A Multiswarm Intelligence Algorithm for Expensive Bound Constrained Optimization Problems

Table 3

The experimental results of (a) MSIA, (b) ACO, and (c) FA by solving the CEC′13 benchmark functions in 10 dimensions [54].

Problem	Optimum	Best	Average	Standard deviation	Maximum	Algorithms
		–1.05787441e + 003	−4.27478554e + 002	5.32520087e + 002	4.51919784e + 003	a
		1.29020039e + 003	1.43497411e + 003	1.52524081e + 002	2.42391695e + 003	b
		–6.97608460e + 001	−5.56706985e + 001	9.83861302e + 001	1.59094345e + 003	c
		–1.41000000e + 003	−1.38038036e + 003	1.51705325e + 002	3.82948621e + 003	a
		1.37302013e + 003	1.81027837e + 003	1.99350254e + 001	1.82017859e + 003	b
		2.60622099e + 003	7.38929816e + 004	8.28530915e + 005	1.68940889e + 007	c
		–1.07775351e + 003	−7.87135563e + 002	5.41473038e + 002	4.68688680e + 003	a
		2.01161840e + 002	2.01275691e + 002	3.26119574e − 001	2.03212837e + 002	b
		–1.19999683e + 003	1.34713183e + 007	2.61331526e + 008	6.96041088e + 009	c
		–1.00000000e + 001	2.97380129e + 006	5.27084138e + 006	7.70958077e + 007	a
		3.38294199e + 002	3.48198354e + 002	2.52233087e + 001	4.52178904e + 002	b
		–1.10000000e + 003	–8.53652774e + 002	1.41482529e + 003	1.45950316e + 004	c
		–7.71635593e + 002	–5.58888645e + 002	2.76514199e + 002	4.56991524e + 003	a
		4.38988097e + 002	4.56925962e + 002	3.70758564e + 001	7.12211302e + 002	b
		–1.00000000e + 003	–9.98683610e + 002	2.96836196e + 001	–1.60926967e + 002	c
		–1.41000000e + 003	–1.38210398e + 003	9.76743330e + 001	5.09148005e + 002	a
		5.02238254e + 002	5.93002146e + 002	4.51529039e + 002	3.20047624e + 003	b
		–8.99935443e + 002	–8.99208513e + 002	5.49981592e + 000	–7.64788173e + 002	c
		–7.34688317e + 002	–6.55445684e + 002	4.26933534e + 002	4.19502288e + 003	a
		6.03841405e + 002	6.04103425e + 002	1.21304155e − 001	6.04659232e + 002	b
		–8.00000000e + 002	–7.99515370e + 002	5.41047502e + 000	–6.89237686e + 002	c
		–1.41000000e + 003	–1.37613278e + 003	1.47628379e + 002	2.70449872e + 003	a
		1.10019387e + 003	1.11529246e + 003	6.39077139e + 001	1.94034991e + 003	b
		–6.79882628e + 002	–6.79814730e + 002	2.70757318e − 002	–6.79706209e + 002	c
		–7.79223446e + 002	–5.87923497e + 002	5.29115496e + 002	6.36559812e + 003	a
		2.71131924e + 003	2.80638128e + 003	7.47686019e + 001	3.35948750e + 003	b
		–5.99730286e + 002	–5.99653895e + 002	4.48506744e − 001	–5.90984947e + 002	c
		–1.41000000e + 003	–1.38722065e + 003	1.35985509e + 002	3.96291901e + 003	a
		2.81293009e + 003	3.03118853e + 003	5.83771758e + 001	3.20391460e + 003	b
		–4.99955742e + 002	–4.99294862e + 002	1.08319919e + 001	–2.62831236e + 002	c
		–1.00003268e + 003	–6.28496611e + 002	5.20374802e + 002	8.18200464e + 003	a
		1.22181090e + 003	1.22284625e + 003	1.61905418e + 000	1.23616915e + 003	b
		–4.00000000e + 002	–3.99480200e + 002	4.13754005e + 000	–3.08463035e + 002	c
		–1.41000000e + 003	–1.37818962e + 003	1.46117712e + 002	2.51374993e + 003	a
		1.32080243e + 003	1.32256986e + 003	1.04244644e + 000	1.33641433e + 003	b
		–2.97015123e + 002	–2.96424650e + 002	4.86448955e + 000	–1.94232316e + 002	c
		–7.55127444e + 002	–5.31346642e + 002	5.59678487e + 002	6.24369518e + 003	a
		–1.40000000e + 003	–1.21823184e + 003	6.99597007e + 002	2.29375556e + 003	b
		–1.97015123e + 002	–1.96411417e + 002	4.60497004e + 000	–7.09293980e + 001	c
		–1.41000000e + 003	–1.37461266e + 003	1.46565437e + 002	2.11257128e + 003	a
		7.79045518e + 006	1.92214598e + 007	1.24536123e + 007	5.64788737e + 007	b
		–8.46930600e + 001	–6.97385530e + 001	1.11122780e + 002	1.69479719e + 003	c