解决动态多中心问题的自学习差异进化算法

doi:10.11959/j.issn.1000-436x.2015154

Abstract

Abstract:

A novel self-learning differential evolution algorithm is proposed to solve dynamical multi-center optimization problems.The approach of re-evaluating some specific individuals is used to monitor environmental changes.The proposed self-learning operator guides the evolutionary group to a new environment,meanwhile maintains the stable topology structure of group to maintain the current evolutionary trend.A neighborhood search mechanism and a random immigrant mechanism are adapted to make a tradeoff between algorithmic convergence and population diversity.The experiment studies on a periodic dynamic function set suits are done,and the comparisons with peer algorithms show that the self-learning differential algorithm outperforms other algorithms in term of convergence and adaptability under dynamical environment.

Key words: evolutionary computation, dynamic optimization, self-learning mechanism, differential evolution

Xing-bao LIU,Jian-ping YIN,Chun-hua HU,Rong-yuan CHEN. Self-learning differential evolution algorithm for dynamic polycentric problems[J]. Journal on Communications, 2015, 36(7): 166-175.

Figures/Tables 9

函数表达式	状态空间	中心1近似最优值	中心2近似最优值
$f_{1} (x) = \sum_{i = 1}^{D} x_{i}^{2}$	-10≤x_i≤10	0	0
$f_{2} (x) = \sum_{i = 1}^{D} \| x_{i} \| + \prod_{i = 1}^{D} \| x_{i} \|$	-10≤x_i≤10	0	0
$f_{3} (x) = - 20 \exp (- 0.2 \sqrt{\frac{1}{D} \sum_{i = 1}^{D} x_{i}^{2}}) - \exp (\frac{1}{D} \sum_{i = 1}^{D} \cos 2 π x_{i}) + 20 + e$	-32≤x_i≤32	0	0
$f_{4} (x) = \frac{1}{4000} \sum_{i = 1}^{D} x_{i}^{2} - \prod_{i = 1}^{D} \cos (\frac{x_{i}}{\sqrt{i}}) + 1$	-20≤x≤20	0	0

References 15

[1]	NGUYEN T T , YANG S , BRANKE J . Evolutionary dynamic optimization:a survey of the state of the art[J]. Swarm and Evolutionary Computation, 2012,6: 1-24.
[2]	CRUZ C , GONZáLEZ J R , PELTA D A . Optimization in dynamic environments:a survey on problems,methods and measures[J]. Soft Computing, 2011,15(7): 1427-1448.
[3]	陈莉, 丁立新 . 动态优化算法综述[J]. 武汉大学学报(理学版), 2011,57(3): 255-264. CHEN L , DING L X . Survey on dynamic optimization algorithms[J]. Journal of Wuhan University(Natural Science Edition), 2011,57(3): 255-264.
[4]	FERNANDES C M , MERELO J J , RAMOS V ,et al. A self organized criticality mutation operator for dynamic optimization problems[A]. Proceedings of the 10th Annual Conference on Genetic and Evolutionary Computation[C]. New York:ACM Press, 2008. 937-944.
[5]	GREFENSTETTE J . Genetic Algorithms for Changing Environments[M]. Navy Center for Applied Research in Artificial Intelligence: Navy Research LaboratoryPress, 1992. 137-144.
[6]	YANG S . Genetic algorithms with memory and elitism-based immigrants in dynamic environments[J]. Evolutionary Computation, 2008,16(3): 385-416.
[7]	YAO X.YANG S . Population-based incremental learning with associative memory for dynamic environments[J]. IEEE Transactions on Evolutionary Computation, 2008,12(5): 542-561.
[8]	GOLDBERG D E , SMITH R E . Nonstationary function optimization using genetic algorithms with dominance and diploidy[A]. Proceedings of the 2nd International Conference on Genetic Algorithms and Their Applications[C]. Hillsdale:Lawrence Erlbaum Associates, 1987. 59-68.
[9]	MAVROVOUNIOTIS M , YANG S . Memory-based immigrants for ant colony optimization in changing environments[A]. Proceedings of the 2011 International Conference on Applications of Evolutionary Computation-Volume Part I,EvoApplications’11[C]. Springer-Verlag,Berlin,Heidelberg, 2011. 324-333.
[10]	BENDTSEN C N , KRINK T . Dynamic memory model for nonstationary optimization[A]. Proceeding of the 2002 Congress on Evolutionary Computation[C]. New York,USA, 2002. 145-150.
[11]	周传华, 谢安世 . 一种机遇动态小生境的自组织学习算法[J]. 软件学报, 2011,57(3): 255-264. ZHOU C H , XIE A S . Dynamic niche-based self-organizing learning algorithm[J]. Journal of Software, 2011,22(8): 1738-1748.
[12]	YANG S . A clustering particle swarm optimizer for locating and tracking multiple optima in dynamic environments[J]. IEEE Transactions on Evolutionary Computation, 2010,14(6): 959-974.
[13]	吴晓军, 杨战中, 赵明 . 均匀搜索粒子群算法[J]. 电子学报, 2012,40(6): 1115-1120. WU X J , YANG Z Z , ZHAO M . The convergence analysis of the uniform search particle swarm optimization[J]. Acta Elctronic Sinica, 2012,40(6): 1115-1120.
[14]	STORN R , PRICE K . Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces[J]. Journal of Global Optimization, 1997,11(4): 341-359.
[15]	BREST J , GREINER S , BOSKOVIC B ,et al. Self-adapting control parameters in differential evolution:a comparative study on numerical benchmark problems[J]. IEEE Transactions on Evolutionary Computation, 2006,10(6): 646-657.

