Fractional calculus-inspired metaheuristic algorithm for solving high-dimensional constrained optimization problems

Wulfran Fendzi Mbasso

doi:10.1007/s12065-025-01114-x

Fractional calculus-inspired metaheuristic algorithm for solving high-dimensional constrained optimization problems

2025-12-06

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Wulfran Fendzi Mbasso *

DOI：10.1007/s12065-025-01114-x

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Metaheuristic algorithms have been very good at addressing hard optimization problems with many dimensions in science and engineering. But most of the methods that are already out there use integer-order update dynamics, which do not take into account the memory-dependent and non-local properties that are typically found in real-world systems. This simplification makes it harder for them to adapt their searches, stay converged, and get out of local optima, especially in changing or limited contexts. We suggest a new Fractional-Order Differential Evolution (FCDE) technique that adds Caputo fractional derivatives to the mutation and update equations of standard Differential Evolution. This would help close the gap. FCDE adds a tunable non-local search mechanism that adaptively balances exploration and exploitation throughout the optimization process by using the long-term memory and heredity aspects of fractional calculus. This new idea makes convergence more reliable and improves global search capabilities. We tested the CEC 2022 and CEC 2025 benchmark suites (30 functions, dimensions up to 1000D) a lot, as well as three real-world engineering issues that involved limited truss design, PV-based MPPT control, and dynamic resource allocation. The results reveal that FCDE always beats 10 state-of-the-art algorithms, such as JADE, LSHADE, CMA-ES, and MRFO. According to statistics, FCDE had: (a) 17 wins out of 30 on CEC 2025 (100D) and 14 wins out of 30 on CEC 2022 (30D); (b) An average improvement of 12.8% in convergence speed; (c) A mean error reduction of up to 38% on highly multimodal functions; (d) A p-value of less than 0.01 in Wilcoxon tests against all baselines, which means it was significant. Also, ablation tests show that the search performance is sensitive to the fractional order alpha is an element of [0.3,1], with the best convergence patterns appearing at alpha = 0.65. This shows how important fractional dynamics are in helping people find their way through intelligent search paths. The suggested FCDE framework presents a new way of thinking about metaheuristics by adding fractional memory-aware behavior. This makes it more useful for solving difficult global optimization problems in theory and in practice.

Keyword:

Fractional calculus

Metaheuristic optimization

Differential evolution (DE)

Memory-aware algorithms

High-dimensional optimization

Fractional calculus-inspired metaheuristic algorithm for solving high-dimensional constrained optimization problems

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