212.8300.0000710.0142
20312.8900.0000710.0142
20412.9500.0000870.0174
20513.0200.0000900.0180
20613.0800.0000820.0164
20713.1400.00001130.0226
20813.2100.0000980.0196
20913.2700.00001360.0272
21013.3300.00001340.0268
21113.4000.00001330.0266
21213.4600.00001480.0296
21313.5200.00001770.0354
21413.5900.00001740.0348
21513.6500.00002020.0404
21613.7100.00002040.0408
21713.7800.00002270.0454
21813.8400.00002230.0446
21913.9000.00002430.0486
22013.9700.00002740.0548
22114.0300.00002780.0556
22214.1000.00003080.0616
22314.1600.00002900.0580
22414.2200.00003380.0676
22514.2900.00003530.0706
22614.3500.00003680.0736
22714.4100.00004070.0814
22814.4800.00004320.0864
22914.5400.00004630.0926
23014.6000.00004900.0980
23114.6700.00004910.0982
23214.7300.00005330.1066
23314.7900.00005650.1130
23414.8600.00006080.1216
23514.9200.00006430.1286
23614.9800.00007110.1422
23715.0500.00007170.1434
23815.1100.00007600.1520
23915.1700.00007970.1594
24015.2400.00008600.1720
24115.3000.00008520.1704
24215.3700.00008980.1796
24315.4300.00008850.1770
24415.4900.00009600.1920
24515.5600.00009990.1998
24615.6200.000010040.2008
24715.6800.000011400.2280
24815.7500.000012120.2424
24915.8100.000012890.2578
25015.8700.000012680.2536
25115.9400.000013480.2696
25216.0000.000013320.2664
25316.0600.000014670.2934
25416.1300.000014830.2966
25516.1900.000015150.3030
25616.2500.000015
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