doi: 10.3934/jimo.2022001
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A multi-objective lion swarm optimization based on multi-agent

Key Lab of Industrial Computer Control Engineering of Hebei Province, Yanshan University, Qinhuangdao, Hebei, 066004, China

*Corresponding author: Zhongqiang Wu

Received  September 2020 Revised  August 2021 Early access January 2022

Fund Project: The first author is supported by the Natural Science Foundation of Hebei Province under Grant F2020203014

This paper proposes a multi-objective lion swarm optimization based on multi-agent (MOMALSO) for solving the increasingly complex multi-objective optimization problem in engineering practice. First, the Multi-agent system is introduced into the lion swarm optimization (LSO) algorithm. The optimization mechanism of LSO and the information exchange between the agents are integrated to enhance the local search and global search ability of the algorithm, and the self-learning operation can accelerate the approximate Pareto front obtained by the algorithm near to real front. Besides, the external archive is introduced for extending the LSO into a multi-objective algorithm. Finally, the simulations compared with other three algorithms are performed, and the results show that MOMALSO has significant advantages in both convergence and coverage, which verifies the superiority and effectiveness of the algorithm in multi-objective optimization.

Citation: Zhongqiang Wu, Zongkui Xie. A multi-objective lion swarm optimization based on multi-agent. Journal of Industrial and Management Optimization, doi: 10.3934/jimo.2022001
References:
[1]

R. AkbariR. AkbariK. Ziarati and B. Hassanizadeh, A multi-objective artificial bee colony algorithm, Swarm and Evolutionary Computation, 2 (2012), 39-52.  doi: 10.1016/j.swevo.2011.08.001.

[2]

D. W. CorneN. R. JerramJ. D. Knowles and M. J. Oates, PESA-Ⅱ: Region-based selection in evolutionary multi-objective optimization, Conference on Genetic and Evolutionary Computation, (2001). 

[3]

K. DebA. PratapS. Agarwal and T. Meyarivan, A fast and elitist multi-objective genetic algorithm: NSGA-Ⅱ, IEEE Transactions on Evolutionary Computation, 6 (2002), 182-197.  doi: 10.1109/4235.996017.

[4]

J. D. Knowles and D. W. Corne, Approximating the non-dominated front using the pareto archived evolution strategy, Evolutionary Computation, 8 (2000), 149-172. 

[5]

S. LiuY. Yan and Y. Zhou, A binary lions warm algorithm for solving 0-1 knapsack problem, Computer Engineering and Science, 41 (2019), 2079-2087.  doi: 10.3969/j.issn.1007-130X.2019.11.024.

[6]

S. J. LiuY. Yan and Y. Q. Zhou, A swarm intelligence algorithm-lion swarm optimization, Pattern Recognition and Artificial Intelligence, 31 (2018), 431-441.  doi: 10.16451/j.cnki.issn1003-6059.201805005.

[7]

S. MirjaliliS. Saremi and S. M. Mirjalili, Multi-objective grey wolf optimizer: A novel algorithm for multi-criterion optimization, Expert Systems with Applications, 47 (2016), 106-119.  doi: 10.1016/j.eswa.2015.10.039.

[8]

S. MirjaliliP. Jangir and S. Saremi, Multi-objective ant lion optimizer: a multi-objective optimization algorithm for solving engineering problems, Applied Intelligence, 46 (2017), 79-95.  doi: 10.1007/s10489-016-0825-8.

[9]

S. MirjaliliP. JangirS. Z. MirjaliliS. Saremi and I.N. Trivedi, Optimization of problems with multiple objectives using the multi-verse optimization algorithm, Knowledge-Based Systems, 134 (2017), 50-71.  doi: 10.1016/j.knosys.2017.07.018.

[10]

N. Srinivas and K. Deb, Multiobjective optimization using non-dominated sorting in genetic algorithms, Evolutionary Computation, 2 (1994), 221-248. 

[11]

Y. Wu and P. Zhang, Common-Mode (CM) Current Sensor Node Design for Distribution Grid Insulation Monitoring Framework Based on Multi-Objective Optimization, IEEE Transactions on Industrial Informatics, 17 (2021), 3836-3846.  doi: 10.1109/TII.2020.3014995.

[12]

Z. WuZ. Xie and C. Liu, An improved lion swarm optimization for parameters identification of photovoltaic cell models, Transactions of the Institute of Measurement and Control, 42 (2020), 1191-1203.  doi: 10.1177/0142331219887844.

[13]

C. XieF. ZhangJ. LuC. Xiao and G. Long, Multi-objective firefly algorithm based on multiply cooperative strategies, Acta Electronica Sinica, 47 (2019), 2359-2367.  doi: 10.3969/j.issn.0372-2112.2019.11.018.

