Новый коллективный метод оптимизации на основе кооперации бионических алгоритмов

Автор: Ахмедова Шахназ Агасувар Кызы, Семенкин Евгений Станиславович

Журнал: Сибирский аэрокосмический журнал @vestnik-sibsau

Рубрика: 2-я международная конференция по математическим моделям и их применению

Статья в выпуске: 4 (50), 2013 года.

Бесплатный доступ

Описывается и рассматривается новый самонастраивающийся коллективный подох, названный кооперацией бионических алгоритмов (COBRA), основанный на пяти хорошо известных бионических алгоритмах: стайные алгоритмы, алгоритмы волчьих стай, мотыльковые алгоритмы, поиск алгоритмом «кукушки». Кроме того, включены две модификации алгоритма COBRA. Также новый коллективный метод используется для настройки весовых коэффициентов нейронной сети в решении различных задач классификации.

Самонастройка, нейронная сеть, классификация, бионический алгоритм

Короткий адрес: https://sciup.org/148177168

IDR: 148177168

Текст научной статьи Новый коллективный метод оптимизации на основе кооперации бионических алгоритмов

Existing metaheuristic algorithms such as Particle Swarm Optimization or Firefly Algorithm, for example, start to demonstrate their power in dealing with tough optimization problems and even NP-hard problems. Five well-known and very similar to each other nature-inspired algorithms such as Particle Swarm Optimization (PSO) [1], Wolf Pack Search (WPS) [2], Firefly Algorithm (FFA) [3], Cuckoo Search Algorithm (CSA) [4] and Bat Algorithm (BA) [5] were investigated by authors of this paper. Each of above listed algorithms was originally developed for solving real-parameter unconstrained optimization problems and imitates a nature process or the behavior of an animal group. For instance Bat Algorithm is based on the echolocation behavior of bats; Cuckoo Search Algorithm was inspired by the obligate brood parasitism of some cuckoo species by laying their eggs in the nests of other host birds (of other species), and so on.

Unconstrained optimization. Various test unconstrained optimization problems with various dimensions were used for the preliminary investigation of all mentioned algorithms: Rosenbrock’s function, Sphere function, Ackley’s function, Griewank’s function, Hyper-Ellipsoidal function and Rastrigin’s functions [6]. The comparison of obtained results showed that we can’t say which approach is the most appropriate for any function and any dimension. The best results were obtained by

different methods for different problems and for different dimensions; in some cases the best algorithm differs even for the same test problem if the dimension varies. Each strategy has its advantages and disadvantages, so a natural question is whether is it possible to combine major advantages of above listed algorithms and try to develop a potentially better algorithm?

These observations brought researchers to the idea of formulating a new metaheuristic approach that combines major advantages of various algorithms. So a new optimization method based on PSO, WPS, FFA, CSA and BA was implemented and investigated. Proposed approach was called Co-Operation of Biology Related Algorithms (COBRA). Its basic idea consists in generating five populations (one population for each algorithm) which are then executed in parallel cooperating with each other (so-called island model).

Proposed algorithm is a self-tuning meta-heuristic. That is why there is no necessity to choose the population size for each algorithm. The number of individuals in each algorithm’s population can increase or decrease depending on the fact weather was the fitness value improving on current stage or not. If the fitness value wasn’t improved during a given number of generations, then the size of all populations increases. And vice versa, if the fitness value was constantly improved, then the size of all populations de-

Table 1

Results obtained by COBRA for the first six test problems

Func	Dimension	Success rate	Average population size	Average number of function evaluations	Average function value	STD
1	2	100	20	263	0.000652238	0.000346687
	3	100	24	605	0.000750922	0.000290652
	4	100	27	757	0.000790054	0.000297926
2	2	100	20	284	0.000753919	0.000272061
	3	100	22	552	0.000783528	0.000290029
	4	100	27	932	0.000817905	0.00028088
3	2	100	29	867	0.000588745	0.000307145
	3	100	33	1470	0.000774339	0.000282613
	4	100	32	1604	0.000739637	0.000372214
4	2	100	20	202	0.000678884	0.000320224
	3	100	25	581	0.000749783	0.000282332
	4	100	28	1085	0.000756105	0.000286405
5	2	100	22	369	0.000806724	0.000140685
	3	100	22	574	0.000989866	0.00140048
	4	100	28	885	0.000695163	0.000159342
6	2	100	27	860	180.001	0.000273844
	3	100	40	2082	170.001	0.000247725
	4	100	56	3877	160.001	0.000336504

