Fractional Order Chaotic Based Fick’s Law Optimization Performance
2026 10th International Artificial Intelligence and Data Processing Symposium (IDAP), Malatya, Türkiye, 6 - 07 Eylül 2026, ss.1-14, (Tam Metin Bildiri)
- Yayın Türü: Bildiri / Tam Metin Bildiri
- Doi Numarası: 10.1109/idap71869.2026.11728183
- Basıldığı Şehir: Malatya
- Basıldığı Ülke: Türkiye
- Sayfa Sayıları: ss.1-14
- İnönü Üniversitesi Adresli: Evet
Özet
High-dimensional and nonlinear problems form a domain that classical derivative-based methods cannot solve. Metaheuristic algorithms fill this gap, but they bring their own weaknesses with them. Search diversity narrows as the iterations proceed, and the population may collect in a local basin. One reason for this behavior is the uniform pseudo-random number generators that the algorithms use as their source of randomness. Chaotic systems are being tried as an alternative to these generators, since they produce unpredictable sequences even though they are deterministic.In this study, the Fick's Law Algorithm (FLA) is extended through two separate contributions. First, the Grünwald–Letnikov fractional-order derivative is used in the update of the molecule position. The update is thus tied not only to the last position but also to past positions with decaying weights. It is shown numerically that when the fractional order equals one, the additional terms vanish and the method gives exactly the same result as the original FLA.Second, the random numbers called by the algorithm are replaced with sequences generated from fifteen fractional-order continuous-time chaotic oscillators. The systems used are Lorenz, Chen, Lü, Liu, Rössler, Newton–Leipnik, Volta, Chua, Arneodo, Genesio–Tesi, Duffing, Van der Pol, Lotka–Volterra, the financial system, and the three-cell cellular neural network. Each one is solved with the Grünwald–Letnikov scheme, and after the transient regime is discarded, the state variables are mapped to the unit interval. The resulting method is named FOC-FLA.The methods are compared with the original FLA on 20 standard benchmark functions. The Wilcoxon rank-sum test and the Friedman mean rank test are used in the comparisons. The preliminary findings obtained reveal a different picture. Although fractional-order memory and chaotic modulation produce a different search behavior on some multimodal functions, the original FLA is seen to reach higher numerical precision on most functions at the scale tested.