research-article

An improved multi-objective population-based extremal optimization algorithm with polynomial mutation

Authors:

Guo-Qiang Zeng,

Chong-Wei ZhengAuthors Info & Claims

Information Sciences—Informatics and Computer Science, Intelligent Systems, Applications: An International Journal, Volume 330, Issue C

Pages 49 - 73

https://doi.org/10.1016/j.ins.2015.10.010

Published: 10 February 2016 Publication History

Abstract

As a recently developed evolutionary algorithm inspired by far-from-equilibrium dynamics of self-organized criticality, extremal optimization (EO) has been successfully applied to a variety of benchmark and engineering optimization problems. However, there are only few reported research works concerning the applications of EO in the field of multi-objective optimization. This paper presents an improved multi-objective population-based EO algorithm with polynomial mutation called IMOPEO-PLM to solve multi-objective optimization problems (MOPs). Unlike the previous multi-objective versions based on EO, the proposed IMOPEO-PLM adopts population-based iterated optimization, a more effective mutation operation called polynomial mutation, and a novel and more effective mechanism of generating new population. From the design perspective of multi-objective evolutionary algorithms (MOEAs), IMOPEO-PLM is relatively simpler than other reported competitive MOEAs due to its fewer adjustable parameters and only mutation operation. Furthermore, the extensive experimental results on some benchmark MOPs show that IMOPEO-PLM performs better than or at least competitive with these reported popular MOEAs, such as MOPEO, MOEO, NSGA-II, A-MOCLPSO, PAES, SPEA, SPEA2, SMS-EMOA, SMPSO, and MOEA/D-DE, by using nonparametric statistical tests, e.g., Kruskal-Wallis test, Mann-Whitney U test, Friedman and Quade tests, in terms of some commonly-used quantitative performance metrics, e.g., convergence, diversity (spread), hypervolume, generational distance, inverted generational distance.

References

[1]

S.F. Adra, P.J. Fleming, Diversity management in evolutionary many-objective optimization, IEEE Trans. Evol. Comput, 15 (2011) 183-195.

Digital Library

[2]

H. Ali, F.A. Khan, Attributed multi-objective comprehensive learning particle swarm optimization for optimal security of networks, Appl. Soft Comput, 13 (2013) 3903-3921.

Digital Library

[3]

P. Bak, K. Sneppen, Punctuated equilibrium and criticality in a simple model of evolution, Phys. Rev. Lett., 71 (1993) 4083-4086.

[4]

N. Beume, B. Naujoks, M. Emmerich, SMS-EMOA: multiobjective selection based on dominated hypervolume, Eur. J. Oper. Res., 181 (2007) 1653-1669.

[5]

S. Boettcher, Extremal optimization: heuristics via coevolutionary avalanches, Comput. Sci. Eng., 2 (2000) 75-82.

Digital Library

[6]

S. Boettcher, A.G. Percus, Nature's way of optimizing, Artif. Intell., 119 (2000) 275-286.

Digital Library

[7]

S. Boettcher, A.G. Percus, Optimization with extremal dynamics, Phys. Rev. Lett., 86 (2001) 5211-5214.

[8]

S. Boettcher, A.G. Percus, Extremal optimization for graph partitioning, Phys. Rev. E, 69 (2004).

[9]

S. Boettcher, A.G. Percus, Extremal optimization at the phase transition for the three-coloring problem, Phys. Rev. E, 69 (2004).

[10]

S. Boettcher, Evolutionary dynamics of extremal optimization, Lect. Notes Comput. Sci., 5581 (2009) 1-14.

[11]

P. Bosman, D. Thierens, The balance between proximity and diversity in multiobjective evolutionary algorithms, IEEE Trans. Evol. Comput., 7 (2003) 174-188.

Digital Library

[12]

X. Cai, Y. Li, Z. Fan, Q. Zhang, An external archive guided multiobjective evolutionary algorithm based on decomposition for combinatorial optimization, IEEE Trans. Evol. Comput, 19 (2015) 508-523.

[13]

M.R. Chen, Y.Z. Lu, A novel elitist multiobjective optimization algorithm: multiobjective extremal optimization, Eur. J. Oper. Res., 188 (2008) 637-651.

[14]

M.R. Chen, Y.Z. Lu, G.K. Yang, Multiobjective optimization using population-based extremal optimization, Neural Comput. Appl., 17 (2008) 101-109.