Table 2

Performance comparison of COBRA and component algorithms (28 test functions from [7])

Func	Best D = 10	Mean D = 10	Best D = 30	Mean D = 30
1	PSO	PSO	PSO	COBRA
2	COBRA	COBRA	COBRA	COBRA
3	COBRA	COBRA	COBRA	COBRA
4	COBRA	COBRA	COBRA	COBRA
5	PSO	PSO	WPS	COBRA
6	COBRA	COBRA	COBRA	COBRA
7	COBRA	COBRA	COBRA	COBRA
8	WPS	COBRA	COBRA	COBRA
9	COBRA	COBRA	COBRA	COBRA
10	COBRA	COBRA	COBRA	COBRA
11	COBRA	COBRA	COBRA	COBRA
12	COBRA	COBRA	COBRA	COBRA
13	COBRA	COBRA	COBRA	COBRA
14	WPS	COBRA	COBRA	COBRA
15	COBRA	COBRA	COBRA	COBRA
16	COBRA	COBRA	COBRA	COBRA
17	PSO	COBRA	COBRA	COBRA
18	COBRA	COBRA	COBRA	COBRA
19	COBRA	COBRA	COBRA	COBRA
20	WPS	COBRA	COBRA	COBRA
21	PSO	COBRA	COBRA	COBRA
22	COBRA	COBRA	COBRA	COBRA
23	WPS	COBRA	COBRA	COBRA
24	COBRA	COBRA	COBRA	COBRA
25	FFA	COBRA	COBRA	COBRA
26	COBRA	COBRA	COBRA	COBRA
27	COBRA	COBRA	COBRA	COBRA
28	PSO	COBRA	COBRA	COBRA

Table 3

Func	Best	Worst	Mean	STD	Feasibility Rate
1	-0.727373	–0.559235	–0.637199	0.0594299	100
2	1.82813	4.34865	2.75755	0.926259	100
3	8.87653	8.89164	8.87895	0.00318718	92
4	5.57793	5.58908	5.58215	0.00312711	28
5	189.952	516.713	338.063	82.963	32
6	103.515	563.247	369.431	72.4124	24
7	0.529035	0.888604	0.566389	0.0676125	100
8	21.8649	53.8881	23.4468	6.23478	100
9	1.9133e+012	2.4654e+012	2.04001e+012	2.12584e+012	68
10	2.30765e+011	2.84432e+012	6.58941e+011	8.31906e+011	84
11	0.0002073305	0.00843533	0.00190705	0.000479151	68
12	–169.36	671.962	-102.82	228.253	0
13	–57.1851	-54.9831	-57.0463	0.429771	100
14	7.9878	1.72346e+007	6.97436e+006	8.37255e+006	100
15	6.9986e+009	4.94244e+011	7.56845e+010	1.22078e+011	100
16	0.724961	1.17519	0.826752	0.165962	56
17	103.275	321.092	111.988	42.6833	100
18	378.76	671.905	425.911	77.383	96

Table 4

Func	Best	Worst	Mean	STD	Feasible rate
1	–0.625073	-0.270351	-0.42015	0.132247	100
2	4.0493	5.03476	4.57562	0.395698	92
3	28.6807	28.707	28.6861	0.00729205	36
4	9.13159	9.13525	9.13303	0.00120324	20
5	478.746	555.016	485.285	18.7327	40
6	493.301	600.586	504.521	25.1907	32
7	0.334309	4.23197	1.61077	1.30831	100
8	470.46	1023.44	896.351	220.978	100
9	2.63268e+012	7.38962e+012	3.12913e+012	1.05068e+012	56
10	1.25487e+012	3.94721e+012	1.96828e+012	5.87269e+011	44
11	–0.00825323	-0.00281327	-0.00443743	0.000266256	16
12	155.45	720.707	403.327	105.636	0
13	-64.3938	-53.8018	-58.2296	4.54096	100
14	398.499	2.90799e+007	1.24046e+006	5.68939e+006	100
15	4.93728e+009	4.92773e+012	2.14661e+012	1.80896e+012	100
16	1.15237	1.37727	1.19964	0.0478142	8
17	332.563	381.055	344.201	20.7101	92
18	290.033	357.092	355.187	13.2994	100

