Journal of Shandong University(Engineering Science) ›› 2019, Vol. 49 ›› Issue (2): 47-53.doi: 10.6040/j.issn.1672-3961.0.2018.194

• Machine Learning & Data Mining • Previous Articles     Next Articles

Epsilon truncation algorithm based on NDX and adaptive mutation operator

Jin LI(),Erchao LI*()   

  1. College of Electrical and Information Engineering, Lanzhou University of Technology, Lanzhou 730050, Gansu, China
  • Received:2018-05-25 Online:2019-04-20 Published:2019-04-19
  • Contact: Erchao LI E-mail:1018823882@qq.com;lecstarr@163.com
  • Supported by:
    国家自然科学基金资助项目(61763026);国家自然科学基金资助项目(61403175)

Abstract:

It was hard for constrained optimization algorithm to maintain a good balance of convergence and distribution. To solve this problem, a ε-truncation algorithm based on the normal distribution crossover (NDX) and adaptive mutation operator was proposed, which introduced the normal distribution into the simulated binary crossover (SBX) operator, so that the algorithm could search wider space and easily jump out of local optimum. The proposed algorithm combined the adaptive mutation operator with the current information of the individual in the population, and guided the population evolving toward the real Pareto front. Moreover, it preserved the Pareto optimal solutions and a certain number of infeasible solutions with the adaptive ε truncation strategy. At the same time using the information of these infeasible solutions, it increased the search intensity of space and improved the diversity of population. According to three standard test functions experimental results, the solution set in this study could well track the real Pareto solution set. The proposed method could effectively coordinate the convergence and distribution of the algorithm.

Key words: constrained, NDX operator, adaptive mutation operator, adaptive εtruncation strategy

CLC Number: 

  • TP273

Table 1

IGD and SP values obtained by two evolutionary algorithms for solving standard test functions"

测试函数SPIGD
NDXAMAENSGA-ⅡFRNSGA-ⅡNDXAMAENSGA-ⅡFRNSGA-Ⅱ
均值 方差 均值 方差 均值 方差 均值 方差
SRN 0.093 2 0.001 4 1.176 2 0.072 3 0.002 8 0.002 5 0.022 3 0.028 6
BNH 0.421 4 0.050 6 0.802 4 0.049 8 0.009 3 0.007 1 0.038 5 0.018 9
CON 0.039 7 0.078 6 0.078 5 1.265 8 0.010 5 0.020 7 0.076 4 0.124 6

Fig.1

True Pareto frontier on SRN function"

Fig.2

Simulation results of NDXAMAENSGA-Ⅱ algorithm on SRN function"

Fig.3

Simulation results of NSGA-Ⅱ Based on Feasibility Rules on SRN function"

Fig.4

True Pareto frontier on BNH function"

Fig.5

Simulation results of NDXAMAENSGA-Ⅱ algorithm on BNH function"

Fig.6

Simulation results of NSGA-Ⅱ Based on Feasibility Rules on BNH function"

Fig.7

True Pareto frontier on CON function"

Fig.8

Simulation results of NDXAMAENSGA-Ⅱ algorithm on CON function"

Fig.9

Simulation results of NSGA-Ⅱ Based on Feasibility Rules on CON function"

