Computer Aided Engineering Design

344 COMPUTER AIDED ENGINEERING DESIGN

Fibonacci search

x 1 = xl + x 2 = xu –

g(N) xl xu g(N)(xu – xl) g(N)(xu – xl) f(x 1 ) f(x 2 )

0.3820 – 1.0000 6.0000 1.6738 3.3262 – 0.8015 – 9.0639

0.3820 –1.0000 3.3262 0.6525 1.6738 1.5743 – 0.8015

0.3820 –1.0000 1.6738 0.0213 0.6525 1.9995 1.5743

0.3820 –1.0000 0.6525 – 0.3688 0.0213 1.8640 1.9995

0.3820 – 0.3688 0.6525 0.0213 0.2624 1.9995 1.9312

0.3820 – 0.3688 0.2624 – 0.1277 0.0213 1.9837 1.9995

0.3820 – 0.1277 0.2624 0.0213 0.1134 1.9995 1.9871

0.3820 – 0.1277 0.1134 – 0.0356 0.0213 1.9987 1.9995

0.3820 – 0.0356 0.1134 0.0213 0.0565 1.9995 1.9968

0.3819 – 0.0356 0.0565 – 0.0005 0.0213 2.0000 1.9995

0.3820 – 0.0356 0.0213 – 0.0139 – 0.0005 1.9998 2.0000

0.3818 – 0.0139 0.0213 – 0.0005 0.0079 2.0000 1.9999

0.3824 – 0.0139 0.0079 – 0.0056 – 0.0005 2.0000 2.0000

0.3810 – 0.0056 0.0079 – 0.0005 0.0027 2.0000 2.0000

0.3846 – 0.0056 0.0027 – 0.0024 – 0.0005 2.0000 2.0000

0.3750 – 0.0024 0.0027 – 0.0005 0.0008 2.0000 2.0000

0.4000 – 0.0024 0.0008 – 0.0011 – 0.0005 2.0000 2.0000

0.3333 – 0.0011 0.0008 – 0.0005 0.0002 2.0000 2.0000

0.5000 – 0.0005 0.0008 0.0002 0.0002 2.0000 2.0000

Golden section search

x 1 = xl + x 1 = xu –

g(N) xl xu g(N)(xu – xl) g(N)(xu – xl) f(x 1 ) f(x 2 )

0.3820 –1.0000 6.0000 1.6740 3.3260 – 0.8023 – 9.0623

0.3820 –1.0000 3.3260 0.6525 1.6735 1.5742 – 0.8005

0.3820 –1.0000 1.6735 0.0213 0.6522 1.9995 1.5746

0.3820 –1.0000 0.6522 – 0.3689 0.0211 1.8639 1.9996

0.3820 – 0.3689 0.6522 0.0212 0.2622 1.9996 1.9313

0.3820 – 0.3689 0.2622 – 0.1278 0.0211 1.9837 1.9996

0.3820 – 0.1278 0.2622 0.0212 0.1132 1.9996 1.9872

0.3820 – 0.1278 0.1132 – 0.0357 0.0211 1.9987 1.9996

0.3820 – 0.0357 0.1132 0.0211 0.0563 1.9996 1.9968

0.3820 – 0.0357 0.0563 – 0.0006 0.0211 2.0000 1.9996

0.3820 – 0.0357 0.0211 – 0.0140 – 0.0006 1.9998 2.0000

0.3820 – 0.0140 0.0211 – 0.0006 0.0077 2.0000 1.9999

0.3820 – 0.0140 0.0077 – 0.0057 – 0.0006 2.0000 2.0000

0.3820 – 0.0057 0.0077 – 0.0006 0.0026 2.0000 2.0000

0.3820 – 0.0057 0.0026 – 0.0026 – 0.0006 2.0000 2.0000

0.3820 – 0.0026 0.0026 – 0.0006 0.0006 2.0000 2.0000

0.3820 – 0.0026 0.0006 – 0.0013 – 0.0006 2.0000 2.0000

0.3820 – 0.0013 0.0006 – 0.0006 – 0.0001 2.0000 2.0000

0.3820 – 0.0006 0.0006 – 0.0001 0.0002 2.0000 2.0000