FOX-TSA: Navigating Complex Search Spaces and Superior Performance in Benchmark and Real-World Optimization Problems

In the dynamic field of optimisation, hybrid algorithms have garnered significant attention for their ability to combine the strengths of multiple methods. This study presents the Hybrid FOX-TSA algorithm, a novel optimisation technique that merges the exploratory capabilities of the FOX algorithm with the exploitative power of the TSA algorithm. The primary objective is to evaluate the efficiency, robustness, and scalability of this hybrid approach across multiple CEC benchmark suites, including CEC2014, CEC2017, CEC2019, CEC2020, and CEC2022, alongside real-world engineering design problems. The results demonstrate that the Hybrid FOX-TSA algorithm consistently outperforms established optimisation techniques, such as PSO, GWO, and the original FOX and TSA algorithms, in terms of convergence speed, solution quality, and computational efficiency. Notably, the hybrid approach avoids premature convergence and navigating complex search spaces, producing optimal or near-optimal solutions in various test cases. For instance, the algorithm achieved superior performance in minimizing design costs in the Pressure Vessel and Welded Beam Design problems, as well as effectively handling the complex landscapes of the CEC2020 and CEC2022 benchmarks. These results affirm the Hybrid FOX-TSA algorithm as a powerful and adaptable tool for tackling complex optimization problems, particularly in high-dimensional and multimodal landscapes. The integration of statistical analyses, such as t-tests and Wilcoxon signed-rank tests, further supports the statistical significance of its performance improvements.