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

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dc.authorid0000-0002-4353-1261
dc.authorid0000-0001-6944-4775
dc.authorid0000-0002-8580-9655
dc.authorid0000-0002-4049-0716
dc.contributor.authorMbasso, Wulfran Fendzi
dc.contributor.authorHarrison, Ambe
dc.contributor.authorDagal, Idriss
dc.contributor.authorJangir, Pradeep
dc.contributor.authorKumar, Raman
dc.contributor.authorLiu, Zhe
dc.date.accessioned2026-01-31T15:08:13Z
dc.date.available2026-01-31T15:08:13Z
dc.date.issued2025
dc.departmentİstanbul Beykent Üniversitesi
dc.description.abstractMetaheuristic 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.
dc.identifier.doi10.1007/s12065-025-01114-x
dc.identifier.issn1864-5909
dc.identifier.issn1864-5917
dc.identifier.issue1
dc.identifier.scopus2-s2.0-105024129168
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://doi.org./10.1007/s12065-025-01114-x
dc.identifier.urihttps://hdl.handle.net/20.500.12662/10625
dc.identifier.volume19
dc.identifier.wosWOS:001631463000004
dc.identifier.wosqualityQ3
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherSpringer Heidelberg
dc.relation.ispartofEvolutionary Intelligence
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.snmzKA_WoS_20260128
dc.subjectFractional calculus
dc.subjectMetaheuristic optimization
dc.subjectDifferential evolution (DE)
dc.subjectMemory-aware algorithms
dc.subjectHigh-dimensional optimization
dc.titleFractional calculus-inspired metaheuristic algorithm for solving high-dimensional constrained optimization problems
dc.typeArticle

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