Modified Bézier Curves with Shape-Preserving Characteristics Using Differential Evolution Optimization Algorithm

Table 1

Table for test function, 𝑓₁.

𝑖	𝑥𝑖	𝑦𝑖	𝑦𝑏𝑖	𝑦𝑚𝑖	𝜁𝑖	Performance
0	0	−0.2	−0.2000	−0.2207	1.1034
1	0.2	0.4	0.3262	0.4005	0.8550
2	0.4	0.8	0.7225	0.7892	2.4631
3	0.6	1.2	0.9747	1.1809	−1.1786	𝜀𝑏𝑐=1.5609
4	0.8	1.3	1.0345	1.4154	2.6882	𝜀𝑚𝑐=0.2710
5	1.0	1.4	0.8562	1.0731	2.9621	𝜀𝑏𝑠=117.7463
6	1.1	0.6	0.6948	0.7126	−2.7567	𝜀𝑚𝑠=77.0282
7	1.2	0.2	0.5154	0.3577	−2.8568	𝑓cost,𝑏=13.3355
8	1.4	0.1	0.2373	0.0419	2.6472	𝑓cost,𝑚=7.9738
9	1.6	0.1	0.1174	0.0998	1.9715
10	1.7	0.1	0.1016	0.1159	0.9570
11	1.8	0.1	0.1000	0.0997	0.9974