Image segmentation is a key stage in image processing because it simplifies the representation of the image and facilitates subsequent analysis. The multi-level thresholding image segmentation technique is considered one of the most popular methods because it is efficient and straightforward. Many relative works use meta-heuristic algorithms (MAs) to determine threshold values, but they have issues such as poor convergence accuracy and stagnation into local optimal solutions. Therefore, to alleviate these shortcomings, in this paper, we present a modified remora optimization algorithm (MROA) for global optimization and image segmentation tasks. We used Brownian motion to promote the exploration ability of ROA and provide a greater opportunity to find the optimal solution. Second, lens opposition-based learning is introduced to enhance the ability of search agents to jump out of the local optimal solution. To substantiate the performance of MROA, we first used 23 benchmark functions to evaluate the performance. We compared it with seven well-known algorithms regarding optimization accuracy, convergence speed, and significant difference. Subsequently, we tested the segmentation quality of MORA on eight grayscale images with cross-entropy as the objective function. The experimental metrics include peak signal-to-noise ratio (PSNR), structure similarity (SSIM), and feature similarity (FSIM). A series of experimental results have proved that the MROA has significant advantages among the compared algorithms. Consequently, the proposed MROA is a promising method for global optimization problems and image segmentation.

Arithmetic Optimization Algorithm (AOA) is a physically inspired optimization algorithm that mimics arithmetic operators in mathematical calculation. Although the AOA has an acceptable exploration and exploitation ability, it also has some shortcomings such as low population diversity, premature convergence, and easy stagnation into local optimal solutions. The Golden Sine Algorithm (Gold-SA) has strong local searchability and fewer coefficients. To alleviate the above issues and improve the performance of AOA, in this paper, we present a hybrid AOA with Gold-SA called HAGSA for solving industrial engineering design problems. We divide the whole population into two subgroups and optimize them using AOA and Gold-SA during the searching process. By dividing these two subgroups, we can exchange and share profitable information and utilize their advantages to find a satisfactory global optimal solution. Furthermore, we used the Levy flight and proposed a new strategy called Brownian mutation to enhance the searchability of the hybrid algorithm. To evaluate the efficiency of the proposed work, HAGSA, we selected the CEC 2014 competition test suite as a benchmark function and compared HAGSA against other well-known algorithms. Moreover, five industrial engineering design problems were introduced to verify the ability of algorithms to solve real-world problems. The experimental results demonstrate that the proposed work HAGSA is significantly better than original AOA, Gold-SA, and other compared algorithms in terms of optimization accuracy and convergence speed.

Particle swarm optimization (PSO) stands as a prominent and robust meta-heuristic algorithm within swarm intelligence (SI). It originated in 1995 by simulating the foraging behavior of bird flocks. In recent years, numerous PSO variants have been proposed to address various optimization applications. However, the overall performance of these variants has not been deemed satisfactory. This article introduces a novel PSO variant, presenting three key contributions: First, a novel dynamic oscillation inertia weight is introduced to strike a balance between exploration and exploitation; Second, the utilization of cosine similarity and dynamic neighborhood strategy enhances both the quality of solution and the diversity of particle populations; Third, a unique worst-best example learning strategy is proposed to enhance the quality of the least favorable solution and consequently improving the overall population. The algorithm’s validation is conducted using a test suite comprised of benchmarks from the CEC2014 and CEC2022 test suites on real-parameter single-objective optimization. The experimental results demonstrate the competitiveness of our algorithm against recently proposed state-of-the-art PSO variants and well-known algorithms.

In this paper, we discuss the statistical inference of interval-censored recurrence event data under an informative observation process. We establish an additive semiparametric mean model for the recurrence event process. Since the observation process may contain relevant information about potential underlying recurrence event processes, which leads to confounding bias, therefore, we introduced a propensity score into the additive semiparametric mean model to adjust for confounding bias, which possibly exists. Furthermore, the estimation equations were used to estimate the parameters of the covariate effects, and the asymptotic normality of the estimator under large samples is proven. Through simulation studies, we illustrated that the proposed method works well, and it was applied to the analysis of bladder cancer data.