Cut Order Planning (COP) optimizes production costs in the apparel industry by efficiently cutting fabric for garments. This complex process involves challenging decision-making due to order specifications and production constraints. This article introduces novel approaches to the COP problem using heuristics, metaheuristic algorithms, and commercial solvers. Two different solution approaches are proposed and tested through experimentation and analysis, demonstrating their effectiveness in real-world scenarios. The first approach uses conventional metaheuristic algorithms, while the second transforms the nonlinear COP mathematical model into a Mixed Integer Linear Programming (MILP) problem and uses commercial solvers for solution. Modifications to existing heuristics, combined with tournament selection in genetic algorithms (GA), improve solution quality and efficiency. Comparative analysis shows that Particle Swarm Optimization (PSO) outperforms GA, especially for small and medium-sized problems. Cost and runtime evaluations confirm the efficiency and practical applicability of the proposed algorithms, with commercial solvers, delivering superior solutions in shorter computation times. This study suggests the use of solvers for the COP problem, especially for smaller orders, and reserves PSO and GA for larger orders where commercial solvers may not provide a solution. © 2025 Universidad Politecnica de Valencia. All rights reserved.