Research Article

Mutation Strategy Based on Step Size and Survival Rate for Evolutionary Programming

Table 4

The results of SSMSEP, SSMSEP-1, SSMSEP-2, SSEP, FEP, CEP, and LEP with on , where “Mean” denotes the mean best fitness values calculated in the final generation over 50 runs, “Min” denotes the minimum fitness value in final generation in 50 runs, and “Std Dev” denotes standard deviations.

SSMSEPSSMSEP-1SSMSEP-2SSEPFEPCEP

Mean3.7814E − 081.0901E − 041.4066E − 075.5197E − 084.5635E − 046.0315E − 052.5421E − 041.6934E − 041.3440E − 041.0516E − 04
Min1.4472E − 082.5524E − 081.3595E − 087.0480E − 093.0863E − 043.2239E − 051.5908E − 041.2202E − 048.8775E − 056.3256E − 05
Std Dev(3.7792E − 08)(2.3378E − 04)(6.1386E − 07)(6.5450E − 08)(7.0235E − 05)(2.5166E − 05)(3.4971E − 05)(2.6149E − 05)(2.7323E − 05)(1.8110E − 05)

Mean3.6408E − 044.0167E − 043.2274E − 042.4660E − 047.0726E − 022.2304E − 025.1594E − 024.2239E − 023.6880E − 023.3471E − 02
Min2.9214E − 043.3439E − 042.6128E − 042.0121E − 045.1482E − 021.8824E − 024.3426E − 023.3697E − 023.2571E − 022.6264E − 02
Std Dev(3.0086E − 05)(3.0845E − 05)(2.8645E − 05)(1.5612E − 05)(5.5881E − 03)(1.5150E − 03)(3.2306E − 03)(3.0114E − 03)(2.1175E − 03)(2.5190E − 03)

Mean1.0407E − 024.8819E − 029.0411E − 039.3736E − 038.7540E − 031.0524E − 029.3985E − 037.1744E − 034.2293E − 033.0734E − 03
Min2.4395E − 038.1053E − 042.4140E − 032.3030E − 031.9117E − 038.5077E − 059.4563E − 047.5277E − 044.5609E − 042.2686E − 04
Std Dev(6.7484E − 03)(5.7250E − 02)(5.5701E − 03)(6.4085E − 03)(6.4514E − 03)(1.9002E − 02)(1.2368E − 02)(1.1998E − 02)(6.5552E − 03)(5.2651E − 03)

Mean6.4065E − 049.7131E − 018.8194E − 041.4405E − 036.7516E − 031.2210E + 006.5288E − 035.4754E − 022.8222E − 015.9637E − 01
Min3.1376E − 052.8928E − 032.8940E − 052.1072E − 055.4115E − 031.4146E − 014.2954E − 033.2552E − 033.6687E − 033.1680E − 03
Std Dev(1.8023E − 03)(8.1875E − 01)(1.4856E − 03)(4.0274E − 03)(7.8715E − 04)(9.0747E − 01)(5.6855E − 03)(1.4088E − 01)(4.8753E − 01)(6.0409E − 01)

Mean2.9275E + 013.15082.9490E + 012.1359E + 012.9350E + 017.54791.9830E + 016.38888.00591.1073E + 01
Min4.6981E − 029.9139E − 041.5319E − 035.5730E − 024.7199E − 011.8391E − 023.3474E − 011.0103E − 018.0644E − 024.2083E − 02
Std Dev(3.2710E + 01)(1.0064E + 01)(3.1230E + 01)(2.6718E + 01)(3.2291E + 01)(1.4348E + 01)(2.3933E + 01)(6.0507E + 00)(1.3649E + 01)(1.9445E + 01)

Mean064.98000136.14000.6229.88
Min0000000000
Std Dev(0)(128.02)(0)(0)(0)(367.07)(0)(0)(2.62)(183.78)

Mean8.4609E − 032.8136E − 028.1618E − 037.9013E − 038.3416E − 032.2382E − 028.4703E − 031.1287E − 021.2451E − 021.5274E − 02
Min2.7008E − 031.4340E − 024.0161E − 033.7373E − 033.7395E − 038.4446E − 034.7781E − 034.8277E − 035.7806E − 037.6249E − 03
Std Dev(2.6809E − 03)(9.8926E − 03)(2.1752E − 03)(2.1289E − 03)(2.8422E − 03)(7.6244E − 03)(2.4166E − 03)(3.6673E − 03)(3.9032E − 03)(5.3375E − 03)

