A Hybrid Evolutionary Immune Algorithm for Multiobjective

Optimization Problems

IEEE Transactions on Evolutionary Computation

Qiuzhen Lin¹    Jianyong Chen¹    Zhi-Hui Zhan²    Wei-Neng Chen²    Carlos A. Coello Coello³    Yilong Yin⁴    Chih-Min Lin⁵    Jun Zhang²

¹Shenzhen University    ²South China University of Technology    

³Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional 

⁴Shandong University    ⁵Yuan Ze University

Abstract

In recent years, multiobjective immune algorithms (MOIAs) have shown promising performance in solving multiobjective optimization problems (MOPs). However, basic MOIAs only use a single hypermutation operation to evolve individuals, which may induce some difficulties in tackling complicated MOPs. In this paper, we propose a novel hybrid evolutionary framework for MOIAs, in which the cloned individuals are divided into several subpopulations and then evolved using different evolutionary strategies. An example of this hybrid framework is implemented, in which simulated binary crossover and differential evolution with polynomial mutation are adopted. A fine-grained selection mechanism and a novel elitism sharing strategy are also adopted for performance enhancement. Various comparative experiments are conducted on 28 test MOPs and our empirical results validate the effectiveness and competitiveness of our proposed algorithm in solving MOPs of different types.

Fig. 1. Proposed framework of HEIA.

Fig. 2. Nondominated solution sets found by HEIA and MOEA/D on the ZDT problems. (a) ZDT1–HEIA. (b) ZDT2–HEIA. (c) ZDT3–HEIA. (d) ZDT4–HEIA. (e) ZDT6–HEIA. (f) ZDT1–MOEA/D. (g) ZDT2–MOEA/D. (h) ZDT3–MOEA/D. (i) ZDT4–MOEA/D. (j) ZDT6–MOEA/D.

Fig. 3. Nondominated solution sets found by all the algorithms on WFG1. (a) WFG1–HEIA. (b) WFG1–MOEA/D. (c) WFG1–SMPSO. (d) WFG1–NSGA-II. (e) WFG1–SPEA2. (f) WFG1–AbYSS.

Fig. 4. Nondominated solution sets found by HEIA and SMPSO on UF1 and UF2. (a) UF1–HEIA. (b) UF1–SMPSO. (c) UF2–HEIA. (d) UF2–SMPSO

Fig. 5. Nondominated solution sets found by HEIA, NSGA-II, and SPEA2 on DTLZ3. (a) HEIA. (b) NSGA-II. (c) SPEA2

Fig. 6. Box plots of the IGD results obtained by HEIA with different NA values on (a) ZDT1, (b) WFG1, and (c) UF1

Fig. 7. Box plots of the IGD results obtained by HEIA with different δ values on (a) ZDT1, (b) WFG1, and (c) UF1

Fig. 8. Box plots of the IGD results obtained by HEIA with different CR values on (a) ZDT1, (b) WFG1, and (c) UF1

Fig. 9. Box plots of the IGD results obtained by HEIA with different F values on (a) ZDT1, (b) WFG1, and (c) UF1.

Fig. 10. Mean computational times (s) obtained by NSGA-II, SPEA2, and HEIA on (a) ZDT1, (b) ZDT2, (c) ZDT3, (d) ZDT4, and (e) ZDT6.

Acknowledgements

This work was supported in part by the National Nature Science Foundation of China (NSFC) under Grant 61402291, Grant 61402545, and Grant 61379061; in part by the National High-Technology Research and Development Program (“863” Program) of China under Grant 2013AA01A212; in part by the NSFC Joint Fund with Guangdong under Key Project U1201258; and in part by the Consejo Nacional de Ciencia y Tecnología under Grant 221551.

Bibtex

@ARTICLE{ 7368156,

author={Lin, Qiuzhen and Chen, Jianyong and Zhan, Zhi-Hui and Chen, Wei-Neng and Coello, Carlos A. Coello and Yin, Yilong and Lin, Chih-Min and Zhang, Jun},

journal={IEEE Transactions on Evolutionary Computation},

title={A Hybrid Evolutionary Immune Algorithm for Multiobjective Optimization Problems},

year={2016},

}

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