Journal of Jilin University(Engineering and Technology Edition) ›› 2022, Vol. 52 ›› Issue (6): 1442-1458.doi: 10.13229/j.cnki.jdxbgxb20210082

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Dynamic multi⁃objective optimization algorithm based on Kalman filter prediction strategy

Yong-jie MA(),Min CHEN   

  1. School of Physics and Electronic Engineering，Northwest Normal University，Lanzhou 730070，China
  • Received:2021-02-19 Online:2022-06-01 Published:2022-06-02

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Abstract:

In order to deal with the environmental changes of dynamic multi-objective optimization more effectively， a dynamic multi-objective optimization algorithm based on Kalman filter prediction strategy is proposed. In the evolution process， a new calculation method is used to calculate the population center point. When the environment changes， the Kalman filter prediction model is used to predict the current population center point， and the approximate true Pareto center point of optimal solution set is used to correct the prediction value， and new individuals are generated based on the modified center point to reinitialize the population during the running of the algorithm； In order to increase the diversity of the population， five new individuals are randomly generated from the search space during the operation of the algorithm， and the corresponding number of individuals in the current population are randomly replaced. Compared with other dynamic multi-objective optimization algorithms in multiple test functions， the results show that the value of Modified Inverted Generational Distance （MIGD） in the whole evolution process is relatively small， and the value of Inverted Generational Distance （IGD） in the evolution is generally smaller than that of the contrast algorithm， and the calculation time is equivalent to that of the comparison algorithm.

Key words: pattern recognition and intelligent system, dynamic multi-objective optimization, evolutionary algorithm, Kalman filter prediction

CLC Number: 

  • TP273

Fig.1

Center point calculation"

Fig.2

Tracking comparison of different centerpoint calculation methods"

Table 1

Comparison of performance evaluation results （1）"

测试

函数

算法MIGD（SD）MIGD
1st stage2nd stage3rd stage
FDA1DNSGA-Ⅱ0.032 4（0.002 7）0.056 80.027 30.009 6
DSS0.008 0（0.000 53）0.011 80.006 90.007 1
KFPS0.007 4（0.000 29）0.008 50.007 40.006 8
DMOP1DNSGA-Ⅱ0.048 8（0.009 8）0.099 60.040 00.029 3
DSS0.025 1（0.007 9）0.069 70.015 30.008 1
KFPS0.013 2（0.002 5）0.012 90.015 50.007 6
DMOP2DNSGA-Ⅱ0.025 1（0.006 1）0.022 90.027 30.020 8
DSS0.013 2（0.000 54）0.010 20.016 00.007 6
KFPS0.012 7（0.000 19）0.007 40.015 60.000 74
DF2DNSGA-Ⅱ0.021 2（0.008 4）0.036 10.017 30.017 0
DSS0.010 1（0.000 67）0.013 20.009 40.009 0
KFPS0.009 9（0.000 66）0.009 50.010 00.009 5
DF3DNSGA-Ⅱ0.025 7（0.006 2）0.173 80.063 00.011 6
DSS0.108 3（0.003 2）0.055 40.020 50.011 2
KFPS0.018 1（0.000 11）0.011 30.021 20.011 4
F5DNSGA-Ⅱ0.311 2（0.023 4）0.611 20.286 60.103 4
DSS0.186 4（0.003 8）0.206 30.198 20.172 9
KFPS0.155 1（0.019 0）0.139 70.184 40.055 2
F6DNSGA-Ⅱ0.536 1（0.219 9）0.872 80.373 80.239 8
DSS0.152 4（0.026 1）0.135 10.145 20.179 5
KFPS0.118 5（0.016 0）0.126 80.134 50.135 4
F7DNSGA-Ⅱ0.374 0（0.519 6）0.319 20.341 60.158 5
DSS0.057 5（0.028 4）0.089 60.050 90.045 9
KFPS0.087 4（0.052 1）0.106 10.088 20.062 8

Table 2

Comparison of performance evaluation results （2）"

测试

函数

算法MIGD（SD）MIGD
1st stage2nd stage3rd stage
FDA1CKPS0.027 6（0.003 60）0.105 10.009 20.009 1
PPS0.052 8（0.009 13）0.240 60.010 20.006 2
KFPS0.008 1（0.000 45）0.008 20.007 50.007 1
DMOP1CKPS0.007 6（0.001 41）0.018 30.005 10.005 1
PPS0.037 9（0.051 52）0.141 30.020 90.005 7
KFPS0.018 9（0.002 5）0.012 70.014 10.014 2
DMOP2CKPS0.027 2（0.006 11）0.102 80.009 40.009 1
PPS0.060 7（0.010 23）0.279 90.011 10.006 1
KFPS0.013 4（0.000 38）0.011 00.014 10.013 8
FDA4CKPS0.021 2（0.001 65）0.138 50.115 90.116 3
PPS0.130 7（0.002 05）0.166 00.124 70.123 1
KFPS0.014 8（0.000 85）0.009 50.014 50.015 0

Table 3

Comparison of performanceevaluation results （3）"

测试函数算法MIGD
FDA1PFMOP0.0227
RLPS0.0137
KFPS0.0125
FDA2PFMOP0.1168
RLPS0.0518
KFPS0.0356
FDA3PFMOP0.2793
RLPS0.2753
KFPS0.5848
FDA4PFMOP0.0244
RLPS0.0228
KFPS0.0121
DMOP1PFMOP0.0088
RLPS0.0049
KFPS0.0158
DMOP2PFMOP0.0920
RLPS0.0693
KFPS0.0194

Fig.3

Pareto front obtained by three algorithms on the test function FDA1"

Fig.4

Pareto front obtained by three algorithms on the test function DMOP1"

Fig.5

Pareto front obtained by three algorithms on the test function DMOP2"

Fig.6

Pareto front obtained by three algorithms on the test function DF2"

Fig.7

Pareto front obtained by three algorithms on the test function DF3"

Fig.8

Pareto front obtained by three algorithms on the test function F5"

Fig.9

Pareto front obtained by three algorithms on the test function F6"

Fig.10

Pareto front obtained by three algorithms on the test function F7"

Fig.11

Pareto front obtained by three algorithms on the test function FDA4"

Fig.12

IGD value obtained by three algorithms on the test function FDA1"

Fig.13

IGD value obtained by three algorithms on the test function DMOP1"

Fig.14

IGD value obtained by three algorithms on the test function DMOP2"

Fig.15

IGD value obtained by three algorithms on the test function DF2"

Fig.16

IGD value obtained by three algorithms on the test function DF3"

Fig.17

IGD value obtained by three algorithms on the test function F5"

Fig.18

IGD value obtained by three algorithms on the test function F6"

Fig.19

IGD value obtained by three algorithms on the test function F7"

Table 4

Average computing time spent by the algorithm to solve different DMOPs"

测试函数DNSGA-ⅡDSSKFPS
FDA1239246258
DMOP1247253259
DMOP2249246255
DF2246279285
DF3254274269
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