Victoria Amazonica optimization algorithm based on adaptive mutation factor and mathematical distribution for solving minimum spanning tree problem

The minimum spanning tree problem is of great importance in the field of graph theory and optimization, which can be regarded as an optimization problem itself, and thus can be solved by intelligent optimization algorithms. Victoria Amazonica Optimization (VAO) algorithm is a meta-heuristic algorithm that performs well and solves optimization problems with varying degrees of complexity. To obtain better optimization performance, a VAO algorithm based on adaptive mutation factor and mathematical distribution (RODVAO) is proposed. Adaptive mutation factors are introduced to dynamically adjust the exploration and exploitation of the algorithm, which is conducive to the algorithm jumping out of the local optimum; Mathematical distributions are employed to guide the search direction of the improved algorithm, which expands the search scope while exploring the solution space more efficiently by varying the ranges and trends of the elements of the stochastic matrices and thus practically altering the directions and magnitudes used by the individuals in adjusting the positions. To assess the optimization performance of the proposed improved algorithm, it is subjected to optimization comparison experiments with six different categories of meta-heuristic algorithms on the CEC 2022 test functions. To assess the practicality of the RODVAO algorithm, it is compared with other algorithms for solving fixed-vertices and random-vertices MST problems. The results of the simulation experiments show that the Victoria Amazonica Optimization algorithm based on adaptive mutation factors and mathematical distributions enhances the algorithm's global and local search capabilities, facilitates the jumping out of local optimal solutions, and shows good performance in solving MST problems.