Golden Poison Dart Frog Optimization Algorithm

To address the limitations of traditional swarm intelligence optimization algorithms in high-dimensional complex problems, such as fixed topology, symmetric search dynamics, empirical dependence on parameter adjustment, and lack of strict dynamic constraints in the convergence process, this paper proposes a golden poison dart frog optimization algorithm based on irreversible risk accumulation and topological metric deformation mechanisms. Starting from the biotoxicity diffusion mechanism, the algorithm introduces a risk field integral model, a topological deformation tensor, a risk entropy modulation mechanism, irreversible energy dissipation constraints, and an asymmetric attraction-repulsion coupling dynamic system to construct a risk-dissipative optimization framework in a dynamic metric space. The algorithm achieves topological reconstruction by altering the local geometric properties of the search space through the second-order structure information of the risk field; it achieves self-organization by controlling the intensity of random perturbations through risk entropy; it suppresses oscillatory behavior by constructing a dissipative system through energy conservation constraints; and it achieves time-dynamic adaptation through a non-stationary toxicity evolution equation. This paper presents the complete mathematical modeling, stability analysis, and complexity analysis of the algorithm, and theoretically proves the monotonicity of the risk integral, the boundedness of the energy function, and weak convergence. The results show that this method theoretically breaks through the Euclidean fixed metric assumption of traditional swarm intelligence algorithms, providing a new dynamic modeling approach for complex optimization problems.