Intelligent manufacturing is an important development direction of the modern manufacturing industry. The one-dimensional cutting stock problem (1D-CSP), as a fundamental and important link in the manufacturing industry, directly affects the utilization rate of raw materials, production efficiency, and cost control. In this chapter, a special variant of 1D-CSP is studied. The problem is characterized by the multiple sizes of the raw materials and the ability to splice parts of the materials together to improve material utilization. Based on this problem, a mathematical model is established with the minimum amount of raw materials and the longest offcut in the last section of raw materials as indicators. A two-stage hybrid algorithm based on a rule-based heuristic algorithm and an improved genetic algorithm (GA) is proposed for this mathematical model. The genetic algorithm combines the fast convergence and high local search accuracy of the mayfly algorithm (MA) in the early stages, effectively improving the convergence and local search capabilities of the algorithm and ensuring the quality of the solution set. The experimental results show that the algorithm can obtain high-quality solutions in a short period of time, indicating that the proposed algorithm is effective and superior in solving such problems.