Pythagorean theorem’s origins are situated in geometry; however, it was not an obstacle for this theorem to find its way into the numerous other scientific branches. Through the centuries of its existence, it managed to obtain hundreds of proofs, some incredibly simple, others breathtakingly complex. In other words, the theorem, either in its pure or applied form, managed to showcase its multifaceted applicability. One of the examples of its usage is highlighted in the study conducted by Hama Rashid et al. (2021), which concerns the ant nesting algorithm (ANA).
ANA takes inspiration from the Leptothorax worker ants, as described in its name. It mimics their behavior when they search for possible places to store grains in the process of building the nest. In short, ants deposit the grains around their queen and then make the wall. The algorithm utilizes several features, such as deposition position, its specification, and the worker ant’s decision factor. The latter is referred to as the deposition weight; Hama Rashid et al. (2021) use the Pythagorean theorem for its computation. Particularly, the ants’ previous and current tendency to deposit a grain serves as the theorem slope sides when compared to the best deposition position.
In general, the ANA serves as an optimization method in single-objective problems. It was tested on real-world applications, such as antenna array design and frequency-modulated synthesis. The former problem consists of optimizing the position of non-uniform array elements to reach the peak sidelobe level. In the latter case, ANA optimized six parameters of a frequency modulation synthesizer to create a harmonic sound. In both cases, the algorithm showed reasonable performance and deserved the right to be consequently studied and improved.
Reference
Hama Rashid, D. N., Rashid, T. A., & Mirjalili, S. (2021). ANA: Ant nesting algorithm for optimizing real-world problems.Mathematics, 9(23).