article · Artificial Intelligence Review
Tianji’s horse racing optimisation is a new metaheuristic algorithm inspired by an ancient Chinese strategic principle of playing one's strengths against an opponent's weaknesses. It targets persistent limitations in convergence speed and solution accuracy found in existing computational solvers. The method applies a dynamic individual matching approach alongside a greedy strategy, matching individuals between populations to drive iterative updates. Mathematical analysis demonstrates that the algorithm converges to the global optimum with probability one. In evaluations across standard benchmark functions and multiple competition suites spanning dimensions from 10 to 100, the algorithm outperformed established methods and top-performing hybrid optimisers. Practical applicability was further shown across six engineering design problems and in determining damping parameters for magnetorheological damper models in mechanical systems. The underlying source code has been released openly.
Complex engineering and computational tasks require optimisers that can locate accurate solutions rapidly without getting stuck. By pairing a novel population matching strategy with mathematical proof of global convergence, this algorithm provides a reliable alternative for computationally intensive tasks, particularly in mechanical engineering design and parameter identification.
The algorithm has reached an applied and tested stage, validated on mechanical parameter identification for magnetorheological dampers and six engineering design problems. Mechanical engineers, simulation software vendors, and control systems specialists could adopt the freely available code to improve design optimisation workflows. Moving towards commercial integration would require embedding the algorithmic code into existing computer-aided engineering software packages or proprietary design suites.
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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 .
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DOI: 10.1007/s10462-025-11269-9
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