## 1 Introduction
Since the color presented on the material surface is jointly influenced by multiple sets of parameters, it is not possible to study the mechanism influencing in from the perspective of a certain parameter in a fragmented way, and the matrix method is not good enough to find all the colors that can be achieved by the material. Regarding the thin-film interference effect produced by laser-induced oxide layers, there have been a large number of studies showing the complex mechanism of color formation, and the relationship between color and laser parameters is nonlinear [28; 29]. With the rapid development of artificial intelligence, some scholars have predicted laser-induced coloring characteristics and the corresponding laser process parameters by constructing color prediction models [23; 25; 29; 30; 31], and this scheme provides a new way of thinking about the color consistency challenges and tedious parameter exploration work involved in laser-induced coloring of metal surfaces. However, the prediction accuracy of a color prediction model is related to the number of samples in the dataset; the accurate color prediction model needs to generate a large number of samples in the training dataset by the matrix method, and the color prediction model is only able to achieve color prediction within the range of the training dataset, which brings a new challenge in color gamut exploration work. A scientific method for color gamut exploration is the use of a genetic algorithm. Genetic algorithms are widely used to solve multi-objective optimization problems because they have a mechanism based on population search [32; 33; 34]. Genetic algorithms use natural selection, crossover, and mutation to continuously generate new parameter populations, and they use non-dominated sorting and elite strategies to obtain the optimal solution set and solve multi-objective optimization problems as well as possible. [PERSON] and others innovatively introduced genetic algorithms into this field to study multi-objective problems from the perspective of genetic crossover mutations to generate new parameters, using the selection of good-looking colors and the dominance of colors to determine whether the process converges or not [35]. However, the convergence achieved in this way is a local convergence, and the results obtained only apply to the hue of the selected good-looking color; no real convergence is achieved for the entire color gamut of the substrate, which just happens to be approximated by the hue of the parameters in this generation, limiting further research. If we wish to conduct a more in-depth study on a material, we urgently need a method that can quickly and accurately find the color gamut of the given material. In the field of laser coloring, drawbacks such as difficulty, a slow pace, and inaccuracy in finding a suitable color gamut have hindered effective color exploration. To address these issues, this study proposes a Color Gamut Exploration Genetic Algorithm, designed to maximize color gamut prediction while ensuring efficient convergence. The Color Gamut Exploration Genetic Algorithm incorporates optimal solution search and color space mapping, employing mutation and crossover to iteratively refine laser parameters and expand the achievable color gamut. This robust approach ensures that the largest possible color gamut can be fully realized on material surfaces, significantly improving efficiency and accuracy compared to traditional methods. Additionally, we propose a complete image color reproduction process, including a toolkit for color mapping and vectorization, enabling the precise reproduction of target image colors onto laser-treated surfaces. Using the discovered color gamut and established parameter relationships, our method successfully reproduces colors on 304 stainless steel, demonstrating promising applications for laser surface image reproduction.