A Multiswarm Intelligence Algorithm for Expensive Bound Constrained Optimization Problems

Table 4

The experimental results of (a) MSIA, (b) ACO, and (c) FA by solving the CEC′13 in 30 dimensions [54].

Problem	Best	Average	Standard deviation	Maximum	Algorithms
	–1.00000000e + 001	–1.34847601e + 004	4.08563270e + 003	7.14781379e + 004	a
	–1.40000000e + 003	–1.31762841e + 003	6.24857337e + 002	5.92866180e + 003	b
	–1.40000000e + 003	–1.39850118e + 003	4.75975593e + 001	4.92018509e + 002	c
	–1.00000000e + 001	1.34847601e + 004	4.08563270e + 003	7.14781379e + 004	a
	5.11053585e + 006	1.70311183e + 007	3.71650087e + 006	3.50229253e + 007	b
	–1.22998756e + 003	2.30092533e + 004	3.40438747e + 005	1.23150007e + 007	c
	–1.00000000e + 001	1.29269959e + 004	4.09476108e + 003	7.75773844e + 004	a
	–1.19999489e + 003	1.12802551e + 009	7.55617940e + 009	8.33553469e + 010	b
	–1.19999029e + 003	4.24092267e + 006	1.35141321e + 008	6.10608129e + 009	c
	–1.00000000e + 001	1.26689291e + 004	4.32681461e + 003	6.93749063e + 004	a
	4.62070602e + 004	5.85905504e + 004	4.32263932e − 009	7.01655272e + 004	b
	–1.10000000e + 003	–1.02665335e + 003	7.40976376e + 002	1.24856684e + 004	c
	–1.00000000e + 001	1.38374537e + 004	3.94289518e + 003	6.73494023e + 004	a
	–1.00000000e + 003	–9.69829937e + 002	1.97609298e + 002	1.70842420e + 003	b
	–1.00000000e + 003	–9.99693929e + 002	1.00936173e + 001	–5.07286413e + 002	c
	–1.00000000e + 001	1.04357828e + 004	3.97031629e + 003	7.52279597e + 004	a
	–8.98211405e + 002	–8.89173945e + 002	4.91621529e + 001	–1.52687789e + 002	b
	–8.99992095e + 002	–8.99652152e + 002	3.12308019e + 000	–7.44410826e + 002	c
	–1.00000000e + 001	1.44303050e + 004	3.09999749e + 003	7.62766568e + 004	a
	–7.99999570e + 002	–7.79560063e + 002	5.40992509e + 001	–4.30716664e + 002	b
	–8.00000000e + 002	–7.99803559e + 002	3.39121331e + 000	–6.65980780e + 002	c
	–1.00000000e + 001	1.33612319e + 004	3.27656564e + 003	7.80617165e + 004	a
	–1.40000000e + 003	–1.33502027e + 003	4.82036178e + 002	6.63206765e + 003	b
	–6.79904212e + 002	–6.79884280e + 002	3.38983850e − 002	–6.79611291e + 002	c
	–1.00000000e + 001	1.14785811e + 004	3.53367480e + 003	6.56185803e + 004	a
	–6.79910546e + 002	–6.79663617e + 002	3.52873906e − 002	–6.79101411e + 002	b
	–5.99163443e + 002	–5.99141005e + 002	2.49386486e − 001	–5.92168717e + 002	c
	–1.00000000e + 001	1.37390386e + 004	3.72354347e + 003	6.09673611e + 004	a
	–5.91820960e + 002	–5.91449793e + 002	3.70460630e − 001	–5.89231846e + 002	b
	–4.99977814e + 002	–4.99721994e + 002	7.57832193e + 000	–1.38027458e + 002	c
	–1.00000000e + 001	1.34848754e + 004	3.63155978e + 003	8.36727298e + 004	a
	–4.99475498e + 002	–4.79337941e + 002	8.14000795e + 001	4.29514179e + 002	b
	–3.99005041e + 002	–3.98830318e + 002	2.95481402e + 000	–2.85890624e + 002	c
	–1.00000000e + 001	1.36075496e + 004	3.82776022e + 003	8.29620099e + 004	a
	–3.75129327e + 002	–3.67133358e + 002	1.37839005e + 001	–2.36996315e + 002	b
	–2.96020169e + 002	–2.95865600e + 002	2.41752229e + 000	–2.13057107e + 002	c
	–1.00000000e + 001	1.23359046e + 004	4.24524249e + 003	7.07813201e + 004	a
	–2.79504176e + 002	–2.73450147e + 002	1.59304444e + 001	–1.28836347e + 002	b
	–1.97107646e + 002	–1.96895621e + 002	2.36431415e + 000	–1.01814893e + 002	c
	–1.00000000e + 001	1.31945555e + 004	4.83006304e + 003	4.55239693e + 004	a
	–1.77607239e + 002	–1.72159776e + 002	1.66448427e + 001	–1.90275590e + 001	b
	–8.82953840e + 001	–8.37815952e + 001	5.75227562e + 001	1.70271789e + 003	c