[14]

J. YangX. HouH. CuiZ. Hu and X. Mu, Improved multi-objectiive particle swarm optimzation algorithm based on integrating multiply strategies, Control and Decision, 33 (2018), 226-234.  doi: 10.13195/j.kzyjc.2016.1451.

[15]

B. Zhao and Y. Cao, A Multi-agent particle swarm optimization algorithm, Proceedings of the CSEE, 25 (2005), 3-9. 

[16]

Q. Zhang, A. Zhou and S. Zhao, Multi-objective optimization test instances for the CEC 2009 special session and competition, Essex: University of Essex, 2008.

[17]

A. ZhouQ. Zhang and G. Zhang, Multi-objective evolutionary algorithm based on mixture Gaussian models, Journal of Software, 25 (2014), 913-928.  doi: 10.13328/j.cnki.jos.004514.

[18]

E. Zitzler and L. Thiele, Multi-objective evolutionary algorithms: A comparative case study and the strength Pareto approach, IEEE Transactions on Evolutionary Computation, 3 (1999), 257-271. 

[19]

E. ZitzlerM. Laumanns and L. Thiele, SPEA2: Improving the strength pareto evolutionary algorithm, Evolutionary Methods for Design, Optimization and Control with Applications to Industrial Problems, (2002), 95-100. 

show all references

References:
[1]

R. AkbariR. AkbariK. Ziarati and B. Hassanizadeh, A multi-objective artificial bee colony algorithm, Swarm and Evolutionary Computation, 2 (2012), 39-52.  doi: 10.1016/j.swevo.2011.08.001.

[2]

D. W. CorneN. R. JerramJ. D. Knowles and M. J. Oates, PESA-Ⅱ: Region-based selection in evolutionary multi-objective optimization, Conference on Genetic and Evolutionary Computation, (2001). 

[3]

K. DebA. PratapS. Agarwal and T. Meyarivan, A fast and elitist multi-objective genetic algorithm: NSGA-Ⅱ, IEEE Transactions on Evolutionary Computation, 6 (2002), 182-197.  doi: 10.1109/4235.996017.

[4]

J. D. Knowles and D. W. Corne, Approximating the non-dominated front using the pareto archived evolution strategy, Evolutionary Computation, 8 (2000), 149-172. 

[5]

S. LiuY. Yan and Y. Zhou, A binary lions warm algorithm for solving 0-1 knapsack problem, Computer Engineering and Science, 41 (2019), 2079-2087.  doi: 10.3969/j.issn.1007-130X.2019.11.024.

[6]

S. J. LiuY. Yan and Y. Q. Zhou, A swarm intelligence algorithm-lion swarm optimization, Pattern Recognition and Artificial Intelligence, 31 (2018), 431-441.  doi: 10.16451/j.cnki.issn1003-6059.201805005.

[7]

S. MirjaliliS. Saremi and S. M. Mirjalili, Multi-objective grey wolf optimizer: A novel algorithm for multi-criterion optimization, Expert Systems with Applications, 47 (2016), 106-119.  doi: 10.1016/j.eswa.2015.10.039.

[8]

S. MirjaliliP. Jangir and S. Saremi, Multi-objective ant lion optimizer: a multi-objective optimization algorithm for solving engineering problems, Applied Intelligence, 46 (2017), 79-95.  doi: 10.1007/s10489-016-0825-8.

[9]

S. MirjaliliP. JangirS. Z. MirjaliliS. Saremi and I.N. Trivedi, Optimization of problems with multiple objectives using the multi-verse optimization algorithm, Knowledge-Based Systems, 134 (2017), 50-71.  doi: 10.1016/j.knosys.2017.07.018.

[10]

N. Srinivas and K. Deb, Multiobjective optimization using non-dominated sorting in genetic algorithms, Evolutionary Computation, 2 (1994), 221-248. 

[11]

Y. Wu and P. Zhang, Common-Mode (CM) Current Sensor Node Design for Distribution Grid Insulation Monitoring Framework Based on Multi-Objective Optimization, IEEE Transactions on Industrial Informatics, 17 (2021), 3836-3846.  doi: 10.1109/TII.2020.3014995.

[12]

Z. WuZ. Xie and C. Liu, An improved lion swarm optimization for parameters identification of photovoltaic cell models, Transactions of the Institute of Measurement and Control, 42 (2020), 1191-1203.  doi: 10.1177/0142331219887844.

[13]

C. XieF. ZhangJ. LuC. Xiao and G. Long, Multi-objective firefly algorithm based on multiply cooperative strategies, Acta Electronica Sinica, 47 (2019), 2359-2367.  doi: 10.3969/j.issn.0372-2112.2019.11.018.

