Black soldier fly algorithm based on swarm intelligence method for solving optimization problems

Meta-heuristic swarm algorithms are vital for resolving complex, non-convex optimization problems. However, contemporary optimizers increasingly suffer from structural stagnation and slow convergence rates when tracking highly rugged engineering surfaces; this limitation stems from their strict reliance on standard linear vector updates or basic random walks that cause search agents to blindly bypass narrow global valleys. To overcome this challenge, this paper introduces a novel swarm-based optimization framework named the black soldier fly algorithm (BSFA), modeled after the biological habitat selection, conspecific grouping, and microclimate oviposition tracking behaviors of certain fly species. Unlike traditional systems that apply uniform position updates across the entire population, BSFA introduces a decoupled non-linear position update architecture. Global exploration is governed by a dynamic, non-linear fractional ratio tracking inter-agent spatial density (cohesion) against target proximity (separation). Local exploitation is driven by a unique algebraic cardioid trajectory operator. This mathematical configuration allows individual agents to loop dynamically around target spaces rather than rushing directly toward them, enabling an omnidirectional sweep of the localized landscape that drastically accelerates fine-scale convergence speed and prevents premature local minima entrapment. The optimization performance of the proposed BSFA was rigorously benchmarked using 23 standard functions and the complex CEC2017 suite against ten powerful competing algorithms, including GA, PSO, GWO, LSHADE, BTA, and CAOA. Experimental and statistical analysis, verified via Wilcoxon non-parametric testing at a strict significance level of \(\:\alpha\:=0.05\) , demonstrates that BSFA achieves absolute global optimum values on key multimodal functions like TF9 and TF11, secures the lowest mean Friedman rank of 2.3 against its ablated variants, and yields competitive computational time metrics of 20.6 s across the entire test suite, ranking second in processing efficiency. These quantitative outcomes confirm that BSFA robustly eliminates suboptimal local valleys while drastically accelerating fine-scale convergence speed across diverse continuous optimization tasks.