Article: A knapsack modelling approach to financial resource allocation problem using a dual search pattern firefly algorithm Journal: International Journal of Bio-Inspired Computation (IJBIC) 2025 Vol.26 No.5 pp.1 - 13 Abstract: The knapsack problem, a paradigm for constrained optimisation, underpins decision-making under scarcity in finance, logistics, and cognitive science. While classical methods (e.g., dynamic programming) handle small instances, real-world complexity demands metaheuristics like the firefly algorithm (FA), which balances exploration-exploitation trade-offs in dynamic, multi-objective scenarios (e.g., ethical resource allocation). Hybrid FA approaches integrating machine learning improve adaptability in noisy environments. Financial applications, however, lack frameworks addressing real-time responsiveness, ethical-risk synergies, and transparency. This study proposes a dual search pattern firefly algorithm based on Gaussian distribution and Lévy flights (DSPFA) for financial resource allocation, dynamically adapting to macroeconomic shifts, harmonising risk-return objectives with ethical imperatives (e.g., ESG criteria), and ensuring auditable decision pathways. Simulations demonstrate efficient optimisation of heterogeneous constraints (liquidity, compliance) with sublinear time complexity. By embedding fairness metrics and leveraging FA's global-local equilibrium, the framework advances ethical finance and portfolio management. Results highlight FA's scalability in evolving financial ecosystems and the knapsack model's versatility in modelling multidimensional trade-offs. This work bridges theoretical optimisation with practical challenges, offering stakeholders a tool for transparent, adaptive allocation under uncertainty. Inderscience Publishers - linking academia, business and industry through research

Title: A knapsack modelling approach to financial resource allocation problem using a dual search pattern firefly algorithm

Authors: Xinyue Xiao; Zhizhen Chen; Lianfeng Quan; Alex Stojanovic; Lijuan Wu

Addresses: Business School, University of Greenwich, London, Park Row, SE10 9LS, UK ' Business School, University of Greenwich, London, Park Row, SE10 9LS, UK ' Business School, University of Greenwich, London, Park Row, SE10 9LS, UK ' Business School, University of Greenwich, London, Park Row, SE10 9LS, UK ' School of Information Engineering, Jiangxi University of Water Resources and Electric Power, Nanchang 330099, China

Abstract: The knapsack problem, a paradigm for constrained optimisation, underpins decision-making under scarcity in finance, logistics, and cognitive science. While classical methods (e.g., dynamic programming) handle small instances, real-world complexity demands metaheuristics like the firefly algorithm (FA), which balances exploration-exploitation trade-offs in dynamic, multi-objective scenarios (e.g., ethical resource allocation). Hybrid FA approaches integrating machine learning improve adaptability in noisy environments. Financial applications, however, lack frameworks addressing real-time responsiveness, ethical-risk synergies, and transparency. This study proposes a dual search pattern firefly algorithm based on Gaussian distribution and Lévy flights (DSPFA) for financial resource allocation, dynamically adapting to macroeconomic shifts, harmonising risk-return objectives with ethical imperatives (e.g., ESG criteria), and ensuring auditable decision pathways. Simulations demonstrate efficient optimisation of heterogeneous constraints (liquidity, compliance) with sublinear time complexity. By embedding fairness metrics and leveraging FA's global-local equilibrium, the framework advances ethical finance and portfolio management. Results highlight FA's scalability in evolving financial ecosystems and the knapsack model's versatility in modelling multidimensional trade-offs. This work bridges theoretical optimisation with practical challenges, offering stakeholders a tool for transparent, adaptive allocation under uncertainty.

Keywords: knapsack model; metaheuristics; dual search pattern firefly algorithm; financial resource allocation.

DOI: 10.1504/IJBIC.2025.149184

International Journal of Bio-Inspired Computation, 2025 Vol.26 No.5, pp.1 - 13

Received: 11 May 2025
Accepted: 13 Aug 2025
Published online: 16 Oct 2025 *

Title: A knapsack modelling approach to financial resource allocation problem using a dual search pattern firefly algorithm

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