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The problem of nesting frequently arises in the industrial environment, and it has a strong ecological and economic impact in the manufacturing processes. It basically consists of placing a set of pieces (polygons) on a material sheet, making sure that the pieces do not overlap and that they do not exceed the boundaries of the sheet. With regard to irregular 2D polygons, the problem is NP-complete. Therefore, different heuristics have been developed so as to cope with the problem. In this paper, the application of the Jaya metaheuristic algorithm to the nesting problem is proposed. This algorithm has been already applied to several engineering problems and has generally demonstrated better results than most metaheuristic algorithms. In this paper, the Jaya algorithm has been adapted to the specific features of the nesting problem so as to optimize the placement of pieces on a sheet, with the objective of minimizing material waste and computational time. The results of our experimentation demonstrate the algorithm’s effectiveness in reducing the convex hull area across various datasets, showing potential in solving complex, irregular shape nesting problems. This research provides a new application of the Jaya algorithm and opens ways for future work in optimization techniques and parameter-free heuristic algorithms for nesting.Graphical Abstract