A Clustering Approach Using Cooperative Artificial Bee Colony Algorithm

Table 1

Results comparison of different optimal algorithms for 30 runs.

30D		ABC	CABC	PSO	CPSO
Sphere	Average	1.1396e −014	1.5046e − 018	2.8575e −008	2.1792e −006
	Best	2.1069e −015	5.9342e −019	1.6427e −009	4.8957e −007
	Worst	3.4078e −014	2.7426e −018	2.1292e −007	5.7575e −006
	Std	8.0826e −015	5.4311e − 019	3.8261e −008	1.4044e −006
Rosenbrock	Average	𝟑.𝟑𝟑𝟐𝟓𝐞−𝟎𝟎𝟏	7.1667𝑒+000	2.6555𝑒+001	1.4528𝑒+001
	Best	1.3804𝑒−002	2.3045𝑒−002	7.8515𝑒+000	1.3222𝑒−003
	Worst	1.1599𝑒+000	7.5039𝑒+001	9.6353𝑒+001	7.7598𝑒+001
	Std	𝟐.𝟑𝟕𝟖𝟒𝐞−𝟎𝟎𝟏	1.3472𝑒+001	1.7080𝑒+001	2.7135𝑒+001
Griewank	Average	𝟔.𝟎𝟐𝟎𝟖𝐞−𝟎𝟎𝟕	3.9523𝑒−003	4.1956𝑒+002	3.2394𝑒−002
	Best	1.3549𝑒−011	0	3.6532𝑒+002	3.3059𝑒−007
	Worst	1.7767𝑒−005	1.2665𝑒−001	4.7479𝑒+002	1.5611𝑒−001
	Std	𝟑.𝟐𝟒𝟏𝟗𝐞−𝟎𝟎𝟔	2.7866𝑒−002	2.9238𝑒+001	4.1144𝑒−002
Rastrigin	Average	1.8603𝑒−001	𝟏.𝟑𝟔𝟒𝟐𝐞−𝟎𝟏𝟑	4.6671𝑒+001	3.0123𝑒−003
	Best	3.8257𝑒−009	0	2.1889𝑒+001	7.4135𝑒−004
	Worst	9.9496𝑒−001	3.4106𝑒−013	8.2581𝑒+001	6.0268𝑒−003
	Std	3.6710𝑒−001	𝟖.𝟏𝟐𝟏𝟔𝐞−𝟎𝟏𝟒	1.2656𝑒+001	1.5145𝑒−003
Ackley	Average	6.0643𝑒−006	𝟖.𝟒𝟗𝟕𝟔𝐞−𝟎𝟏𝟐	4.2520𝑒+000	9.0169𝑒−003
	Best	1.5905𝑒−006	2.5553𝑒−012	2.8872𝑒+000	4.5035𝑒−003
	Worst	1.7602𝑒−005	2.9208𝑒−011	5.7625𝑒+000	1.4871𝑒−002
	Std	3.5254𝑒−006	𝟕.𝟐𝟏𝟔𝟏𝐞−𝟎𝟏𝟐	8.3370𝑒−001	2.6789𝑒−003
Schwefel	Average	1.9897𝑒+002	𝟑.𝟖𝟏𝟖𝟑𝐞−𝟎𝟎𝟒	9.5252𝑒+003	7.8976𝑒+000
	Best	4.1238𝑒−004	3.8183𝑒−004	8.7622𝑒+003	7.2405𝑒−004
	Worst	4.7389𝑒+002	3.8186𝑒−004	1.0151𝑒+004	1.1844𝑒+002
	Std	1.1697𝑒+002	𝟔.𝟑𝟏𝟕𝟓𝐞−𝟎𝟎𝟗	3.7111𝑒+002	3.0049𝑒+001