An Efficient Algorithm for Unconstrained Optimization

Table 11

Normalized Score (NS) versus Problem (P) and dimension (Dim.).

NS versus P	Ackley			Griewank			Rastrigin			Rosenbrock				Sphere		Zakharov
Dim.	30	50	100	30	50	100	30	50	100	30	40	50	100	30	100	30	100
1	7	27	36	26	27	36	9	10	32, 36	26	10	27	36	8	36	26	31
0.9	3, 4
0.8	5		31
0.7	6				28											24
0.6	2		32, 34				7
0.5			35						31								36
0.4	9						3
0.3			30			31	2, 5, 6		33						31
0.2	26						4, 21, 25	11	35			PSO-3P	31				32
0.1	1, 21, 25					32, 35	1, 17, 26		30		11				32	7, 22	34
0	8, 14–20					29, 30	8, 14–20	12, 13		1–9		28	29, 30	1–7, 9	29, 30	1–6, 8	29, 30
	22–24	28	29, 33	1–25	10–13	33, 34	22–24	27, 28	29, 34	14–25	12, 13		32–35	14–26	33–35	15–23, 25	33, 35
	PSO-3P	PSO-3P	PSO-3P	PSO-3P	PSO-3P	PSO-3P	PSO-3P	PSO-3P	PSO-3P	PSO-3P	PSO-3P		PSO-3P	PSO-3P	PSO-3P	PSO-3P	PSO-3P

Note: ELIPSO is represented by 1 [19]; LDWIPSO is represented by 2 [19]; FIWPSO is represented by 3 [19]; CIWPSO is represented by 4 [19]; RIWPSO is represented by 5 [19]; TVACPSO is represented by 6 [19]; COPSO is represented by 7 [19]; IRPEO is represented by 8 [13]; pPSA is represented by 9 [20]; PSO is represented by 10 [21]; SFLA is represented by 11 [21]; MSFLA is represented by 12 [21]; MSFLA-EO is represented by 13 [21]; PSO-EO is represented by 14 [22]; LX-PM is represented by 15 [23]; LX-MPTM is represented by 16 [23]; LX-NUM is represented by 17 [23]; HX-PM is represented by 18 [23]; HX-MPTM is represented by 19 [23]; HX-NUM is represented by 20 [23]; ADM is represented by 21 [24]; RM is represented by 22 [24]; PLM is represented by 23 [24]; NUM is represented by 24 [24]; MNUM is represented by 25 [24]; PM is represented by 26 [24]; CSA is represented by 27 [25]; ACSA is represented by 28 [25]; ELPSO is represented by 29 [19]; CPSO is represented by 30 [19]; HS is represented by 31 [19]; GA is represented by 32 [19]; FSO is represented by 33 [19]; GSA is represented by 34 [19]; BSOA is represented by 35 [19]; ABC is represented by 36 [19].