Digital Library

[15]

M.R. Chen, X. Li, X. Zhang, Y.Z. Lu, A novel particle swarm optimizer hybridized with extremal optimization, Appl. Soft Comput., 10 (2010) 367-373.

Digital Library

[16]

Y.W. Chen, Y.Z. Lu, P. Chen, Optimization with extremal dynamics for the travelling salesman problem, Physica A, 385 (2007) 115-123.

[17]

Y.W. Chen, Y.Z. Lu, G.K. Yang, Hybrid evolutionary algorithm with marriage of genetic algorithm and extremal optimization for production scheduling, Int. J. Adv. Manuf. Technol., 36 (2008) 959-968.

[18]

C.A.C. Coello, G.T. Pulido, M.S. Leehuga, Handling multiple objectives with particle swarm optimization, IEEE Trans. Evol. Comput., 8 (2004) 256-279.

Digital Library

[19]

C.A.C. Coello, Evolutionary multiobjective optimization: a historical view of the field, IEEE Comput. Intell. Mag., 1 (2006) 28-36.

Digital Library

[20]

C.A.C. Coello, G. Lamont, D. Van Veldhuizen, Evolutionary Algorithms for Solving Multiobjective Problems, Springer, New York, 2007.

[21]

K. Deb, M. Goyal, A combined genetic adaptive search (GeneAS) for engineering design, Comput. Sci. Inf., 26 (1996) 30-45.

[22]

K. Deb, Multiobjective Optimization Using Evolutionary Algorithms, Wiley, New York, 2001.

[23]

K. Deb, A. Pratab, S. Agrawal, T. Meyarivan, A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE Trans. Evol. Comput., 6 (2002) 182-197.

Digital Library

[24]

K. Deb, M. Mohan, S. Mishra, Towards a quick computation of well-spread Pareto-optimal solutions, evolutionary multi-criterion optimization (EMO 2003), LNCS, 2632 (2003) 222-236.

[25]

J. Derrac, S. García, D. Molina, F. Herrera, A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms, Swarm Evol. Comput., 1 (2011) 3-18.

[26]

J. Ding, Y.Z. Lu, J. Chu, Extremal optimization for unit commitment problem for power systems, in: IEEE Power and Energy Society General Meeting, 2012, pp. 1-8.

[27]

J. Duch, A. Arenas, Community detection in complex networks using extremal optimization, Phys. Rev. E, 72 (2005).

[28]

S. García, D. Molina, M. Lozano, F. Herrera, A study on the use of non-parametric tests for analyzing the evolutionary algorithms' behaviour: a case study on the CEC'2005 special session on real parameter optimization, J. Heuristics, 15 (2009) 617-644.

Digital Library

[29]

S.B. Gee, K.C. Tan, V.A. Shim, N.R. Pal, Online diversity assessment in evolutionary multiobjective optimization: a geometrical perspective, IEEE Trans. Evol. Comput., 19 (2015) 542-559.

[30]

I. Giagkiozis, R.C. Purshouse, P.J. Fleming, Generalized decomposition and cross entropy methods for many-objective optimization, Inf. Sci., 282 (2014) 363-387.

Digital Library

[31]

S. Huband, P. Hingston, L. Barone, L. While, A review of multiobjective test problems and a scalable test problem toolkit, IEEE Trans. Evol. Comput., 10 (2006) 477-496.

Digital Library

[32]

C. Janikow, Z. Michalewicz, Experimental comparison of binary and floating point representations in genetic algorithms, in: Proceedings of the Fourth International Conference of Genetic Algorithms, 1991, pp. 151-157.

[33]

S.W. Jiang, Y.S. Ong, J. Zhang, L. Feng, Consistencies and contradictions of performance metrics in multiobjective optimization, IEEE Trans. Cybern., 44 (2014) 2391-2404.

[34]

S.W. Jiang, J. Zhang, Y.S. Ong, Multiobjective optimization based on reputation, Inf. Sci., 286 (2014) 125-146.

Digital Library

[35]

H. Kim, M.S. Liou, Adaptive directional local search strategy for hybrid evolutionary multiobjective optimization, Appl. Soft Comput., 19 (2014) 290-311.

[36]

J. Knowles, D. Corne, The Pareto archived evolution strategy: a new baseline algorithm for multiobjective optimization, in: Proceedings of the 1999 Congress on Evolutionary Computation, IEEE Press, Piscataway, NJ, 1999, pp. 98-105.