Table 5

Results obtained by binary modification of COBRA

Func	Dimension	Success rate	Average population size	Average number of function evaluations	Average function value	STD
1	2	100	31	740	0.000182069	0.000248506
	3	99	68	3473	0.000188191	0.000689647
	4	93	80	6730	0.00579879	0.0242297
2	2	100	27	567	0.000236274	0.000265351
	3	100	30	775	0.000150127	0.000168235
	4	100	32	916	0.000355086	0.00029257
3	2	100	32	1439	0.00019874	0.000330485
	3	91	51	2046	0.00150713	0.00245315
	4	83	62	3030	0.00126295	0.00281119
4	2	100	33	931	0.000209168	0.000268542
	3	100	32	868	0.000191162	0.000233884
	4	92	79	1710	0.000347666	0.000257291
5	2	100	30	899	0.00032841	0.000468681
	3	90	65	1332	0.000506847	0.00140048
	4	90	160	2258	0.00411721	0.158903
6	2	100	28	1734	180.0002	0.000185362
	3	98	36	3294	169.801	0.169149
	4	96	41	5462	159.2	0.279294

Table 6

Classifier	Scoring in Australia	Scoring in Germany
2SGP	0.9027	0.8015
C4.5	0.8986	0.7773
Fuzzy	0.8910	0.7940
GP	0.8889	0.7834
CART	0.8744	0.7565
LR	0.8696	0.7837
CCEL	0.8660	0.7460
RSM	0,8520	0,6770
Bagging	0.8470	0.6840
Bayesian	0.8470	0.6790
Boosting	0.7600	0.7000
k-NN	0.7150	0.7151
This study: ANN+COBRA (5)	0,8907	0,7829
This study: ANN+COBRA (3)	0,8898	0,7809

Table 7

Author (year)	Method	Classification accuracy (%)
Quinlan (1996)	C4.5	94.74
Hamiton et al. (1996)	RAIC	95.00
Ster and Dobnikar (1996)	LDA	96.80
Nauck and Kruse (1999)	NEFCLASS	95.06
Pena-Reyes and Sipper (1999)	Fuzzy-GA1	97.36
Setiono (2000)	Neuro-rule 2a	98.10
Albrecht et al. (2002)	LSA machine	98.80
Abonyi and Szeifert (2003)	SFC	95.57
Übeyli (2007)	SVM	99.54
Polat and Günes (2007)	LS-SVM	98.53
Guijarro-Berdias et al. (2007)	LLS	96.00
Akay (2009)	SVM-CFS	99.51
Karabatak and Cevdet-Ince (2009)	AR + NN	97.40
Peng et al. (2009)	CFW	99.50
A. Marcano-Cedeño, J. Quintanilla-Domínguez, D. Andina (2011)	AMMLP	99.26
This study (2013)	ANN+COBRA (3x1)	97.62
	ANN+COBRA (5x1)	97.67
	ANN+COBRA (3x3)	98.16

Table 8

Classification accuracies obtained with COBRA and other classifiers for diabetes problem

Author (year)	Method	Classification accuracy (%)
Mehmet Recep Bozkurt1, Nilüfer Yur-tay, Ziynet Yilmaz1, Cengiz Sertkaya (2012)	PNN	72.00
	LVQ	73.60
	FFN	68.80
	CFN	68.00
	DTDN	76.00
	TDN	66.80
	Gini	65.97
	AIS	68.80
H. Temurtas, N. Yumusak, F. Temurtas (2009)	MLNN with LM(10xFC)	79.62
	PNN (10xFC)	78.05
	MLNN with LM	82.37
	PNN	78.13
S. M. Kamruzzaman, Ahmed Ryadh Hasan (2005)	FCNN with PA	77.344
K. Kayaer., T. Yildirim (2003)	GRNN	80.21
K. Kayaer., T. Yildirim (2003)	MLNN with LM	77.08
L. Meng, P. Putten, H. Wang (2005)	AIRS	67.40
This study (2013)	ANN+COBRA (3x1)	79.65
	ANN+COBRA (5x1)	79.71
	ANN+COBRA (3x3)	79.83

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