1. Determinated optimization

I.1 The single-extremum differentiated functions

Table 1

Test functions

The analytical expression

Solution

Arguments vector

Rosenbroke function

0

1,...,1

Mill-Cantrell function

0

0,1,...,1

Grague-Levy function

0

0,1,...,1

Function ¹ 4

0

1,.....,1

Function ¹5

0

1,.....,1

Function ¹6

0

0,.....,0

 

Function ¹9

0

1,.....,1

Function ¹10

0

1,.....,1

Function ¹11

0

0,.....,0

Function ¹12

0

1,.....,1

Function ¹14

0

0,.....,0

 

Function ¹16

0

0,.....,0

Function ¹17

0

0,.....,0

Dicson function

0

1,.....,1

Oren function

0

1,.....,1

Vood function

0

0,.....,0

1.2 The single-extremum nondifferentiated functions

Problem ¹ 1

0

0,1,.....,1

Problem ¹ 2

0

0,1,.....,1

Problem ¹ 3

0

0,1.....,1

Problem ¹ 4

0

0,1.....,1

Problem ¹ 5

0

0,1.....,1

1.3. The multi-extremum differentiated functions

Problem ¹ 6

0

0,.....,0

1.4. The multi-extremum nondifferentiated functions

Problem ¹ 7

0

0,1.....,1

Problem ¹ 8

0

0,1.....,1

Problem ¹ 9

0

0,1.....,1

Problem ¹ 10

0

0,1.....,1

Problem ¹ 11

0

0,1.....,1

  1. The stochastic optimization

II.1 The stochastic optimization for the single-extremum functions

 

a -accidental value spreaded according to the normal law

 

 

 

a -accidental value spreaded according to the normal law

 

 

 

a -accidental value spreaded according to the normal law

 

 

 

a -accidental value spreaded according to the normal law

 

 

 

a -accidental value spreaded according to the normal law

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

II.2 Multiextremum functions