# Adaptive differential evolution with multi-population-based mutation operators for constrained optimization

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## Abstract

Constrained optimization problems (COPs) are most commonly encountered problems in science and engineering design field. To solve such kind of problem effectively, in this paper, we put forward a new approach named CAMDE which integrates adaptive differential evolution (DE) with new multi-population-based mutation operators. In CAMDE, some inferior solutions with low objective values are maintained in an external population. During mutation process, this external population is combined with main population to generate promising progress directions toward optimal region. Furthermore, DE’s control parameters *F* and CR are adaptively adjusted according to the statistical information learnt from the previous searches in generating improved solutions. The advantageous performance of CAMDE is validated by comparisons with some representatives of state of the art in constrained optimization over 24 test instances. Moreover, four widely used constrained mechanical engineering problems are selected to validate the search ability of CAMDE for real-world problems. The performance results show that CAMDE is an effective approach to solving COPs, which is basically enabled by the integration of multi-population-based mutation operators and adaptive control strategy for DE’s control parameters.

## Keywords

Constrained optimization Differential evolution Multi-population Adaptive strategy Feasibility rule## Notes

### Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grants 61703268 and 51605277, the Fundamental Research Funds for the Central Universities under Grant 222201717006, the China Postdoctoral Science Foundation under Grant 2016M591783, and the Natural Science Foundation of Jiangsu Province under Grant BK20160540.

### Compliance with ethical standards

### Conflict of interest

The authors declare that they have no conflict of interest.

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