Table 3 Raw data of experiments.

From: Public security patrol path planning recommendation method based on wolf-pack optimization algorithm using DAF and BRS

Function	Algorithm	Optimal value	Worst value	Average value	Standard deviation	Average iteration	Average time
1 Ackley min f = 0	GA	7.92E−06	0.00012803	0.000051735	6.95E−10	176.7	0.23365
	PSO	1.71E−05	0.00057189	0.00011362	6.89E−09	600	0.046053
	WDX-WPOA	0	0	0	0	37.6333	0.053561
	DAF-BRS-CWOA	0	0	0	0	22.2667	0.033704
2 Bukin6 min f = 0	GA	0.6912	11.2453	3.7961	2.6443	600	0.013
	PSO	0.0012517	0.13	0.058051	0.041452	600	0.013559
	WDX-WPOA	0.0023801	0.082569	0.029872	0.022073	600	0.80598
	DAF-BRS-CWOA	0.075576	0.50493	0.28726	0.12965	600	0.64729
3 Drop-Wave min f = − 1	GA	− 0.99992	− 0.78573	− 0.93986	0.04808	600	0.012028
	PSO	− 1	− 0.93625	− 0.98512	0.026965	218.6333	0.004777
	WDX-WPOA	− 1	− 1	− 1	0	14.4333	0.018366
	DAF-BRS-CWOA	− 1	− 1	− 1	0	12.1333	0.016619
4 Eggholder min f = − 959.6407	GA	− 959.6387	− 629.6112	− 876.5954	78.8508	600	0.012111
	PSO	− 959.6407	− 718.1675	− 926.7076	53.5701	600	0.012546
	WDX-WPOA	− 959.6407	− 935.338	− 947.2171	11.904	600	1.0656
	DAF-BRS-CWOA	− 959.6404	− 935.3379	− 948.744	11.7553	600	0.72768
5 Griewank min f = 0	GA	0.004788	0.31789	0.075813	0.063402	600	0.013661
	PSO	0	0.019719	0.0026303	0.0045421	339.3	0.0085504
	WDX-WPOA	0	0	0	0	17.5667	0.025562
	DAF-BRS-CWOA	0	0	0	0	13.5	0.020979
6 Levy min f = 0	GA	0.00024335	1.1263	0.12324	0.21281	600	0.038618
	PSO	1.50E−32	1.50E−32	1.50E−32	1.09E−47	600	0.039204
	WDX-WPOA	0	5.98E−01	0.019935	0.10735	549.9	0.84128
	DAF-BRS-CWOA	0	0.39478	0.013159	0.070865	479.1333	0.7371
7 Levy13 min f = 0	GA	0.011247	2.2797	0.22303	0.76184	600	0.01238
	PSO	0.00010961	− 0.97283	− 0.97283	3.33E−16	600	0.012789
	WDX-WPOA	0	0	0	0	25.1333	0.038007
	DAF-BRS-CWOA	0	0	0	0	21.7	0.03573
8 Rastrigin min f = 0	GA	0.013678	6.3489	2.2711	1.7587	600	0.0119
	PSO	0	0.99496	0.066331	0.24819	110.4333	0.0023772
	WDX-WPOA	0	0	0	0	12.3	0.018345
	DAF-BRS-CWOA	0	0	0	0	10.9	0.016472
9 Schaffer2 min f = 0	GA	1.03E−06	0.042464	0.010477	0.0093243	600	0.01321
	PSO	0	0	0	0	66.9667	0.0019346
	WDX-WPOA	0	0	0	0	11.7333	0.016255
	DAF-BRS-CWOA	0	0	0	0	9.7	0.01489
10 Bohachevsky1 min f = 0	GA	0.011268	0.91934	0.48134	0.25563	600	0.011984
	PSO	0	0	0	0	78.1667	0.0017231
	WDX-WPOA	0	0	0	0	14.5	0.020572
	DAF-BRS-CWOA	0	0	0	0	12.3	0.018081
