GBO:AMulti-Granularity Optimization Algorithm via Granular-ball for Continuous Problems
Shuyin Xia, Xinyu Lin, Guan Wang, De-Gang Chen, Sen Zhao, Guoyin Wang, Jing Liang
TL;DR
GBO introduces a multi-granularity optimization framework that uses granular-balls to cover the solution space and progressively split toward finer granularity, enabling coarse-to-fine, region-based search. By replacing point-based search with cooperative, non-overlapping granular-ball exploration and gradient-guided guiding GBs, GBO enhances exploration robustness and convergence behavior. Empirical results on the CEC2013 benchmark and a Spread Spectrum Radar design problem demonstrate superior performance against classical evolutionary algorithms and modern Fireworks Algorithm variants, particularly on complex, multimodal landscapes. The work underscores the potential of granular-ball representations for efficient, robust continuous optimization and points to adaptive-radius extensions as future work.
Abstract
Optimization problems aim to find the optimal solution, which is becoming increasingly complex and difficult to solve. Traditional evolutionary optimization methods always overlook the granular characteristics of solution space. In the real scenario of numerous optimizations, the solution space is typically partitioned into sub-regions characterized by varying degree distributions. These sub-regions present different granularity characteristics at search potential and difficulty. Considering the granular characteristics of the solution space, the number of coarse-grained regions is smaller than the number of points, so the calculation is more efficient. On the other hand, coarse-grained characteristics are not easily affected by fine-grained sample points, so the calculation is more robust. To this end, this paper proposes a new multi-granularity evolutionary optimization method, namely the Granular-ball Optimization (GBO) algorithm, which characterizes and searches the solution space from coarse to fine. Specifically, using granular-balls instead of traditional points for optimization increases the diversity and robustness of the random search process. At the same time, the search range in different iteration processes is limited by the radius of granular-balls, covering the solution space from large to small. The mechanism of granular-ball splitting is applied to continuously split and evolve the large granular-balls into smaller ones for refining the solution space. Extensive experiments on commonly used benchmarks have shown that GBO outperforms popular and advanced evolutionary algorithms. The code can be found in the supporting materials.