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The optimization of the cutting path of the sample can effectively reduce the cutting time, thereby improving the production efficiency of numerical control processing. This paper comprehensively considers the impact of the cutting order and the position of the knife entry point on the cutting path, converts the cutting path problem into a type of traveling salesman problem (TSP), and proposes an improved genetic-particle swarm optimization algorithm. The selection mechanism of the algorithm combines the elitist retention strategy and roulette wheel selection method to accelerate the search for the optimal solution; the mutation strategy designs a linear decreasing mutation rate, which enhances the global search ability; at the same time, introduces the ant colony optimization algorithm to process the fitness function, adjusts the population evolution difference, and speeds up the optimization process. Through this hybrid algorithm, the cutting order of the sample can be quickly optimized, and the nearest neighbor algorithm is used to determine the position of the knife entry point. Tests are conducted on clothing patterning charts and standard examples. Compared with several commonly used algorithms, experimental results verify the feasibility and effectiveness of this algorithm. [ABSTRACT FROM AUTHOR]