A Multiswarm Intelligence Algorithm for Expensive Bound Constrained Optimization Problems

Table 5

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	1.17678517e + 004	4.19260801e + 003	6.99119354e + 004	a
	1.43222909e + 003	1.54101244e + 003	9.23279003e + 001	2.13679767e + 003	b
	3.91260701e + 002	4.02599646e + 002	5.30758844e + 001	1.60528931e + 003	c
	–1.00000000e + 001	1.36000342e + 004	4.41649078e + 003	7.47814557e + 004	a
	1.42113678e + 003	1.64027890e + 003	8.49407985e + 001	2.26938740e + 003	b
	2.00459133e + 002	2.00514033e + 002	9.39412344e − 002	2.01269803e + 002	c
	–1.00000000e + 001	1.05879624e + 004	4.09410778e + 003	7.21491129e + 004	a
	2.00689911e + 002	2.00962796e + 002	2.15379730e − 001	2.02372908e + 002	b
	3.10965091e + 002	3.11851445e + 002	4.17063288e + 000	4.50075796e + 002	c
	–1.00000000e + 001	1.14961501e + 004	4.67131822e + 003	7.21145444e + 004	a
	3.29079929e + 002	3.41977697e + 002	2.44899705e + 001	7.20851725e + 002	b
	4.10780091e + 002	4.12501042e + 002	5.36744967e + 000	5.98143774e + 002	c
	–1.00000000e + 001	1.28019919e + 004	4.19423733e + 003	6.22023871e + 004	a
	4.33379354e + 002	4.43469268e + 002	2.42019177e + 001	7.20032703e + 002	b
	5.00402182e + 002	5.00819260e + 002	4.11858268e + 000	7.02659326e + 002	c
	–1.00000000e + 001	1.27712941e + 004	4.14302012e + 003	7.09567962e + 004	a
	5.01645112e + 002	5.66417564e + 002	6.60883380e + 002	9.19019400e + 003	b
	6.01283828e + 002	6.01309059e + 002	4.33502708e − 002	6.04538503e + 002	c
	–1.00000000e + 001	1.21557177e + 004	4.43525864e + 003	8.19245032e + 004	a
	6.03858981e + 002	6.03913568e + 002	1.02479998e − 001	6.04932488e + 002	b
	9.00000000e + 002	9.00531224e + 002	4.24046971e + 000	1.29892286e + 003	c
	–1.00000000e + 001	1.35325013e + 004	4.37606868e + 003	7.89091921e + 004	a
	1.10019387e + 003	1.10667394e + 003	5.01088911e + 001	1.65340183e + 003	b
	8.23273710e + 002	8.28211025e + 002	6.35219641e + 001	2.71638792e + 003	c
	–1.00000000e + 001	1.25997912e + 004	3.66188342e + 003	8.42953291e + 004	a
	2.37530690e + 003	2.59453594e + 003	7.39652314e + 001	3.32431330e + 003	b
	9.68507849e + 002	9.75416587e + 002	2.07440950e + 001	2.93823230e + 003	c
	–1.00000000e + 001	1.27023976e + 004	3.34330239e + 003	5.65528731e + 004	a
	2.45776158e + 003	2.47866550e + 003	8.14277485e + 001	3.73865930e + 003	b
	1.12532990e + 003	1.12559980e + 003	7.80349602e − 001	1.21437056e + 003	c
	–1.00000000e + 001	1.32972583e + 004	4.04146240e + 003	5.93783435e + 004	a
	1.22116690e + 003	1.22322675e + 003	1.24341107e + 000	1.23724897e + 003	b
	1.20781404e + 003	1.20810635e + 003	7.04658281e − 001	1.31771006e + 003	c
	–1.00000000e + 001	1.42197213e + 004	4.42812498e + 003	8.82240668e + 004	a
	1.31935053e + 003	1.32228110e + 003	1.02488069e + 000	1.33308473e + 003	b
	1.30397984e + 003	1.30430397e + 003	7.93146115e − 002	1.40422272e + 003	c
	–1.00000000e + 001	1.35961931e + 004	4.55021230e + 003	6.87856577e + 004	a
	–1.40000000e + 003	–1.32567902e + 003	5.89965900e + 002	4.90025229e + 003	b
	1.60000000e + 003	1.60044806e + 003	6.63397786e + 000	1.99305962e + 003	c
	–1.00000000e + 001	1.27913603e + 004	3.67355028e + 003	8.33154374e + 004	a
	2.46276416e + 006	9.67035007e + 006	3.45689813e + 006	1.89713016e + 007	b
	1.50000000e + 003	1.50123431e + 003	2.08826897e + 001	2.49319245e + 003	c