Solving Irregular Strip Packing Problems With Free Rotations Using Separation Lines

Solving nesting problems or irregular strip packing problems is to position polygons in a fixed width and unlimited length strip, obeying polygon integrity containment constraints and non-overlapping constraints, in order to minimize the used length of the strip. To ensure non-overlapping, we used separation lines. A straight line is a separation line if given two polygons, all vertices of one of the polygons are on one side of the line or on the line, and all vertices 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 use the nonlinear programming solver IPOPT (an algorithm of interior points type), which is part of COIN-OR. Computational tests were run using established benchmark instances and the results were compared with the ones obtained with other methodologies in the literature that use free rotation

A general genetic algorithm for one and two dimensional cutting and packing problems

Cutting and packing problems are combinatorial optimisation problems. The major interest in these problems is their practical significance, in manufacturing and other business sectors. In most manufacturing situations a raw material usually in some standard size has to be divided or be cut into smaller items to complete the production of some product. Since the cost of this raw material usually forms a significant portion of the input costs, it is therefore desirable that this resource be used efficiently. A hybrid general genetic algorithm is presented in this work to solve one and two dimensional problems of this nature. The novelties with this algorithm are: A novel placement heuristic hybridised with a Genetic Algorithm is introduced and a general solution encoding scheme which is used to encode one dimensional and two dimensional problems is also introduced

A comparison of different recombination operators for the 2-dimensional strip packing problem

In this paper, the three-stage two-dimensional rectangular strip packing problem is tackled using genetic algorithms. A new problem dependent recombination operator, called best inherited levels recombination (BIL), is introduced. A comparison of its performance is carried out with respect to four classical recombination operators. A complete study of the influence of the recombination operators on the genetic search, including the trade-off between exploration and exploitation in the search process, is presented. The results show that the use of our specialized BIL recombination outperforms the others more generic on all problem instances for all the metrics testedVII Workshop de Agentes y Sistemas Inteligentes (WASI)Red de Universidades con Carreras en Informática (RedUNCI

Meta-heuristic Algorithms for Nesting Problem of Rectangular Pieces

Nesting problems consist of placing multiple items onto larger shapes finding a good arrangement. The goal of the nesting process is to minimize the waste of material. It is common to assume, as in the present work, that the stock sheet has fixed width and infinite height, since in the real world a company may have to cut pieces from a roll of material. The complexity of such problems is often faced with a two-stage approach, so-called \u201chybrid algorithm\u201d, combining a placement routine and a meta-heuristic algorithm. Starting from a given positioning sequence, the placement routine generates a non-overlapping configuration. The encoded solution is manipulated and modified by the meta-heuristic algorithm to generate a new sequence that brings to a better value of the objective function (in this case the height of the strip). The proposed method consists in placing the rectangles inside a strip and in combining the meta-heuristic algorithms with the No Fit Polygon algorithm. The software has been developed in Python language using proper libraries to solve the meta-heuristic techniques (Inspyred) and the geometric problems (Polygon). The results show the effectiveness of the proposed method; moreover, with regard to problems reported in literature employed as benchmark of the nesting algorithms, the degree of occupation values (Efficiency Ratio, ER) are shown to be higher than 90%

Greedy seeding procedure for GAs solving a strip packing problem

In this paper, the two-dimensional strip packing problem with 3-stage level patterns is tackled using genetic algorithms (GAs). We evaluate the usefulness of a greedy seeding procedure for creating the initial population, incorporating problem knowledge. This is motivated by the expectation that the seeding will speed up the GA by starting the search in promising regions of the search space. An analysis of the impact of the seeded initial population is offered, together with a complete study of the influence of these modifications on the genetic search. The results show that the use of an appropriate seeding of the initial population outperforms existing GA approaches on all the used problem instances, for all the metrics used, and in fact it represents the new state of the art for this problem.Red de Universidades con Carreras en Informática (RedUNCI

Greedy seeding procedure for GAs solving a strip packing problem

In this paper, the two-dimensional strip packing problem with 3-stage level patterns is tackled using genetic algorithms (GAs). We evaluate the usefulness of a greedy seeding procedure for creating the initial population, incorporating problem knowledge. This is motivated by the expectation that the seeding will speed up the GA by starting the search in promising regions of the search space. An analysis of the impact of the seeded initial population is offered, together with a complete study of the influence of these modifications on the genetic search. The results show that the use of an appropriate seeding of the initial population outperforms existing GA approaches on all the used problem instances, for all the metrics used, and in fact it represents the new state of the art for this problem.Red de Universidades con Carreras en Informática (RedUNCI

Two-dimensional placement compaction using an evolutionary approach: a study

The placement problem of two-dimensional objects over planar surfaces optimizing given utility functions is a combinatorial optimization problem. Our main drive is that of surveying genetic algorithms and hybrid metaheuristics in terms of final positioning area compaction of the solution. Furthermore, a new hybrid evolutionary approach, combining a genetic algorithm merged with a non-linear compaction method is introduced and compared with referenced literature heuristics using both randomly generated instances and benchmark problems. A wide variety of experiments is made, and the respective results and discussions are presented. Finally, conclusions are drawn, and future research is defined