Random Walk Method

Random walk method (Fig. 6.105) is based on the claim that the optimum point is most often located on the edge of the permissible area Ф. The size of the cell T =10 mm, the length of the favourable series to = 100 and the length of the unfavourable series po = 100 were assumed arbitrarily, similar to the multiplexing of increase or reduction of the size of the cell s = 2. The above selection of the values to and po provides the same search for both the interior and the edge of the permissible area Ф.

Results of optimisation of the construction of a chair with a bar are presented in Tables 6.9 and 6.10 and in Fig. 6.106. Table 6.9 presents the criteria allowing for the assessment of the efficiency of each of the applied methods of numerical optimisation. This table shows that the fastest are random methods, consisting in selective searching of the permissible area Ф. The optimal solution is achieved already after a few minutes of the computer work. The time required to determine the optimal solution in the systematic search method is, however, a few dozen times

Next

node

Fig. 6.105 Algorithm of optimisation using random walk method

Table 6.9 Efficiency of numerical methods of optimisation of construction of a chair with a muntin

Method

Node

Cross section of the element [mm2]

Number of drawings

Time of

optimisation [min]

Vertical

A1

Horizontal

A2

General

Successful

Systematic

search

2

522.0

616.3

11 x 107

248

245.0

3

806.0

922.2

52 x 105

186

130.0

6

525.0

547.5

27 x 105

88

70.0

7

643.3

922.3

10 x 106

270

210.0

Monte Carlo

2

549.3

531.2

73,589

8

4.0

3

853.2

921.3

88,289

8

5.0

6

589.3

650.9

384

3

0.5

7

912.5

978.5

5600

6

1.5

Random

walk

2

617.1

644.3

83,892

10

4.5

3

795.9

906.1

63,148

8

3.5

6

770.7

436.7

5275

8

1.5

7

788.3

601.5

83,892

7

4.5

Table 6.10 Optimised dimensions of joints

Method of optimisation

Node

Dimensions of mortise and tenon joints [mm]

g

g1

h

1

h

k

k3

Systematic

search

2

36.00

24.00

14.50

42.50

28.33

14.50

6.21

3

52.00

34.67

15.50

59.50

38.67

15.50

6.64

6

35.00

23.33

15.00

36.50

24.33

15.00

6.43

7

41.50

27.67

15.55

59.50

39.67

15.50

6.64

Monte Carlo

2

30.82

20.55

17.82

50.97

33.98

10.42

4.46

3

54.83

36.56

15.56

59.70

39.80

15.43

6.61

6

32.73

21.82

18.01

40.17

26.78

16.20

6.94

7

46.79

31.19

19.50

59.55

39.70

16.43

7.04

Random walk

2

39.85

26.56

15.49

42.03

28.02

15.33

6.57

3

43.41

28.91

18.34

59.62

39.75

15.20

6.51

6

50.29

33.53

15.32

28.53

19.02

15.31

6.56

7

52.19

34.80

15.10

40.09

26.07

15.01

6.43

longer. The obtained result is, however, most beneficial in comparison with the results obtained using the Monte Carlo or random walk method. This does not mean, however, that these two methods have doubtful application in the process of optimisation of wooden structures. On the contrary, their solutions are completely satisfactory for the engineering practice, and the argument for the advisability of their use is the extremely short time of calculations.

Optimised dimensions of mortise and tenon joints of a construction of a chair are presented in Table 6.10. These dimensions allow for rational designing of the furniture construction. The furniture can have the shape as in Fig. 6.106b. It is a theoretical model, matched only for the given loading scheme. It can be appro­priately shaped, taking into account aesthetic qualities, which is shown in Fig. 6.106c.