[14]

J. YangX. HouH. CuiZ. Hu and X. Mu, Improved multi-objectiive particle swarm optimzation algorithm based on integrating multiply strategies, Control and Decision, 33 (2018), 226-234.  doi: 10.13195/j.kzyjc.2016.1451.

[15]

B. Zhao and Y. Cao, A Multi-agent particle swarm optimization algorithm, Proceedings of the CSEE, 25 (2005), 3-9. 

[16]

Q. Zhang, A. Zhou and S. Zhao, Multi-objective optimization test instances for the CEC 2009 special session and competition, Essex: University of Essex, 2008.

[17]

A. ZhouQ. Zhang and G. Zhang, Multi-objective evolutionary algorithm based on mixture Gaussian models, Journal of Software, 25 (2014), 913-928.  doi: 10.13328/j.cnki.jos.004514.

[18]

E. Zitzler and L. Thiele, Multi-objective evolutionary algorithms: A comparative case study and the strength Pareto approach, IEEE Transactions on Evolutionary Computation, 3 (1999), 257-271. 

[19]

E. ZitzlerM. Laumanns and L. Thiele, SPEA2: Improving the strength pareto evolutionary algorithm, Evolutionary Methods for Design, Optimization and Control with Applications to Industrial Problems, (2002), 95-100. 

Figure 1.  The topology structure of the MAS
Figure 2.  Flow chart of update and maintenance of external archives
Figure 3.  Obtained Pareto optimal solutions by 4 algorithms
Figure 4.  IGD convergence curves of four algorithms
Table 1.  Statistical results for IGD on UF1-UF10
Fun. MOMALSO MOGWO MOALO MOMVO
Avg. Std. Avg. Std. Avg. Std. Avg. Std.
UF1 5.94e-3 2.02e-4 1.38e-2 1.27e-3 1.97e-2 2.50e-3 1.29e-2 1.24e-3
UF2 7.14e-3 1.01e-3 9.26e-3 5.47e-4 2.03e-2 2.79e-3 9.70e-3 1.32e-3
UF3 1.88e-2 2.10e-3 3.33e-2 1.16e-3 3.86e-2 4.84e-3 4.89e-2 5.28e-3
UF4 5.16e-3 3.07e-4 7.45e-3 5.92e-4 8.81e-3 3.45e-4 1.03e-2 1.54e-4
UF5 1.53e-1 4.26e-2 1.71e-1 3.35e-2 3.12e-1 2.76e-2 2.13e-1 4.86e-2
UF6 3.65e-2 1.41e-3 3.64e-2 4.92e-4 7.87e-2 8.99e-3 4.17e-2 6.37e-3
UF7 5.53e-3 2.78e-3 1.09e-2 3.34e-2 2.82e-2 4.12e-3 4.57e-2 2.02e-2
UF8 3.29e-2 4.64e-3 3.67e-2 1.18e-2 8.59e-2 2.46e-2 6.17e-2 1.30e-2
UF9 2.69e-2 4.64e-3 2.54e-2 3.16e-3 8.65e-2 1.04e-2 3.93e-2 2.72e-3
UF10 2.67e-2 1.01e-2 7.49e-2 3.01e-2 4.21e-1 4.44e-2 1.21e-1 6.33e-2
Fun. MOMALSO MOGWO MOALO MOMVO
Avg. Std. Avg. Std. Avg. Std. Avg. Std.
UF1 5.94e-3 2.02e-4 1.38e-2 1.27e-3 1.97e-2 2.50e-3 1.29e-2 1.24e-3
UF2 7.14e-3 1.01e-3 9.26e-3 5.47e-4 2.03e-2 2.79e-3 9.70e-3 1.32e-3
UF3 1.88e-2 2.10e-3 3.33e-2 1.16e-3 3.86e-2 4.84e-3 4.89e-2 5.28e-3
UF4 5.16e-3 3.07e-4 7.45e-3 5.92e-4 8.81e-3 3.45e-4 1.03e-2 1.54e-4
UF5 1.53e-1 4.26e-2 1.71e-1 3.35e-2 3.12e-1 2.76e-2 2.13e-1 4.86e-2
UF6 3.65e-2 1.41e-3 3.64e-2 4.92e-4 7.87e-2 8.99e-3 4.17e-2 6.37e-3
UF7 5.53e-3 2.78e-3 1.09e-2 3.34e-2 2.82e-2 4.12e-3 4.57e-2 2.02e-2
UF8 3.29e-2 4.64e-3 3.67e-2 1.18e-2 8.59e-2 2.46e-2 6.17e-2 1.30e-2
UF9 2.69e-2 4.64e-3 2.54e-2 3.16e-3 8.65e-2 1.04e-2 3.93e-2 2.72e-3
UF10 2.67e-2 1.01e-2 7.49e-2 3.01e-2 4.21e-1 4.44e-2 1.21e-1 6.33e-2
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