[37]

M. Laumanns, L. Thiele, K. Deb, E. Zitzler, Combining convergence and diversity in evolutionary multi-objective optimization, Evol. Comput., 10 (2002) 263-282.

Digital Library

[38]

H. Li, Q.F. Zhang, Multiobjective optimization problems with complicated Pareto sets, MOEA/D and NSGA-II, IEEE Trans. Evol. Comput., 13 (2009) 284-302.

Digital Library

[39]

K. Li, S. Kwong, J.J. Cao, M.Q. Li, J.H. Zheng, R.M. Shen, Achieving balance between proximity and diversity in multi-objective evolutionary algorithm, Inf. Sci., 182 (2012) 220-242.

Digital Library

[40]

K. Li, S. Kwong, K. Deb, A dual-population paradigm for evolutionary multiobjective optimization, Inf. Sci., 309 (2015) 50-72.

Digital Library

[41]

X. Li, J. Luo, M.R. Chen, N. Wang, An improved shuffled frog-leaping algorithm with extremal optimization for continuous optimization, Inf. Sci., 192 (2012) 143-151.

Digital Library

[42]

Y.Z. Lu, M.R. Chen, Y.W. Chen, Studies on extremal optimization and its applications in solving real world optimization problems, in: Proceedings of the 2007 IEEE Symposium on Foundations of Computational Intelligence, 2007, pp. 162-168.

[43]

M.B. Menaï, M. Batouche, An effective heuristic algorithm for the maximum satisfiability problem, Appl. Intell., 24 (2006) 227-239.

Digital Library

[44]

M. Mernik, S.H. Liu, D. Karaboga, M. ¿repinšek, On clarifying misconceptions when comparing variants of the Artificial Bee Colony Algorithm by offering a new implementation, Inf. Sci., 291 (2015) 115-127.

Digital Library

[45]

P.G. Menese, M. Randall, A. Lewis, A hybrid multi-objective extremal optimization approach for multi-objective combinatorial optimization problems, in: Proceedings of IEEE Congress on Evolutionary Computation (CEC), 2010, pp. 1-8.

[46]

A.A. Montano, C.A.C. Coello, E.M. Montes, Multiobjective evolutionary algorithms in aeronautical and aerospace engineering, IEEE Trans. Evol. Comput., 16 (2012) 662-694.

Digital Library

[47]

A. Mukhopadhyay, U. Maulik, S. Bandyopadhyay, C.A.C. Coello, A survey of multiobjective evolutionary algorithms for data mining: part I, IEEE Trans. Evol. Comput., 18 (2014) 4-19.

[48]

A. Mukhopadhyay, U. Maulik, S. Bandyopadhyay, C.A.C. Coello, A survey of multiobjective evolutionary algorithms for data mining: part II, IEEE Trans. Evol. Comput., 18 (2014) 20-35.

[49]

A.J. Nebro, J.J. Durillo, J. García-Nieto, C.A.C. Coello, F. Luna, E. Alba, SMPSO: a new PSO-based metaheuristic for multi-objective optimization, in: MCDM, 2009, pp. 66-73.

[50]

Q. Qin, S. Cheng, Q. Zhang, Y. Wei, Y. Shi, Multiple strategies based orthogonal design particle swarm optimizer for numerical optimization, Comput. Oper. Res., 60 (2015) 91-110.

Digital Library

[51]

R.G. Regis, Evolutionary programming for high-dimensional constrained expensive black-box optimization using radial basis functions, IEEE Trans. Evol. Comput., 18 (2014) 326-347.

[52]

A.A. Rodriguez, G. Ault, S. Galloway, Multi-objective planning of distributed energy resources: a review of the state-of-the-art, Renewable Sustainable Energy Rev., 14 (2010) 1353-1366.

[53]

A. Rubio-Largo, Q.F. Zhang, M.A. Vega-Rodr¿guez, A multiobjective evolutionary algorithm based on decomposition with normal boundary intersection for traffic grooming in optical networks, Inf. Sci., 289 (2014) 91-116.

[54]

A.K. Salman, Application of extremal optimization algorithm to multi-objective topology design of enterprise networks, in: 2013 International Conference on Computer, Control, Informatics, and Its Applications (IC3INA), 2013, pp. 135-140.

[55]

F.L. Sousa, V. Vlassov, F.M. Ramos, Heat pipe design through generalized extremal optimization, Heat Transfer Eng., 25 (2004) 34-45.