1 ASAFUDDOULA M , RAY T , SARKER R . A decomposition-based evolutionary algorithm for many objective optimization[J]. IEEE Transactions on Evolutionary Computation, 2015, 19 (3): 445- 460.
doi: 10.1109/TEVC.2014.2339823
2 YANG S , LI M , LIU X , et al. A grid-based evolutionary algorithm for many-objective optimization[J]. IEEE Transactions on Evolutionary Computation, 2013, 17 (5): 721- 736.
doi: 10.1109/TEVC.2012.2227145
3 MATIAS J , CORREIA A , MESTRE P , et al. Adaptive penalty and barrier function based on fuzzy logic[J]. Expert Systems with Applications, 2015, 42 (19): 6777- 6783.
doi: 10.1016/j.eswa.2015.04.070
4 ELHOSSINI A , AREIBI S , DONY R . Strength Pareto particle swarm optimization and hybrid EA-PSO for multi-objective optimization[J]. Evolutionary Computation, 2014, 18 (1): 127- 156.
5 YANG D , JIAO L , GONG M . Adaptive multi-objective optimization based on nondominated solutions[J]. Computational Intelligence, 2010, 25 (2): 84- 108.
6 LIN C H . A rough penalty genetic algorithm for constrained optimization[J]. Information Sciences, 2013, 241 (241): 119- 137.
7 MEZURAMONTES E , COELLO C A C . A simple multimembered evolution strategy to solve constrained optimization problems[J]. IEEE Transactions on Evolutionary Computation, 2005, 9 (1): 1- 17.
8 WANG Y , CAI Z , GUO G , et al. Multiobjective optimization and hybrid evolutionary algorithm to solve constrained optimization problems[J]. IEEE Transactions on Systems Man & Cybernetics Part B, 2007, 37 (3): 560- 575.
9 LEMONGE A C C , BARBOSA H J C , BERNARDINO H S . Variants of an adaptive penalty scheme for steady-state genetic algorithms in engineering optimization[J]. Engineering Computations, 2015, 32 (8): 2182- 2155.
doi: 10.1108/EC-07-2014-0158
10 DEB K . An efficient constraint handling method for genetic algorithms[J]. Computer Methods in Applied Mechanics & Engineering, 2000, 186 (2): 311- 338.
11 CAI Zixing , WANG Yong . A multiobjective optimization-based evolutionary algorithm for constrained optimization[J]. Evolutionary Computation, IEEE Transactions on, 2006, 10 (6): 658- 675.
doi: 10.1109/TEVC.2006.872344
12 WANG Yong , CAI Zixing , ZHOU Yuren , et al. An adaptive tradeoff model for constrained evolutionary optimization[J]. Evolutionary Computation, IEEE Transactions on, IEEE Transactions on, 2008, 12 (1): 80- 92.
13 WOLDESENBET Y G , Yen G G , TESSEMA B G . Constraint handling in multiobjective evolutionary optimization[J]. IEEE Transactions on Evolutionary Computation, 2009, 13 (3): 514- 525.
doi: 10.1109/TEVC.2008.2009032
14 王勇, 蔡自兴, 周育人, 等. 约束优化进化算法[J]. 软件学报, 2009, 20 (1): 11- 29.
WANG Yong , CAI Zixing , ZHOU Yuren , et al. Constrained optimization evolutionary algorithms[J]. Journal of Software, 2009, 20 (1): 11- 29.
15 李智勇, 黄滔, 陈少淼, 等. 约束优化进化算法综述[J]. 软件学报, 2017, 28 (6): 1529- 1546.
LI Zhiyong , HUANG Tao , CHEN Shaomiao , et al. Overview of constrained optimization evolutionary algorithms[J]. Journal of Software, 2017, 28 (6): 1529- 1546.
16 张敏.约束优化和多目标优化的进化算法研究[D].合肥:中国科学技术大学, 2008.
ZHANG Min. Research on evolutionary algorithms for constrained optimization and multiobjective optimization[D]. Hefei: University of Science and Technology of China, 2008.
17 肖易寒, 李明逵, 陈立伟. 基于改进NSGA-Ⅱ算法的多光谱测温数据处理[J]. 应用科技, 2017, 44 (1): 33- 39.
XIAO Yihan , LI Mingkui , CHEN Liwei . Multispectral temperature measurement based on improved adaptive NSGA-Ⅱ algorithm[J]. Applied Science and Technology, 2017, 44 (1): 33- 39.
18 毕晓君, 张磊. 基于自适应ε截断策略的约束多目标优化算法[J]. 电子与信息学报, 2016, 38 (8): 2047- 2053.
BI Xiaojun , ZHANG Lei . Constrained multi-objective optimization algorithm with adaptive ε truncation strategy[J]. Journal of Electronics & Information Technology, 2016, 38 (8): 2047- 2053.
