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 article, the new crossover operator BBX for Evolutionary Algorithms (EAs) for traveling salesman problems (TSPs) is introduced. It uses branch-and-bound to find the optimal combination of the (directed) edges present in the parent solutions. The offspring solutions created are at least as good as their parents and are only composed of parental building blocks. The operator is closer to the ideal concept of crossover in EAs than existing operators. This article provides the most extensive study on crossover operators on the TSP, comparing BBX to ten other operators on the 110 instances of the TSPLib benchmark set in EAs with four different population sizes. BBX, with its better ability to reuse and combine building blocks, surprisingly does not generally outperform the other operators. However, it performs well in certain scenarios. Besides presenting a novel approach to crossover on the TSP, the study significantly extends and refines the body of knowledge on the field with new conclusions and comparison results.

We model the time-quality relationship of optimization processes by either fitting curves or training artificial neural networks. On the example of the MAX-SAT problem, we investigate 1) the interpretation of fitted curves based on the values of their parameters using their fixed semantics, 2) the classification of performance measurements to algorithms, i.e., the detection of which algorithm was used to solve a given problem just by its runtime behavior, 3) the prediction of how an algorithm may perform on a yet-unseen problem with yet-unseen features based on its performance on other problems, and 4) the prediction of future progress based on models fitted to data measured so far.