[56]

P.H. Tang, M.H. Tseng, Adaptive directed mutation for real-coded genetic algorithms, Appl. Soft Comput., 13 (2013) 600-614.

Digital Library

[57]

T. Tusar, B. Filipic, Visualization of Pareto front approximations in evolutionary multiobjective optimization: a critical review and the prosection method, IEEE Trans. Evol. Comput., 19 (2015) 225-245.

[58]

J. Wang, Y. Cai, Multiobjective evolutionary algorithm for frequency assignment problem in satellite communications, Soft Comput., 19 (2015) 1229-1253.

Digital Library

[59]

J.H. Wang, Y. Zhou, Y. Wang, J. Zhang, C.L. Chen, Z. Zheng, Multiobjective vehicle routing problems with simultaneous delivery and pickup and time windows: formulation, instances, and algorithms, IEEE Trans Cybern. (2015).

[60]

R. Wang, P.J. Fleming, R.C. Purshouse, General framework for localised multi-objective evolutionary algorithms, Inf. Sci., 258 (2014) 29-53.

Digital Library

[61]

G.Q. Zeng, Y.Z. Lu, Survey on computational complexity with phase transitions and extremal optimization, in: Proceedings of the 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, 2009, pp. 4352-4359.

[62]

G.Q. Zeng, Y.Z. Lu, W.J. Mao, Multistage extremal optimization for hard travelling salesman problem, Physica A, 389 (2010) 5037-5044.

[63]

G.Q. Zeng, Y.Z. Lu, W.J. Mao, Modified extremal optimization for the maximum satisfiability problem, J. Zhejiang Univ.-Sci. C (Comput. & Electron.), 12 (2011) 589-596.

[64]

S.Z. Zhao, M.W. Iruthayarajan, S. Baskar, P.N. Suganthan, Multi-objective robust PID controller tuning using two lbests multi-objective particle swarm optimization, Inf. Sci., 18 (2011) 3323-3335.

Digital Library

[65]

E. Zitzler, L. Thiele, Multiobjective optimization using evolutionary algorithms-A comparative case study, in: Proceedings the Seventh International Conference on Parallel Problem Solving From Nature, PPSN-V, Springer, Berlin, 1998.

[66]

E. Zitzler, M. Laumanns, L. Thiele, SPEA2: improving the performance of the Strength Pareto Evolutionary Algorithm, Technical report 103, Computer Engineering and Communication Networks Lab (TIK), Swiss Federal Institute of Technology (ETH) Zurich, Zurich, May 2001.

Cited By

Cao JYan ZChen ZZhang J(2024)A coevolutionary constrained multi-objective algorithm with a learning constraint boundaryApplied Soft Computing10.1016/j.asoc.2023.110845148:COnline publication date: 27-Feb-2024
https://dl.acm.org/doi/10.1016/j.asoc.2023.110845
Osaba EDiaz-De-Arcaya JAlonso JLobo JBenguria GEtxaniz I(2023)Multiobjective Optimization Analysis for Finding Infrastructure-as-Code Deployment ConfigurationsProceedings of the 2023 11th International Conference on Computer and Communications Management10.1145/3617733.3617777(26-31)Online publication date: 4-Aug-2023
https://dl.acm.org/doi/10.1145/3617733.3617777
Bo YGu F(2022)Dual-Population Co-Evolution Multi-Objective Optimization Algorithm and Its ApplicationInternational Journal of Cognitive Informatics and Natural Intelligence10.4018/IJCINI.29625816:1(1-21)Online publication date: 14-Jun-2022
https://dl.acm.org/doi/10.4018/IJCINI.296258
Show More Cited By

An improved multi-objective population-based extremal optimization algorithm with polynomial mutation
1. Information systems
  1. Data management systems
    1. Database administration
2. Theory of computation
  1. Design and analysis of algorithms

Recommendations

A novel real-coded population-based extremal optimization algorithm with polynomial mutation

As a recently developed optimization method inspired by far-from-equilibrium dynamics of self-organized criticality, extremal optimization (EO) has been successfully applied to a variety of combinatorial optimization problems while its applications in ...
A new multi-objective evolutionary algorithm based on a performance assessment indicator
GECCO '12: Proceedings of the 14th annual conference on Genetic and evolutionary computation

An emerging trend in the design of multi-objective evolutionary algorithms (MOEAs) is to select individuals through the optimization of a quality assessment indicator. However, the most commonly adopted indicator in current use is the hypervolume which ...
Multiobjective optimization using population-based extremal optimization

In recent years, a general-purpose local-search heuristic method called Extremal Optimization (EO) has been successfully applied in some NP-hard combinatorial optimization problems. In this paper, we present a novel Pareto-based algorithm, which can be ...

