Companies generally set a standard color for product color design to enhance the corporate brand image. When a given color and the planned combination of given areas contain multiple constraints, the exhaustive process that has traditionally been used to obtain the optimal color scheme is often time consuming. Therefore, this study proposes the use of binary programming theory to solve the problem of product color planning with multiple constraints. In this research, binary programming theory is first used to determine the variables of the product color matching design. Thereafter, multiple constraints are established based on various color requirements from the product color matching design, following which the color matching design goal is determined according to the aesthetic experience of the designer on the color matching design. Finally, the constrained formula is converted into a language that can be recognized by the Matlab software and input into the Optimization Tool application to calculate the final color planning scheme. The color design of an intelligent assembly product in the rail transit field is used as an example to demonstrate the operation process of the proposed solution, and the calculation results are verified by subjective questionnaires. The results reveal that the proposed method can effectively solve the problem of product color matching design with multiple constraints, can improve the efficiency of product color matching design with multiple constraints, and offers certain reliability and practicability.

中文翻译：

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二元规划理论在多约束产品色彩规划中的应用

企业一般为产品色彩设计设定标准色，以提升企业品牌形象。当给定颜色和给定区域的计划组合包含多个约束时，传统上用于获得最佳配色方案的详尽过程通常非常耗时。因此，本研究提出利用二元规划理论解决多约束的产品色彩规划问题。本研究首先利用二元规划理论确定产品配色设计的变量。此后，从产品配色设计中根据各种色彩要求建立多重约束，然后根据设计师对配色设计的审美体验确定配色设计目标。最后，将受约束的公式转换为 Matlab 软件可以识别的语言，输入到优化工具应用程序中，计算出最终的色彩规划方案。以轨道交通领域某智能装配产品的色彩设计为例，演示了所提出方案的运行过程，并通过主观问卷对计算结果进行了验证。结果表明，该方法能有效解决多约束产品配色设计问题，提高多约束产品配色设计的效率，具有一定的可靠性和实用性。