Nonlinear equation systems (NESs) usually have more than one optimal solution. However, locating all the optimal solutions in a single run, is one of the most challenging issues for evolutionary optimization. In this paper, we address this issue by transforming all the optimal solutions of an NES to the nondominated solutions of a constructed multiobjective optimization problem (MOP). In the general case, we prove that the proposed transformation fully matches the requirement of multiobjective optimization. That is, the multiple objectives always conflict with each other. In this way, multiobjective optimization techniques can be used to locate these multiple optimal solutions simultaneously as they locate the nondominated solutions of the MOPs. Our proposed approach is evaluated on 22 NESs with different features, such as linear and nonlinear equations, different numbers of optimal solutions, and infinite optimal solutions. Experimental results reveal that the proposed approach is highly competitive with some other state-of-the-art algorithms for NES.
|Title of host publication||Evolutionary Multi-Criterion Optimization - 10th International Conference, EMO 2019, Proceedings|
|Editors||Carlos A. Coello Coello, Sanaz Mostaghim, Kalyanmoy Deb, Erik Goodman, Kathrin Klamroth, Patrick Reed, Kaisa Miettinen|
|Publisher||Springer-Verlag GmbH and Co. KG|
|Number of pages||12|
|Publication status||Published - Feb 2019|
|Event||10th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2019 - East Lansing, United States|
Duration: 10 Mar 2019 → 13 Mar 2019
|Name||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Conference||10th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2019|
|Period||10/03/19 → 13/03/19|
Bibliographical noteFunding Information:
Acknowledgement. This work was supported by the Science and Technology Planning Project of Guangdong Province, China (Grant No. 2014B050504005).
© Springer Nature Switzerland AG 2019.
- Differential evolution
- Multiobjective optimization
- Nonlinear equation systems