Comments

Information & Contributors

Information

Published In

cover image Information Sciences: an International Journal

Information Sciences: an International Journal Volume 330, Issue C

February 2016

510 pages

ISSN:0020-0255

Issue’s Table of Contents

Copyright © Elsevier Inc.

Publisher

Elsevier Science Inc.

United States

Publication History

Published: 10 February 2016

Author Tags

Qualifiers

Research-article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

19
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 25 Dec 2024

Other Metrics

View Author Metrics

Citations

Cited By

Cao JYan ZChen ZZhang J(2024)A coevolutionary constrained multi-objective algorithm with a learning constraint boundaryApplied Soft Computing10.1016/j.asoc.2023.110845148:COnline publication date: 27-Feb-2024
https://dl.acm.org/doi/10.1016/j.asoc.2023.110845
Osaba EDiaz-De-Arcaya JAlonso JLobo JBenguria GEtxaniz I(2023)Multiobjective Optimization Analysis for Finding Infrastructure-as-Code Deployment ConfigurationsProceedings of the 2023 11th International Conference on Computer and Communications Management10.1145/3617733.3617777(26-31)Online publication date: 4-Aug-2023
https://dl.acm.org/doi/10.1145/3617733.3617777
Bo YGu F(2022)Dual-Population Co-Evolution Multi-Objective Optimization Algorithm and Its ApplicationInternational Journal of Cognitive Informatics and Natural Intelligence10.4018/IJCINI.29625816:1(1-21)Online publication date: 14-Jun-2022
https://dl.acm.org/doi/10.4018/IJCINI.296258
Wang ZGong MLi PGu JTian W(2022)A hypervolume distribution entropy guided computation resource allocation mechanism for the multiobjective evolutionary algorithm based on decompositionApplied Soft Computing10.1016/j.asoc.2021.108297116:COnline publication date: 1-Feb-2022
https://dl.acm.org/doi/10.1016/j.asoc.2021.108297
Cao JYan ZChen ZZhang J(2022)A Pareto front estimation-based constrained multi-objective evolutionary algorithmApplied Intelligence10.1007/s10489-022-03990-753:9(10380-10416)Online publication date: 18-Aug-2022
https://dl.acm.org/doi/10.1007/s10489-022-03990-7
Elsisi M(2022)Improved grey wolf optimizer based on opposition and quasi learning approaches for optimization: case study autonomous vehicle including vision systemArtificial Intelligence Review10.1007/s10462-022-10137-055:7(5597-5620)Online publication date: 1-Oct-2022
https://dl.acm.org/doi/10.1007/s10462-022-10137-0
Zhao SWang PHeidari AZhao XMa CChen H(2022)An enhanced Cauchy mutation grasshopper optimization with trigonometric substitution: engineering design and feature selectionEngineering with Computers10.1007/s00366-021-01448-x38:Suppl 5(4583-4616)Online publication date: 1-Dec-2022
https://dl.acm.org/doi/10.1007/s00366-021-01448-x
Dong RChen HHeidari ATurabieh HMafarja MWang S(2021)Boosted kernel searchKnowledge-Based Systems10.1016/j.knosys.2021.107529233:COnline publication date: 5-Dec-2021
https://dl.acm.org/doi/10.1016/j.knosys.2021.107529
Wu XWang SPan YShao H(2021)A knee point-driven multi-objective artificial flora optimization algorithmWireless Networks10.1007/s11276-019-02228-827:5(3573-3583)Online publication date: 1-Jul-2021
https://dl.acm.org/doi/10.1007/s11276-019-02228-8
Chen JXu YSun WHuang L(2021)Joint sparse neural network compression via multi-application multi-objective optimizationApplied Intelligence10.1007/s10489-021-02243-351:11(7837-7854)Online publication date: 1-Nov-2021
https://dl.acm.org/doi/10.1007/s10489-021-02243-3
Show More Cited By

View Options

View options

Media

Figures

Other

Tables

View Issue’s Table of Contents