Blue Poison Dart Frog Optimization Algorithm

To address the problems of static search space, short-term memory structure, symmetric information interaction, and lack of irreversible dynamic structure in traditional swarm intelligence algorithms, this paper proposes a novel swarm intelligence optimization method—the Blue Poison Dart Frog Optimization Algorithm. Inspired by the toxic residue, territorial awareness, and color-based deterrence behavior of the blue poison dart frog, this algorithm constructs a toxicity memory accumulation field, an irreversible territory solidification mechanism, a toxicity phase transition regulation structure, a topological self-reconstruction search space model, an asymmetric information diffusion mechanism, and an energy-toxicity coupling conservation structure. The algorithm constructs a history-dependent toxicity field, causing the search space to evolve over time, thus forming a time-varying topological manifold structure; it constructs an irreversible search trajectory through the solidification mechanism; and it achieves spontaneous regulation of exploration and development through the phase transition mechanism. Theoretically, the algorithm can be modeled as a non-Markov dynamical system and can be derived as a reaction-diffusion type partial differential equation under continuous limits. This paper provides complete mathematical modeling, dynamic analysis, and stability discussion, offering new ideas for constructing swarm intelligence algorithms with historical memory and topological evolution characteristics.