From collective intelligence to evolutionary computation and machine learning, symmetry can be leveraged to enhance algorithm performance, streamline computational procedures, and elevate solution quality. Grasping and leveraging symmetry can give rise to more resilient, scalable, and understandable algorithms. In view of the flaws of the original Sailfish Optimization Algorithm (SFO), such as low convergence precision and a propensity to get stuck in local optima, this paper puts forward an Osprey and Cauchy Mutation Integrated Sailfish Optimization Algorithm (OCSFO). The enhancements are mainly carried out in three aspects: (1) Using the Logistic map to initialize the sailfish and sardine populations. (2) In the first stage of the local development phase of sailfish individual position update, adopting the global exploration strategy of the Osprey Optimization Algorithm to boost the algorithm’s global search capability. (3) Introducing Cauchy mutation to activate the sailfish and sardine populations during the prey capture stage. Through the comparative analysis of OCSFO and seven other swarm intelligence optimization algorithms in the optimization of 23 classic benchmark test functions, as well as the Wilcoxon rank-sum test, it is evident that the optimization speed and convergence precision of OCSFO have been notably improved. To confirm the practicality and viability of the OCSFO algorithm, it is applied to solve the optimization problems of piston rods, three-bar trusses, cantilever beams, and topology. Through experimental analysis, it can be concluded that the OCSFO algorithm has certain advantages in solving practical optimization problems.

To address the drawbacks of the traditional snake optimization method, such as a random population initialization, slow convergence speed, and low accuracy, an adaptive t-distribution mixed mutation snake optimization strategy is proposed. Initially, Tent-based chaotic mapping and the quasi-reverse learning approach are utilized to enhance the quality of the initial solution and the population initialization process of the original method. During the evolution stage, a novel adaptive t-distribution mixed mutation foraging strategy is introduced to substitute the original foraging stage method. This strategy perturbs and mutates at the optimal solution position to generate new solutions, thereby improving the algorithm’s ability to escape local optima. The mating mode in the evolution stage is replaced with an opposite-sex attraction mechanism, providing the algorithm with more opportunities for global exploration and exploitation. The improved snake optimization method accelerates convergence and improves accuracy while balancing the algorithm’s local and global exploitation capabilities. The experimental results demonstrate that the improved method outperforms other optimization methods, including the standard snake optimization technique, in terms of solution robustness and accuracy. Additionally, each improvement technique complements and amplifies the effects of the others.

WSN coverage optimization faces two key challenges: firstly, traditional algorithms are prone to getting stuck in local optima, leading to ‘coverage holes’ in node deployment; Secondly, in dynamic scenarios (such as imbalanced energy consumption of nodes), the convergence speed of the algorithm is slow, making it difficult to maintain high coverage in real time. This study focuses on the coverage optimization problem of wireless sensor networks (WSNs) and proposes improvements to the Flamingo Search Optimization Algorithm (FSA). Specifically, the algorithm is enhanced by integrating the elite opposition-based learning strategy and the stagewise step-size control strategy, which significantly improves its overall performance. Additionally, the introduction of a cosine variation factor combined with the stagewise step-size control strategy enables the algorithm to effectively break free from local optima constraints in the later stages of iteration. The improved Flamingo Algorithm is applied to optimize the deployment strategy of sensing nodes, thereby enhancing the coverage rate of the sensor network. First, an appropriate number of sensing nodes is selected according to the target area, and the population is initialized using a chaotic sequence. Subsequently, the improved Flamingo Algorithm is adopted to optimize and solve the coverage model, with the coverage rate as the fitness function and the coordinates of all randomly distributed sensing nodes as the initial foraging positions. Next, a search for candidate foraging sources is performed to obtain the coordinates of sensing nodes with higher fitness; the coordinate components of these candidate foraging sources are further optimized through chaos theory to derive the foraging source with the highest fitness. Finally, the coordinates of the optimal foraging source are output, which correspond to the coordinate values of all sensing nodes in the target area. Experimental results show that after 100 and 200 iterations, the coverage rate of the improved Flamingo Search Optimization Algorithm is 7.48% and 5.68% higher than that of the original FSA, respectively. Furthermore, the findings indicate that, by properly configuring the Flamingo population size and the number of iterations, the improved algorithm achieves a higher coverage rate compared to other benchmark algorithms.

