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• A generalized decoupling metaheuristic RBDO framework is proposed. • A particle's memory saving strategy is developed to provide effective guidance. • A new adaptive fractional-order equilibrium optimizer algorithm is developed. • Numerical and engineering examples illustrate the superiority of the proposed algorithm. Reliability-based design optimization (RBDO) algorithm is to minimize the objective under the probabilistic factors. While gradient-based and classical evolutionary RBDO algorithms provide promising performance on simple optimization problems, they are likely to perform poorly on challenging problems, including the multimodal functions, discrete design spaces, non-differential problems, etc. This paper proposes a unified framework to improve the performance of existing RBDO algorithms for complex RBDO problems. Our framework is based on three new strategies: generalized decoupling evolutionary and metaheuristic RBDO framework, particle's memory saving strategy, and adaptive fractional-order equilibrium optimizer algorithm. The proposed algorithm is characterized by a decoupling strategy to enable the parallel operation of the inner reliability computation and outer deterministic optimization, a particle's memory saving strategy to provide effective guidance from the previous iteration, and the adaptive fractional-order equilibrium optimizer algorithm to enhance the search efficiency and global convergence capacity. To evaluate the performance of the proposed algorithm, a wide range of experiments are conducted on different types of use cases. The experimental results demonstrate that our algorithm provides superior performance over other comparative algorithms. [ABSTRACT FROM AUTHOR]

• A human mental search is used for cross entropy-based image thresholding. • For improved performance, four modifications are applied on HMS algorithm. • The performance of our algorithm is evaluated based on a variety of metrics. • The obtained results indicate a very competitive performance. The minimum cross-entropy (MCIT) is introduced as a multi-level image thresholding approach, but it suffers from time complexity, in particular, when the number of thresholds is high. To address this issue, this paper proposes a novel MCIT-based image thresholding based on improved human mental search (HMS) algorithm, a recently proposed population-based metaheuristic algorithm to tackle complex optimisation problems. To further enhance the efficacy, we improve HMS algorithm, IHMSMLIT, with four improvements, including, adaptively selection of the number of mental searches instead of randomly selection, proposing one-step k-means clustering for region clustering, updating based on global and personal experiences, and proposing a random clustering strategy. To assess our proposed algorithm, we conduct an extensive set of experiments with several state-of-the-art and the most recent approaches on a benchmark set of images and in terms of several criteria including objective function, peak signal to noise ratio (PSNR), feature similarity index (FSIM), structural similarity index (SSIM), and stability analysis. The obtained results apparently demonstrate the competitive performance of our proposed algorithm. [ABSTRACT FROM AUTHOR]