Random Walk Method | Furniture Design Ideas

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

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.

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