In this study, we introduce a novel metaheuristic algorithm named Tianji’s horse racing optimization (THRO), inspired by the Chinese historical story of Tianji’s horse racing. The story illustrates how Tianji leveraged his strengths to counteract his opponent’s weaknesses, ultimately leading to his victory in the competition. This strategic principle, which led to Tianji’s victory, forms the foundation of THRO’s design. The need for such a proposal arises from the limitations of existing optimization algorithms, which often struggle with convergence speed and solution accuracy when solving complex problems. THRO addresses these challenges by employing a unique dynamic individual matching strategy that enhances the algorithm’s convergence rate and solution precision. In this algorithm, an effective greedy strategy is employed to maximize benefits by selecting individuals from its population and matching them with individuals from the opponent’s population, thereby facilitating individual updates. This paper provides mathematically grounded explanations and analysis of how the algorithm converges to the global optimum with probability 1. To validate the efficacy of THRO, comparative experiments with 12 popular algorithms are conducted on 23 classical benchmark functions and the CEC2017 test suite. For the 29 CEC2017 functions across 10, 30, 50, and 100 dimensions, THRO achieves the slowest Friedman average ranking values among all competing methods, which are 2.052, 2.500, 2.293, and 2.259, respectively. Additionally, we conduct a comprehensive comparison with several advanced algorithms, including high-performance hybrid optimizers and the CEC winners, across the CEC2014, CEC2017, CEC2020, and CEC2022 suites, where THRO again achieves the slowest Friedman average ranking value of 1.729. Furthermore, six engineering design problems are employed to comprehensively check the applicability of THRO. Eventually, THRO’s proficiency extends to the application of identifying damping parameters of magnetorheological damper (MRD) models in mechanical systems. The results confirm that THRO exhibits remarkable competitiveness in solving various complex problems.The source code of THRO is publicly available at https://github.com/zwg770123/THRO.

This study introduces the Multi-objective Generalized Normal Distribution Optimization (MOGNDO) algorithm, an advancement of the Generalized Normal Distribution Optimization (GNDO) algorithm, now adapted for multi-objective optimization tasks. The GNDO algorithm, previously known for its effectiveness in single-objective optimization, has been enhanced with two key features for multi-objective optimization. The first is the addition of an archival mechanism to store non-dominated Pareto optimal solutions, ensuring a detailed record of the best outcomes. The second enhancement is a new leader selection mechanism, designed to strategically identify and select the best solutions from the archive to guide the optimization process. This enhancement positions MOGNDO as a cutting-edge solution in multi-objective optimization, setting a new benchmark for evaluating its performance against leading algorithms in the field. The algorithm's effectiveness is rigorously tested across 35 varied case studies, encompassing both mathematical and engineering challenges, and benchmarked against prominent algorithms like MOPSO, MOGWO, MOHHO, MSSA, MOALO, MOMVO, and MOAOS. Utilizing metrics such as Generational Distance (GD), Inverted Generational Distance (IGD), and Maximum Spread (MS), the study underscores MOGNDO's ability to produce Pareto fronts of high quality, marked by exceptional precision and diversity. The results affirm MOGNDO's superior performance and versatility, not only in theoretical tests but also in addressing complex real-world engineering problems, showcasing its high convergence and coverage capabilities. The source codes of the MOGNDO algorithm are publicly available at https://nimakhodadadi.com/algorithms-%2B-codes.

Magnetorheological (MR) dampers play a crucial role in various engineering systems, and how to identify the control parameters of MR damper models without any prior knowledge has become a burning problem. In this study, to identify the control parameters of MR damper models more accurately, an improved manta ray foraging optimization (IMRFO) is proposed. The new algorithm designs a searching control factor according to a weak exploration ability of MRFO, which can effectively increase the global exploration of the algorithm. To prevent the premature convergence of the local optima, an adaptive weight coefficient based on the Levy flight is designed. Moreover, by introducing the Morlet wavelet mutation strategy to the algorithm, the mutation space is adaptively adjusted to enhance the ability of the algorithm to step out of stagnation and the convergence rate. The performance of the IMRFO is evaluated on two sets of benchmark functions and the results confirm the competitiveness of the proposed algorithm. Additionally, the IMRFO is applied in identifying the control parameters of MR dampers, the simulation results reveal the effectiveness and practicality of the IMRFO in the engineering applications.

Parameter identification is an important method to establish the governing system of a pumped storage unit. Appropriate parameters will make the governing system obtain better control performance. Therefore, in this study, an improved artificial hummingbird algorithm (IAHA) is proposed for the parameter identification of the governing system in a pumped storage unit. The algorithm integrates two key strategies to improve the optimization ability of the algorithm. First, the Chebyshev chaotic map is employed to initialize the artificial hummingbirds, which in turn increases and enhances the global search capability of the initial population. Second, the Levy flight is introduced in the guided foraging phase to expand the search space and avoid premature convergence. The performance of the proposed IAHA algorithm is compared with that of four other algorithms on 23 standard test functions, and the results show that IAHA has higher accuracy and faster convergence than the other four algorithms. Finally, IAHA was applied to the parameter identification of the governing system of a pumped storage unit to verify the effectiveness of the algorithm in tracking real-world problems.