Greedy Brownian - Continuous Ant Colony Optimization (GB-CACO)

This research introduces and evaluates the use of fractional Brownian motion (fBm) as a means extending the Brownian motion (Bm) bridge of the Brownian bridge - continuous ant colony optimization (BB-CACO) algorithm. The bridge functionality is removed to avoid returning ant agent paths back to the nest or point of origin. This frees up many path steps that can be used to generate additional paths, for greater search space coverage. We create two varieties of non-gradient based descent (NGD) algorithms; fBm-CACO and its greedy variant GfBm-CACO. Comprehensive testing on complex non-convex surfaces demonstrates that GfBm-CACO consistently finds superior minima compared to SGD, RMSProp, and Adam, when the loss landscape surface (LLS) is nonconvex and has many local minima. Results reveal that while gradient-based methods follow direct trajectories with faster initial convergence, they frequently become trapped in suboptimal local minima on multimodal landscapes, whereas our NGD approaches, despite their erratic convergence patterns, explore broader portions of the function landscape and find the global minimum in various scenarios. We adopt GfBm-CACO as the new innovative algorithm, call it GB-CACO for short, and detail how this NGD approach can be of value in Loss Landscape Surface(LLS) optimisation.