Improved Chaotic Quantum-Behaved Particle Swarm Optimization Algorithm for Fuzzy Neural Network and Its Application

Table 3

Statistical results of different test function.

	Best	Mean	Worst
Ackley
PSO	2.0861e + 00	3.5337e + 00	5.0738e + 00
APSO	2.6173e − 01	1.5059e + 00	2.5767e + 00
SINPSO	7.5123e − 02	1.5673e + 00	2.2246e + 00
QPSO	4.8376e − 08	3.1851e + 00	5.5752e + 00
HCQPSO	8.8888e − 16	8.8888e − 16	8.8888e − 16
ICQPSO	0	3.3159e − 15	3.5527e − 15
Rastrigin
PSO	4.4773e + 01	5.2945e + 01	6.3585e + 01
APSO	3.7384e − 01	1.6870e + 01	2.2759e + 01
SINPSO	3.3364e − 04	4.1799e − 04	4.5238e − 03
QPSO	1.5946e + 00	2.5262e + 00	3.4837e + 00
HCQPSO	0	0	0
ICQPSO	0	0	0
Griewank
PSO	1.1751e + 00	3.7878e + 00	7.9665e + 00
APSO	4.8418e − 03	1.0163e − 03	1.1055e − 01
SINPSO	8.9135e − 01	9.8711e − 01	9.9887e − 01
QPSO	0	2.4653e − 04	7.3144e − 03
HCQPSO	0	0	0
ICQPSO	0	0	0
Sphere
PSO	7.9163e − 03	2.2771e − 02	4.9712e − 02
APSO	2.2724e − 14	6.9874e − 12	6.5521e − 11
SINPSO	1.2264e − 09	3.2379e − 10	4.2347e − 10
QPSO	4.3948e − 19	3.2996e − 15	8.1298e − 14
HCQPSO	4.3454e − 39	1.1921e − 34	8.4116e − 33
ICQPSO	7.9196e − 91	5.3151e − 82	6.0556e − 81
Rosenbrock
PSO	2.4057e + 01	5.4534e + 01	1.0105e + 02
APSO	1.1128e + 01	1.4055e + 01	3.0779e + 01
SINPSO	8.5902e + 00	1.0317e + 01	1.1547e + 01
QPSO	1.2473e + 01	4.0305e + 01	1.2017e + 02
HCQPSO	3.5643e + 00	4.6541e + 00	8.3287e + 00
ICQPSO	4.0444e + 00	5.2713e + 00	6.5344e + 00
Schwefel’s 1.2
PSO	5.3828e + 01	1.4982 ee + 02	3.2404e + 02
APSO	2.1917e + 00	9.0975e + 00	2.1640e + 01
SINPSO	3.5402e + 00	8.1004e + 00	1.2023e + 01
QPSO	1.2287e + 00	5.5542e + 00	7.7122e + 00
HCQPSO	1.6231e − 14	1.0412e + 00	3.2824e + 00
ICQPSO	1.3000e − 24	1.0612e − 01	8.0364e + 00