## 1 Introduction  
Cultural sustainability is a comprehensive concept that emphasizes the need to focus not only on protecting and preserving the core values of traditional culture in heritage conservation but also on its adaptability and sustainable development in the context of modern society. This concept aims to ensure that traditional culture, while maintaining its authenticity and core spirit, can be harmonized with contemporary life and social needs, thereby enabling the dynamic transmission of cultural heritage and infusing it with new vitality and value [1,2]. In the practical implementation of cultural heritage conservation, science, and technology provide essential support for achieving cultural sustainability. Advanced methods such as digital technologies, 3D scanning, and artificial intelligence analysis enable more accurate reproduction and optimization of the unique characteristics of traditional arts. Beyond physical preservation, these technologies further offer possibilities for the creative transmission of cultural heritage [3,4]. For example, scientific technologies can assist in restoring or recreating art features that have become blurred or damaged, accurately analyzing the forms and color logic in traditional culture, and using modern techniques to transform them into more accessible and contemporary art forms. This innovative practice opens new pathways for the sustainable transmission of cultural heritage while enhancing public awareness and participation in traditional culture. In recent years, the widespread application of intelligent algorithms in art design has injected new momentum and possibilities into cultural heritage conservation. In the realm of cultural innovation and transmission, artificial intelligence technology is gradually demonstrating its unique advantages by analyzing artistic rules through deep learning algorithms and generating design solutions that align with both traditional artistic features and modern aesthetic demands [5]. Among these, color regeneration and design play a key role. The color art of traditional cultural heritage often carries profound historical and cultural meanings. Color regeneration technology not only allows for the precise restoration of the colors of historical artifacts but also integrates modern design language to imbue them with new aesthetic value. This intelligent algorithm-based color regeneration technology provides crucial support for the dynamic protection and innovative transmission of cultural heritage, fostering dialogue and symbiosis between traditional arts and modern society [6,7]. However, the current approach still exhibits certain limitations in the automation of color regeneration, optimization of user interaction, and accuracy of color harmony prediction. To address the aforementioned issues, this study proposes the Cultural Color IGA algorithm, which integrates an interactive genetic algorithm (IGA) as the core, a color network model as the source of initial color genes, and a color harmony prediction model as the fitness evaluation surrogate. By leveraging the color characteristics of cultural heritage, this approach facilitates the regeneration and modernization of cultural heritage colors. Specifically, the objectives of this study include the following:  
1. Enhancing the cultural adaptability of color-matching--Extracting color features specific to cultural contexts based on the color network model to construct an initial color gene set that aligns with traditional color imagery;
2. Improving the automation of color evaluation--Employing a color harmony prediction model to partially replace manual evaluation, thereby reducing user fatigue and enhancing optimization efficiency;
3. Developing an efficient color regeneration system--Building a Python-based color optimization system (Python 3.9.7) and conducting case studies and comparative analyses using the Yungang Grottoes as an experimental subject. The main contributions of this study are as follows:  
1.