Solving nesting problems or irregular strip packing problems is to positionpolygons in a fixed width and unlimited length strip, obeying polygon integritycontainment constraints and non-overlapping constraints, in order to minimizethe used length of the strip. To ensure non-overlapping, we used separationlines. A straight line is a separation line if given two polygons, all verticesof one of the polygons are on one side of the line or on the line, and allvertices of the other polygon are on the other side of the line or on the line.Since we are considering free rotations of the polygons and separation lines,the mathematical model of the studied problem is nonlinear. Therefore, we usethe nonlinear programming solver IPOPT (an algorithm of interior points type),which is part of COIN-OR. Computational tests were run using establishedbenchmark instances and the results were compared with the ones obtained withother methodologies in the literature that use free rotation.
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