Mean−1.1243E + 04−9.0460E + 03−1.1053E + 04−1.1113E + 04−1.1300E + 04−7.9096E + 03−1.0582E + 04−1.0070E + 04−9.4480E + 03−8.7650E + 03
Min−1.1977E + 04−1.1145E + 04−1.1740E + 04−1.1976E + 04−1.1977E + 04−9.0739E + 03−1.1661E + 04−1.0892E + 04−1.0870E + 04−1.0418E + 04
Std Dev(2.7196E + 02)(6.4104E + 02)(3.5576E + 02)(4.0896E + 02)(2.7570E + 02)(5.9723E + 02)(4.8018E + 02)(4.3464E + 02)(5.3691E + 02)(6.0867E + 02)

Mean3.3160E − 018.4770E + 013.8155E + 014.3687E + 013.7750E − 029.0465E + 012.9352E − 022.8450E + 001.9402E + 016.6639E + 01
Min2.9129E − 023.3829E + 013.1528E − 022.2605E − 022.3464E − 024.1792E + 011.8232E − 022.1729E − 025.9871E + 003.2844E + 01
Std Dev(1.0996E + 00)(2.4674E + 01)(2.3952E + 01)(2.9723E + 01)(8.6261E − 03)(2.3879E + 01)(1.3161E − 02)(1.7927E + 00)(6.9163E + 00)(2.1773E + 01)

Mean1.6879E − 031.9694E + 012.4643E − 038.7447E − 021.6157E − 028.1049E + 001.1862E − 021.1219E − 028.8736E − 014.4735E + 00
Min6.8753E − 056.7988E + 006.6043E − 054.7010E − 051.4046E − 023.4041E + 009.2344E − 037.6683E − 038.4415E − 031.1552E + 00
Std Dev(4.8030E − 03)(1.8609E + 00)(5.9462E − 03)(4.1917E − 01)(1.1968E − 03)(2.5300E + 00)(1.3762E − 03)(4.7517E − 03)(1.4152E + 00)(2.1722E + 00)

Mean2.2300E − 027.4742E − 022.2230E − 021.7921E − 022.4342E − 021.2093E − 014.1413E − 024.3552E − 026.7181E − 021.1395E − 01
Min1.4659E − 082.1056E − 099.3328E − 104.5294E − 101.5764E − 052.5166E − 069.3085E − 064.6435E − 065.5552E − 063.7370E − 06
Std Dev(2.7383E − 02)(5.9743E − 02)(3.4994E − 02)(1.9481E − 02)(2.8117E − 02)(1.6475E − 01)(4.3791E − 02)(7.0052E − 02)(7.6744E − 02)(2.2874E − 01)

Mean4.1633E − 031.3546E + 004.1507E − 034.1515E − 032.0812E − 031.1365E + 002.0741E − 021.5691E − 013.5859E − 014.4462E − 01
Min6.5400E − 102.0109E − 064.0296E − 101.5497E − 104.0330E − 068.8123E − 072.0292E − 061.8880E − 061.2414E − 069.6019E − 07
Std Dev(2.0519E − 02)(2.3403E + 00)(2.0521E − 02)(2.0520E − 02)(1.4661E − 02)(1.6131E + 00)(7.5513E − 02)(3.6762E − 01)(5.7222E − 01)(6.2836E − 01)

Mean3.9555E − 056.4014E + 006.8845E − 042.5325E − 048.5921E − 054.5179E + 007.1911E − 054.9155E − 035.8544E − 012.0819E + 00
Min6.3527E − 091.2170E − 062.2008E − 091.7797E − 095.6319E − 059.0896E − 063.2237E − 052.3006E − 051.9697E − 053.5239E − 05
Std Dev(5.0506E − 05)(6.9850E + 00)(2.6287E − 03)(1.5500E − 03)(1.8465E − 05)(5.9895E + 00)(4.6632E − 05)(1.4952E − 02)(1.7692E + 00)(3.2842E + 00)

Mean1.39461.75631.22051.39461.28051.63211.45421.53711.31771.7693
Min0.9980.9980.9980.9980.9980.9980.9980.9980.9980.998
Std Dev(8.7265E − 01)(1.1928E + 00)(5.0212E − 01)(8.7181E − 01)(5.7523E − 01)(1.1595E + 00)(8.9826E − 01)(9.8139E − 01)(6.7645E − 01)(1.4785E + 00)

