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Abstract This paper proposes a novel membrane algorithm based on artificial protozoa optimizer (MAAPO) for global optimization problems. The artificial protozoa optimizer (APO) is adopted as the base meta-heuristic algorithm due to its novelty and competitive performance. MAAPO integrates two key innovations: (1) a membrane computing (MC) framework that introduces a parallel distributed paradigm to improve population diversity and search dynamics, and (2) an enhanced autotrophic model within APO that uses a roulette-based fitness-distance balance (RFDB) mechanism for adaptive reference point selection. These strategies collectively enhance the algorithm’s exploration-exploitation balance and global search capabilities. To validate its performance, MAAPO is tested against 12 advanced algorithms on the CEC2017 test suite, and further applied to the multilevel thresholding image segmentation problem using Otsu and Kapur entropy as objective functions. The quality of segmented images is assessed using peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), and feature similarity index (FSIM) metrics. Experimental results demonstrate that MAAPO outperforms its counterparts, delivering superior segmentation quality. This research on MAAPO contributes an effective enhancement strategy to meta-heuristic algorithms and introduces a novel, highly applicable approach for complex image segmentation tasks. The source codes of MAAPO are publicly available at https://ww2.mathworks.cn/matlabcentral/fileexchange/181534-maapo .
Wang et al. (Sat,) studied this question.