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算法	Mean(bestFit),r=2				Mean(bestFit),r =3				Mean(bestFit),r =4				Mean(bestFit),r =5
算法	f₁	f₂	f₃	f₄	f₁	f₂	f₃	f₄	f₁	f₂	f₃	f₄	f₁	f₂	f₃	f₄
SeDE	1.6×10^-4	2.4×10^-2	3.5	6.2×10^-3	8.9×10^-6	1.5×10^-2	1.9×10^-2	3.7×10^-3	5.6×10^-5	1.3×10^-2	3.0×10^-2	2.3×10^-5	9.5×10^-6	9.5×10^-3	3.2×10^-2	5.7×10^-6
DE	1.3×10²	4.0×10¹	1.6×10¹	1.1	6.3×10¹	3.9×10¹	1.5×10¹	1.1	5.5×10¹	3.4×10¹	1.3×10¹	1.1	2.7×10¹	3.5×10¹	1.4×10¹	1.0
jDE	8.7×10¹	4.7×10¹	1.5×10¹	1.1	3.8×10¹	3.0×10¹	1.2×10¹	1.0	2.2×10¹	2.3×10¹	1.0×10¹	9.8×10^-1	1.2×10¹	1.8×10¹	8.6	9.2×10^-1
UPSO	9.2×10^-2	1.3	1.4	5.4×10^-2	5.5×10^-1	1.0×10¹	3.5	9.6×10^-2	2.8×10¹	1.9×10¹	6.3	7.5×10^-1	3.9	3.7×10¹	1.5	4.1×10^-1
+	+3	+3	+2	+3	+3	+3	+3	+3	+3	+3	+3	+3	+3	+3	+3	+3
“+”表示SeDE算法相比于其他3种算法占优的个数。

算法	mean(APE),genLmt=25				mean(APE),genLmt=50				mean(APE),genLmt=100				mean(APE),genLmt=150
算法	f₁	f₂	f₃	f₄	f₁	f₂	f₃	f₄	f₁	f₂	f₃	f₄	f₁	f₂	f₃	f₄
SeDE	1.34	2.59	1.13	0.27	0.74	1.00	0.65	0.04	0.41	3.16	0.50	0.03	0.24	3.62	0.90	0.04
DE	73.53	394.77	8.612	0.57	48.42	26.71	8.10	0.58	8.18	16.8	5.65	0.50	4.51	13.56	4.09	0.37
jDE	38.45	24.67	7.35	0.55	23.31	16.56	6.59	0.55	8.25	9.00	5.03	0.52	2.28	3.82	5.68	0.26
UPSO	11.26	15.58	3.79	0.36	9.69	11.87	2.87	0.30	13.16	10.33	5.66	0.23	16.80	8.67	4.97	0.15
+	+3	+3	+3	+3	+3	+3	+3	+3	+3	+3	+3	+3	+3	+3	+3	+3
“+”表示SeDE算法相比于其他3种算法占优的个数。

Self-learning differential evolution algorithm for dynamic polycentric problems

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