11 Perm0-d-β min f = 0	GA	0.011057	388.7314	26.2837	71.8592	600	0.01213
	PSO	0	0	0	0	175.3667	0.0052171
	WDX-WPOA	0	0	0	0	25.8	0.030897
	DAF-BRS-CWOA	0	0	0	0	21.7667	0.026103
12 Rotated Hyper-Ellipsoi min f = 0	GA	0.00039244	0.12985	0.034819	0.03493	600	0.012687
	PSO	1.96E−134	1.02E−129	8.56E−131	2.28E−130	600	0.013828
	WDX-WPOA	0	0	0	0	25.9667	0.029679
	DAF-BRS-CWOA	0	0	0	0	22.7	0.027767
13 Sum Squares min f = 0	GA	2.42E−06	0.0025094	0.00051005	0.00048937	600	0.012084
	PSO	5.91E−137	2.18E−132	3.76E−133	5.82E−133	600	0.013233
	WDX-WPOA	0	0	0	0	24.3667	0.029123
	DAF-BRS-CWOA	0	0	0	0	21.1667	0.027215
14 Trid min f = − 2	GA	− 0.037736	− 1.9991	− 1.8925	0.11219	600	0.01241
	PSO	− 2	− 2	− 2	0	600	0.014356
	WDX-WPOA	− 2	− 2	− 2	0	10.6667	0.013702
	DAF-BRS-CWOA	− 2	− 2	− 2	0	9.1667	0.011635
15 Booth min f = 0	GA	4.93E−12	4.92E−09	8.73E−10	1.11E−18	74.79	0.088336
	PSO	5.62E−23	8.78E−17	5.13E−18	2.36E−34	600	0.02997
	WDX-WPOA	0	0	0	0	24.0667	0.027151
	DAF-BRS-CWOA	0	0	0	0	20.4	0.025748
16 Matyas min f = 0	GA	9.11E−06	0.042161	0.010059	0.010711	600	0.01241
	PSO	1.76E−120	2.71E−116	2.87E−117	5.48E−117	600	0.013081
	WDX-WPOA	0	0	0	0	24.5	0.030189
	DAF-BRS-CWOA	0	0	0	0	20.3333	0.025239
17 Zakharov min f = 0	GA	2.32E−06	0.0016735	0.00069625	0.00057972	600	0.015955
	PSO	3.10E−137	7.27E−131	3.57E−132	1.30E−131	600	0.016975
	WDX-WPOA	0	0	0	0	24.8	0.053188
	DAF-BRS-CWOA	0	0	0	0	21.1	0.045726
18 Easom min f = − 1	GA	− 1	0	− 0.75001	0.18749	72.91	0.084762
	PSO	− 1	− 6.30E−61	− 0.90001	0.089988	593.02	0.033852
	WDX-WPOA	− 1	− 1	− 1	0	13.6667	0.018649
	DAF-BRS-CWOA	− 1	− 1	− 1	0	11.7333	0.016503
19 Eggcrate min f = 0	GA	2.01E−02	6.72E−01	2.91E−01	1.61E−01	600	0.024449
	PSO	6.23E−24	1.42E−08	1.42E−10	1.99E−18	597.56	0.030566
	WDX-WPOA	0	0	0	0	14.9667	0.020518
	DAF-BRS-CWOA	0	0	0	0	12.9	0.018693
20 Bohachevsky3 min f = 0	GA	0.032611	0.7588	0.26482	0.18579	600	0.024356
	PSO	0	0	0	0	87.4667	0.016874
	WDX-WPOA	0	0	0	0	14.2333	0.023575
	DAF-BRS-CWOA	0	0	0	0	11.9	0.017347
21 3P-Function	GA	15442.6497	24126.8603	19416.3543	1816.0666	600	0.79052
	PSO	9629.7786	13812.6688	11390.4309	844.0894	600	5.0392
	WDX-WPOA	8586.7186	11586.8103	10318.2428	762.6918	600	79.7046
	DAF-BRS-CWOA	8586.7186	11387.3388	9997.6471	710.5523	600	73.1483

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Table 3 Raw data of experiments.

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