Italian Cave Salamander Optimization Algorithm

To address the multimodality, structural degradation, gradient unavailability, and premature convergence issues in high-dimensional complex optimization problems, a novel optimization algorithm for the Italian cave salamander, based on a coupling mechanism of topological memory manifold and dual-mode dynamics, is proposed. Inspired by behavioral characteristics such as low-light perception, structural memory, energy constraints, and path invertibility in cave ecosystems, the algorithm constructs five core mathematical modules: a topological evolutionary memory manifold, a dual-mode update mechanism (reversible and irreversible), a darkness perception uncertainty tensor, a hierarchical channel scale adjustment mechanism, and an entropy-driven energy constraint system. By embedding historical high-quality solutions into a low-dimensional structural subspace, a transformation from point contraction to structural contraction is achieved; an adaptive switching between exploration and development is realized through a local fitness fluctuation risk function; directional stability is characterized by a direction sampling covariance tensor; multi-scale search is controlled by local Lipschitz estimation; and energy evolution equations are constructed using population entropy to maintain diversity. Furthermore, boundedness analysis, expected contraction analysis, and stability discussions based on Lyapunov functions are presented. Theoretically, this algorithm possesses both structural preservation and adaptive contraction, providing a novel topologically coupled meta-heuristic framework for complex non-convex optimization problems.