Mean4.3569E − 044.5400E − 044.3569E − 045.0894E − 044.5400E − 044.0332E − 043.9906E − 045.0894E − 043.8074E − 044.9063E − 04
Min3.0749E − 043.0749E − 043.0749E − 043.0749E − 043.0749E − 043.0749E − 043.0749E − 043.0749E − 043.0749E − 043.0749E − 04
Std Dev(3.2096E − 04)(3.3910E − 04)(3.2096E − 04)(3.8317E − 04)(3.3910E − 04)(2.9089E − 04)(2.7749E − 04)(3.8317E − 04)(2.5094E − 04)(3.6999E − 04)

Mean−1.0316−1.0316−1.0316−1.0316−1.0316−1.0316−1.0316−1.0316−1.0316−1.0316
Min−1.0316−1.0316−1.0316−1.0316−1.0316−1.0316−1.0316−1.0316−1.0316−1.0316
Std Dev(1.0087E − 09)(3.1347E − 10)(3.9007E − 11)(1.7266E − 12)(3.0332E − 08)7.9887E − 09)(3.3852E − 08)(2.0453E − 08)(2.2805E − 08)(1.9422E − 08)

Mean0.39790.39790.39790.39790.39790.39790.39790.39790.39790.3979
Min0.39790.39790.39790.39790.39790.39790.39790.39790.39790.3979
Std Dev(1.2995E − 10)(3.0825E − 11)(2.2603E − 11)(7.8869E − 13)(7.0398E − 09)5.1135E − 09)(1.4545E − 08)(9.8416E − 09)(8.3266E − 09)(8.0297E − 09)

Mean3.00003.00003.00003.00003.00003.00003.00003.00003.00003.0000
Min3.00003.00003.00003.00003.00003.00003.00003.00003.00003.0000
Std Dev(3.5756E − 08)(4.3186E − 09)(2.8254E − 09)(1.0494E − 10)(1.1868E − 06)8.8630E − 07)(1.1530E − 06)(1.3493E − 06)(1.4221E − 06)(7.6097E − 07)

Mean−3.8628−3.8628−3.8628−3.8628−3.8628−3.8628−3.8628−3.8628−3.8628−3.8628
Min−3.8628−3.8628−3.8628−3.8628−3.8628−3.8628−3.8628−3.8628−3.8628−3.8628
Std Dev(2.6613E − 06)(2.0399E − 08)(2.0050E − 06)(1.3995E − 06)(1.9028E − 06)6.1612E − 07)(1.5250E − 06)(9.6434E − 07)(1.0641E − 06)(1.2872E − 06)

Mean−3.2842−3.2675−3.2563−3.2675−3.2437−3.2794−3.2675−3.2675−3.2651−3.2842
Min−3.3224−3.3224−3.3224−3.3224−3.3223−3.3224−3.3224−3.3224−3.3224−3.3224
Std Dev(5.9431E − 02)(6.0015E − 02)(5.9333E − 02)(6.0014E − 02)(5.7039E − 02)(5.6169E − 02)(6.0012E − 02)(6.0014E − 02)(6.0159E − 02)(5.6174E − 02)

Mean−6.4811−5.4657−6.5003−6.6111−6.4439−8.4928−6.3396−7.0739−7.3097−7.8652
Min−10.1532−10.1532−10.1532−10.1532−10.1531−10.1532−10.1532−10.1532−10.1532−10.1532
Std Dev(2.4491E + 00)(1.3963E + 00)(2.3030E + 00)(2.7105E + 00)(2.5162E + 00)(2.4704E + 00)(2.3080E + 00)(2.5335E + 00)(2.6909E + 00)(2.6294E + 00)

Mean−8.2317−5.8052−8.3806−8.3522−7.5690−9.6849−7.7189−8.1391−8.3426−8.5489
Min−10.4029−10.4029−10.4029−10.4029−10.4029−10.4029−10.4029−10.4029−10.4029−10.4029
Std Dev(2.7034E + 00)(2.2835E + 00)(2.8997E + 00)(2.8100E + 00)(2.9246E + 00)(1.9791E + 00)(3.0032E + 00)(2.8505E + 00)(2.8157E + 00)(2.7805E + 00)

Mean−8.7721−8.5261−8.3264−8.1230−8.5698−9.6378−8.7256−8.9864−8.5304−8.9635
Min−10.5364−10.5364−10.5364−10.5364−10.5364−10.5364−10.5364−10.5364−10.5364−10.5364
Std Dev(3.0564E + 00)(2.8798E + 00)(3.3848E + 00)(3.3768E + 00)(2.8178E + 00)(2.1817E + 00)(3.1400E + 00)(2.6928E + 00)(3.1457E + 00)(2.8776E + 00)