In response to the decline in population diversity, the imbalance between exploration and exploitation, and the low convergence efficiency in the middle and later stages of the Red-billed Blue Magpie Optimizer (RBMO) when addressing complex optimization problems, this study proposes a multi-strategy enhanced variant termed CLD-RBMO. The proposed algorithm improves the original search mechanism from three perspectives: strengthened global exploration, enhanced local refinement, and directed exploitation in the middle and later stages. During the exploration phase, a hierarchical perturbation mechanism based on Logistic chaotic mapping and Lévy flight is introduced to enhance randomness and spatial coverage in the early search process. In the local exploitation phase, a Cauchy–Gauss hybrid mutation operator is employed to improve the algorithm’s capability to escape from local optima. In the middle and later search stages, a stochastic differential mutation strategy is incorporated to provide population-structure-based directional guidance for individuals, thereby accelerating convergence and improving optimization accuracy. Simulation results on the CEC2017 benchmark test functions indicate that CLD-RBMO demonstrates clear superiority over the original algorithm and several representative swarm intelligence optimization algorithms in terms of optimization accuracy, stability, and overall performance ranking. Convergence curve analysis confirms its dynamic performance improvements across different search stages, and the Wilcoxon rank-sum test further statistically validates the significance of the performance enhancement achieved by the proposed improvements compared with the original algorithm. Moreover, evaluations on two representative mechanical engineering optimization case studies further demonstrate the algorithm’s strong stability and engineering generalization capability.

In this study, a brand-new algorithm called the Comprehensive Adaptive Enterprise Development Optimizer (CAED) is proposed to overcome the drawbacks of the Enterprise Development (ED) algorithm in complex optimization tasks. In particular, it aims to tackle the problems of slow convergence and low precision. To enhance the algorithm’s ability to break free from local optima, a lens imaging reverse learning approach is incorporated. This approach creates reverse solutions by utilizing the concepts of optical imaging. As a result, it expands the search range and boosts the probability of finding superior solutions beyond local optima. Moreover, an environmental sensitivity-driven adaptive inertial weight approach is developed. This approach dynamically modifies the equilibrium between global exploration, which enables the algorithm to search for new promising areas in the solution space, and local development, which is centered on refining the solutions close to the currently best-found areas. To evaluate the efficacy of the CAED, 23 benchmark functions from CEC2005 are chosen for testing. The performance of the CAED is contrasted with that of nine other algorithms, such as the Particle Swarm Optimization (PSO), Gray Wolf Optimization (GWO), and the Antlion Optimizer (AOA). Experimental findings show that for unimodal functions, the standard deviation of the CAED is almost 0, which reflects its high accuracy and stability. In the case of multimodal functions, the optimal value obtained by the CAED is notably better than those of other algorithms, further emphasizing its outstanding performance. The CAED algorithm is also applied to engineering optimization challenges, like the design of cantilever beams and three-bar trusses. For the cantilever beam problem, the optimal solution achieved by the CAED is 13.3925, with a standard deviation of merely 0.0098. For the three-bar truss problem, the optimal solution is 259.805047, and the standard deviation is an extremely small 1.11 × 10⁻⁷. These results are much better than those achieved by the traditional ED algorithm and the other comparative algorithms. Overall, through the coordinated implementation of multiple optimization strategies, the CAED algorithm exhibits high precision, strong robustness, and rapid convergence when searching in complex solution spaces. As such, it offers an efficient approach for solving various engineering optimization problems.

Coverage optimization of wireless sensor networks (WSNs) faces challenges such as uneven node distribution and vulnerability to coverage blind spots. This paper introduces and improves the Northern Goshawk Optimization (NGO) algorithm: the Logistic chaotic map is adopted to initialize the population for enhanced ergodicity, a nonlinear dynamic weight is introduced to balance global exploration and local exploitation, and a Gaussian–Lévy hybrid mutation mechanism is integrated to strengthen the ability to escape from local optima. Experiments on standard test functions show that the improved algorithm (INGO) can stably approach the theoretical optimal values for both unimodal and multimodal functions. The convergence speed and solution accuracy are significantly superior to those of the original NGO, with a smaller standard deviation and stronger robustness. INGO is applied to the coverage optimization of 2D and 3D WSNs, with coverage rate as the fitness function, and the optimal node deployment coordinates are output through iterative optimization. Simulation results show that INGO achieves a best coverage rate of 98.32% in the 2D scenario, which is 7.72 percentage points higher than the 90.6% of NGO. In the 3D scenario, the best coverage rate reaches 72.32%, 6.78 percentage points higher than the 65.54% of NGO. Meanwhile, INGO yields more uniform node deployment and effectively reduces coverage blind spots. Its convergence curve is smooth and oscillation-free in the late iteration stage, and the stability is significantly better than that of NGO. With proper settings of population size and iteration times, INGO can achieve better coverage performance, providing a reliable technical solution for the efficient deployment of wireless sensor networks in complex environments.