NLAPSMjSO-EDA: A Nonlinear Shrinking Population Strategy Algorithm for Elite Group Exploration with Symmetry Applications

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Abstract
This work effectively modifies APSM-jSO (a novel jSO variant with an adaptive parameter selection mechanism and a new external archive updating mechanism) to offer a new jSO (single objective real-parameter optimization: Algorithm jSO) version called NLAPSMjSO-EDA. There are three main distinctions between NLAPSMjSO-EDA and APSM-jSO. Firstly, in the linear population reduction strategy, the number of individuals eliminated in each generation is insufficient. This results in a higher number of inferior individuals remaining, and since the total number of iterations is fixed, these inferior individuals will also consume iteration counts for their evolution. Therefore, it is essential to allocate more iterations to the elite population to promote the emergence of superior individuals. The nonlinear population reduction strategy effectively addresses this issue. Secondly, we have introduced an Estimation of Distribution Algorithm (EDA) to sample and generate individuals from the elite population, aiming to produce higher-quality individuals that can drive the iterative evolution of the population. Furthermore, to enhance algorithmic diversity, we increased the number of individuals in the initial population during subsequent experiments to ensure a diverse early population while maintaining a constant total number of iterations. Symmetry plays an essential role in the design and performance of NLAPSMjSO-EDA. The nonlinear population reduction strategy inherently introduces a form of asymmetry that mimics natural evolutionary processes, favoring elite individuals while reducing the influence of inferior ones. This asymmetric yet balanced approach ensures a dynamic equilibrium between exploration and exploitation, aligning with the principles of symmetry and asymmetry in optimization. Additionally, the incorporation of EDA utilizes probabilistic symmetry in sampling from the elite population, maintaining structural coherence while promoting diversity. Such applications of symmetry in algorithm design not only improve performance but also provide insights into balancing diverse algorithmic components. NLAPSMjSO-EDA, evaluated on the CEC 2017 benchmark suite, significantly outperforms recent differential evolution algorithms. In conclusion, NLAPSMjSO-EDA effectively enhances the overall performance of APSM-jSO, establishing itself as an outstanding variant combining jSO and EDA algorithms. The algorithm code has been open-sourced.
Funding Information
  • National Natural Science Foundation of China (62366057, 2020SE308, 2020SE309)
  • Open Foundation of Key Laboratory of Software Engineering of Yunnan Province (62366057, 2020SE308, 2020SE309)

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