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An improved indicator-based two-archive algorithm for many-objective optimization problems

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Abstract

The large number of objectives in many-objective optimization problems (MaOPs) has posed significant challenges to the performance of multi-objective evolutionary algorithms (MOEAs) in terms of convergence and diversity. To design a more balanced MOEA, a multiple indicator-based two-archive algorithm named IBTA is proposed to deal with problems with complicated Pareto fronts. Specifically, a two-archive framework is introduced to focus on convergence and diversity separately. In IBTA, we assign different selection principles to the two archives. In the convergence archive, the inverted generational distance with noncontributing solution detection (IGD-NS) indicator is applied to choose the solutions with favorable convergence in each generation. In the diversity archive, we use crowdedness and fitness to select solutions with favorable diversity. To evaluate the performance of IBTA on MaOPs, we compare it with several state-of-the-art MOEAs on various benchmark problems with different Pareto fronts. The experimental results demonstrate that IBTA can deal with multi-objective optimization problems (MOPs)/MaOPs with satisfactory convergence and diversity.

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Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Notes

  1. For \( x_1, x_2 \in X \), \(x_1\) Pareto dominates \(x_2\)(denoted as \(x_1 \prec x_2\)) means: 1) for all objectives, \(f_i(x_1) \le f_i(x_2)\) \(i = 1,..., m\), and 2) at least one objective satisfies that \(f_j(x_1) < f_j(x_2)\). Sequentially, A solution \(x^* \in X\) is Pareto optimal if there is no solution \(x \in X \) satisfies \(x \succ x^* \).

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Funding

This work is supported by the National Natural Science Foundation of China under Grant 61802153.

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Authors and Affiliations

  1. School of Internet of Things Engineering, Jiangnan University, Wuxi, 214122, Jiangsu, China

    Weida Song, Shanxin Zhang, Wenlong Ge & Wei Wang

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  1. Weida Song
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Contributions

Weida Song: Methodology, Investigation, Writing—original draft. Shanxin Zhang: Writing—review & editing. Wenlong Ge: Methodology. Wei Wang: Methodology.

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Correspondence to Shanxin Zhang.

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Song, W., Zhang, S., Ge, W. et al. An improved indicator-based two-archive algorithm for many-objective optimization problems. Computing 106, 1395–1429 (2024). https://doi.org/10.1007/s00607-024-01272-3

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