Hybrid Mutation Fruit Fly Optimization Algorithm for Solving the Inverse Kinematics of a Redundant Robot Manipulator

Table 3

Comparison results of benchmark functions.

		FOA	LGMS-FOA	AELGMS-FOA	IFOA	SFOA	HMFOA
f1	Best	1.411770e − 4	3.466251e − 40	1.911653e − 19	1.356467e − 4	3.625604e − 5	0
	Mean	4.623815e − 4	5.019091e − 40	3.351138e − 18	1.387048e − 4	3.721975e − 5	0
	Worst	4.794164e − 4	7.370712e − 40	1.821983e − 17	1.411770e − 4	3.830758e − 5	0
	Std.	1.432076e − 6	9.099148e − 41	3.523805e − 18	1.432076e − 6	4.633699e − 7	0
f2	Best	27.244893	26.430489	26.945519	27.752978	28.688393	0
	Mean	28.693051	28.056813	27.956949	28.228172	28.722672	0
	Worst	32.020138	29.377247	28.994375	28.596902	28.774159	0
	Std.	0.892672	0.640186	0.497804	0.232890	0.024310	0
f3	Best	0.133342	0.029958	3.335927e − 4	0.039419	1.503231e − 5	0
	Mean	0.138847	0.923459	0.006701	0.040155	2.124765e − 5	0
	Worst	0.143332	4.750825	0.036739	0.040996	3.583190e − 5	0
	Std.	0.001782	1.030883	0.007965	3.230054e − 4	4.625523e − 6	0
f4	Best	0.118299	2.814927e − 13	7.590946e − 9	0.063400	0.035800	0
	Mean	0.119498	0.010992	4.956341e − 6	0.064237	0.035856	0
	Worst	0.121374	0.103356	2.242247e − 4	0.064880	0.035957	0
	Std.	6.145446e − 4	0.021724	3.133953e − 5	2.749579e − 4	3.254229e − 5	0
f5	Best	2.409987e − 5	0	1.920686e − 14	6.970412e − 6	1.028335e − 6	0
	Mean	2.481638e − 5	0.005076	0.003841	7.121020e − 6	1.226157e − 6	0
	Worst	2.562478e − 5	0.019697	0.024573	7.284919e − 6	1.517875e − 6	0
	Std.	3.167733e − 7	0.005384	0.006266	7.113268e − 8	9.531260e − 8	0
f6	Best	0.092326	0	0	0.026792	0.008531	0
	Mean	11.785692	5.968559e − 15	6.430412e − 15	0.027441	0.008581	0
	Worst	79.015636	1.598721e − 14	1.598721e − 14	0.028106	0.008613	0
	Std.	16.989014	3.440084e − 15	4.603335e − 15	2.965811e − 4	1.659589e − 5	0
f7	Best	0.016704	1.509903e − 14	1.443619e − 10	0.008752	0.004740	8.881784e − 16
	Mean	0.016867	2.376765e − 14	4.627204e − 10	0.008835	0.004774	8.881784e − 16
	Worst	0.017080	3.996803e − 14	1.311684e − 09	0.008934	0.004807	8.881784e − 16
	Std.	9.602465e − 5	6.518431e − 15	2.675685e − 10	4.148766e − 5	1.263296e − 5	0
f8	Best	9.296021e − 4	0	0	2.719695e − 4	7.178698e − 5	0
	Mean	0.067527	1.554312e − 17	1.831868e − 16	2.772358e − 4	7.458798e − 5	0
	Worst	1.109406	2.220446e − 16	8.881784e − 16	2.829657e − 4	7.696815e − 5	0
	Std.	0.163524	5.329071e − 17	2.332129e − 16	2.697164e − 6	9.418096e − 7	0