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The irregular strip packing problem (ISPP) is a class of cutting and packing problem (C&P) in which a set of items with arbitrary formats must be placed in a container with a variable length. The aim of this work is to minimize the area needed to accommodate the given demand. ISPP is present in various types of industries from manufacturers to exporters (e.g., shipbuilding, clothes, and glass). In this paper, we propose a parallel Biased Random-Key Genetic Algorithm (µ-BRKGA) with multiple populations for the ISPP by applying a collision-free region (CFR) concept as the positioning method, in order to obtain an efficient and fast layout solution. The layout problem for the proposed algorithm is represented by the placement order into the container and the corresponding orientation. In order to evaluate the proposed (µ-BRKGA) algorithm, computational tests using benchmark problems were applied, analyzed, and compared with different approaches.

This paper addresses the irregular strip packing problem, a particular two-dimensional cutting and packing problem in which convex/nonconvex shapes (polygons) have to be packed onto a single rectangular object. We propose an approach that prescribes the integration of a metaheuristic engine (i.e., genetic algorithm) and a placement rule (i.e., greedy bottom-left). Moreover, a shrinking algorithm is encapsulated into the metaheuristic engine to improve good quality solutions. To accomplish this task, we propose a no-fit polygon based heuristic that shifts polygons closer to each other. Computational experiments performed on standard benchmark problems, as well as practical case studies developed in the ambit of a large textile industry, are also reported and discussed here in order to testify the potentialities of proposed approach.

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