19 DEB K, PRATAP A, MEYARIVAN T. Constrained test problems for multi-objective evolutionary optimization[C]//Proceedings of First International Conference on Evolutionary Multi-Criterion Optimization, EMO 2001, Zurich, Switzerland: EMO, 2001: 284-298.
20 韩红艳.基于Pareto支配的高维多目标进化算法研究[D].大连:大连理工大学, 2016.
HAN Hongyan. Research of Pareto dominance based many-objective evolutionary algorithm[D]. Dalian: Dalian University of Technology, 2016.
21 JIANG S , YANG S . A steadystate and generational evolutionary algorithm for dynamic multi-objective optimization[J]. IEEE Transactions on Evolutionary Computation, 2017, 21 (1): 65- 82.
[1] Jianping HU,Xin LI,Qi XIE,Ling LI,Daochang ZHANG. An unconstrained optimization EMD approach in 2D based on Delaunay triangulation [J]. Journal of Shandong University(Engineering Science), 2018, 48(5): 9-15, 37.
[2] QIAN Shuqu, WU Huihong, XU Guofeng, JIN Jingliang. Immune clonal evolutionary algorithm of dynamic economic dispatch considering gas pollution emission [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2018, 48(4): 1-9.
[3] LIU Dakun, TAN Xiaoyang. Fitting of constrained local model based on manifold [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2016, 46(3): 31-36.
[4] ZHANG Xiao-dan, ZHAO Li, ZOU Cai-rong*. An improved shuffled frog leaping algorithm for solving constrained optimization problems [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2013, 43(1): 1-8.
[5] SUN Hai-Ying, CHEN Ling. A new approach for solving continuous optimizationusing ant colony optimization [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2009, 39(6): 24-30.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
[1] WANG Su-yu,<\sup>,AI Xing<\sup>,ZHAO Jun<\sup>,LI Zuo-li<\sup>,LIU Zeng-wen<\sup> . Milling force prediction model for highspeed end milling 3Cr2Mo steel[J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2006, 36(1): 1 -5 .
[2] LI Kan . Empolder and implement of the embedded weld control system[J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2008, 38(4): 37 -41 .
[3] LI Liang, LUO Qiming, CHEN Enhong. Graph-based ranking model for object-level search
[J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2009, 39(1): 15 -21 .
[4] CHEN Rui, LI Hongwei, TIAN Jing. The relationship between the number of magnetic poles and the bearing capacity of radial magnetic bearing[J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2018, 48(2): 81 -85 .
[5] JI Tao,GAO Xu/sup>,SUN Tong-jing,XUE Yong-duan/sup>,XU Bing-yin/sup> . Characteristic analysis of fault generated traveling waves in 10 Kv automatic blocking and continuous power transmission lines[J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2006, 36(2): 111 -116 .
[6] . [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2009, 39(1): 27 -32 .
[7] QIN Tong, SUN Fengrong*, WANG Limei, WANG Qinghao, LI Xincai. 3D surface reconstruction using the shape based interpolation guided by maximal discs[J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2010, 40(3): 1 -5 .
[8] LIU Wen-liang, ZHU Wei-hong, CHEN Di, ZHANG Hong-quan. Detection and tracking of moving targets using the morphology match in radar images[J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2010, 40(3): 31 -36 .
[9] Yue Khing Toh1, XIAO Wendong2, XIE Lihua1. Wireless sensor network for distributed target tracking: practices via real test bed development[J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2009, 39(1): 50 -56 .
[10] SUN Guohua, WU Yaohua, LI Wei. The effect of excise tax control strategy on the supply chain system performance[J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2009, 39(1): 63 -68 .