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Strip-packing problem is apparent in textile industry where a set of items, i.e. cutting parts (2D convex or non-convex polygons) need to be placed on a rectangular container (fabric with an m×n area) so that cutting parts do not overlap and do not exceed the boundaries of the container. The goal is to find a placement that utilizes the area of a container. In this paper three methods (random search, greedy algorithm and genetic algorithm) are tested on sets of regular (convex polygons) and irregular (cutting parts) items. The goal is to find the optimal items placement that minimizes the cover area. In this paper a no-fit polygon (NFP) is used to assure two items touch without overlapping. NFP is constructed by rotating polygon B around a static polygon A in a way their edges always touch and never overlap. The result is a polygonal area enclosed by trajectory of rotating polygon's reference point which represents the overlapping area of A and B. Items touch if polygon B is placed on the NFP's border. Non-convex cutting parts are approximated with their convex hull since a NFP version for convex polygons is used in this paper.

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Marker planning is an optimization arrangement problem, where a set of cutting parts need to be placed on a thin paper without overlapping to create a marker – an exact diagram of cutting parts that will be cut from a single spread. An optimal marker that utilizes the length of textile material has to be obtained. The aim of this research was to develop novel algorithms for obtaining an efficient marker that would achieve competitive results and optimize the garment production in terms of improving the utilization of textile material. In this research, a novel Grid heuristic was introduced for obtaining a marker, alongside its improvement methods: Grid-BLP and Grid-Shaking. These heuristics were hybridized with genetic algorithm that determined the placement order of cutting parts using the newly introduced All Equal First (AEF) placement order. A novel individual representation for genetic algorithm was designed that was composed of order sequence, rotation detection and the choice of placement algorithm (hyper-heuristic). Experiments were conducted to determine the best marker making method, and hyper-heuristic efficiency. The implementation and experiments were conducted in MATLAB using GEATbx toolbox on five datasets from the garment industry: ALBANO, DAGLI, MAO, MARQUES and MAN SHIRT. Marker efficiency in percentage was recorded with best results: 84.50%, 80.13%, 79.54%, 84.67% and 86.02% obtained for the datasets respectively. The most efficient heuristic was Grid-Shaking. Hyper-heuristic applied Grid-Shaking in 88% of times. The created algorithm is independent of cutting parts’ shape. It can produce markers of arbitrary shape and is flexible in terms of expansion to new instances from the garment industry (leather nesting, avoiding damaged areas of material, marker making with materials with patterns).

Strip-packing problem (marker making) is an optimization problem, where a set of cutting parts needs to be placed on a marker so that the items do not overlap, and do not exceed the boundaries of a marker. In this research a novel Grid algorithm is introduced, and improvement methods: Grid-BLP and Grid-Shaking. These algorithms were combined with genetic algorithm, and a novel placement order All equal first. An individual representation of a genetic algorithm has been developed that is consisted of placement sequence, rotation of a cutting part, the choice of a placement algorithm, and dynamic grid parameter. Experiments were conducted to determine the best placement algorithm for a dataset, and hyper-heuristic efficiency. The implementation has been developed and experiments were conducted in MATLAB using GEATbx toolbox on five datasets from textile industry: ALBANO, DAGLI, MAO, MARQUES and MAN SHIRT. The marker efficiency in percentage was recorded with best results: 85.17, 81.76, 78.67, 84.67 and 87.19% obtained for the datasets, respectively.