Solving Irregular Strip Packing problems by hybridising simulated annealing and linear programming (original) (raw)
Related papers
2013
This paper addresses the Irregular Strip Packing problem, a particular case of Cutting and Packing problems in which a set of polygons has to be packed within a rectangular object. To identify good quality solutions, we propose a hybrid methodology based on a meta-heuristic engine (i.e., Genetic Algorithm) and a well known placement heuristic called Bottom-Left. In addition, differently from several approaches presented in the literature, we investigate the application of the No-fit Polygon as a placement tool for obtaining local optima. The results are further improved by a shrinking algorithm that works within the meta-heuristic component. To assess the potentials of the proposed methodology, computational experiments performed on a set of diffcult benchmark instances of the Irregular Strip Packing problem are discussed here for evaluation purposes.
2006
The irregular strip packing problem asks to place a set of polygons within a rectangular strip of fixed height without overlap, so as to minimize the strip width required. We consider an overlap minimization problem which minimizes the amount of overlap penalty for all pairs of polygons within a given bound of strip width. We propose a local search algorithm which translates a polygon in horizontal and vertical directions iteratively, and incorporate it in metaheuristic approaches called the iterated local search and the guided local search. Computational results show that our algorithm is competitive with other existing algorithms.
Extended local search and polygon grouping for 2D irregular strip packing problem
International Conference on ICT for Smart Society, 2013
Strip Packing Problem (SPP) is a problem of laying a set of objects into a rectangular container with minimum length. Objects can be regular and irregular polygons, while the container has fixed width and length. This study used modified extended local search (ELS) and grouping polygon to solve the SPP. First, polygons are grouped based on convex hull and bounding box to produce tight combination of polygons and near to rectangular shape clusters. Second, layout initialization using a bottom-left algorithm is performed, in which each group of polygon is placed on the most left and bottom position. Then, we start the iterative ELS to change the layout by increasing/reducing the length of the container and rearrange the position of the polygons to be fit in the container. Experiments using DAGLI, DIGHE1, FU, JAKOBS2, MAO and MARQUES dataset showed that polygon grouping was able to reduce the number of polygons 37% on average and the average container efficiency using the proposed method was 77.28%. ƒ Keywords -2D Irregular Strip Packing Problem, local search, tabu search, polygon grouping.
A two-stage intelligent search algorithm for the two-dimensional strip packing problem
2011
This paper presents a two-stage intelligent search algorithm for a two-dimensional strip packing problem without guillotine constraint. In the first stage, a heuristic algorithm is proposed, which is based on a simple scoring rule that selects one rectangle from all rectangles to be packed, for a given space. In the second stage, a local search and a simulated annealing algorithm are combined to improve solutions of the problem. In particular, a multi-start strategy is designed to enhance the search capability of the simulated annealing algorithm. Extensive computational experiments on a wide range of benchmark problems from zero-waste to non-zero-waste instances are implemented. Computational results obtained in less than 60 seconds of computation time show that the proposed algorithm outperforms the supposedly excellent algorithms reported recently, on average. It performs particularly better for large instances.
A two-phase heuristic for strip packing: Algorithm and probabilistic analysis
Operations Research Letters, 1987
The strip packing problem consists in laying out a specified list of rectangular pieces on a rectangular strip of fixed width but infinite length, in such a way as to minimize the length of ~Lrip used. We present a novel heuristic algorithm for this problem, based on a two-phased approach: the strategic and the tactical; the former has a global view of the problem and proposes a list of patterns to the latter, which in turn is in charge of actually laying out these patterns. The strategic module is based on a linear programming relaxation of the problem, whereas the tactical module is a recursive algorithm based on repeated knapsack operations. The performance of the algoriti~m is analyzed through a probalistic analysis on its relative deviation from the (unknown) optimal solution: the deviation is found to converge to zero as problem size increases under some conditions on the problem data.
Strip packing based on local search and a randomized best-fit
We present an incomplete algorithm with no user-defined parameter for handling the strip-packing problem, a variant of the famous 2D bin-packing. The performance of our approach is due to several devices. We propose a move, based on the geometry of the layout, which is made incremental by maintaining the set of maximal holes. For escaping from local minima, the Intensification Diversification Walk (ID Walk) metaheuristic is used. ID Walk manages only one parameter that is automatically tuned by our tool. We focus here on the greedy heuristics used to perform the moves and to compute the first layout before running the metaheuristic. In particular, we propose a variant of the well-known Best-fit (decreasing) (BF), called RBF, in which the criterion (i.e., height, width, perimeter, surface) changes every time a hole is selected. This simple way to randomize the most efficient greedy strategy is a key for obtaining good bounds while diversifying the layouts. This paper provides an experimental evidence that a local search approach can be competitive with the best known incomplete algorithms.
An improved algorithm for the strip packing problem
2012
This paper solves the strip packing problem (SPP) that consists in packing a set of circular objects into a rectangle of fixed width and unlimited length. The objective is to minimize the length of the rectangle that will contain all the objects such that no object overlaps another one. The proposed algorithm uses a look-ahead method combined with beam search and a restarting strategy. The particularity of this algorithm is that it can achieve good results quickly (faster than other known methods and algorithms) even when the number of objects is large. The results obtained on well-known benchmark instances from the literature show that the algorithm improves a lot of best known solutions.
A new metaheuristic genetic-based placement algorithm for 2D strip packing
Journal of Industrial Engineering International, 2014
Given a container of fixed width, infinite height and a set of rectangular block, the 2D-strip packing problem consists of orthogonally placing all the rectangles such that the height is minimized. The position is subject to confinement of no overlapping of blocks. The problem is a complex NP-hard combinatorial optimization, thus a heuristic based on genetic algorithm is proposed to solve it. In this paper, we give a hybrid approach which combined genetic encoding and evolution scheme with the proposed placement approach. Such a combination resulted in better population evolution and faster solution convergence to optimal. The approach is subjected to a comprehensive test using benchmark instances. The computation results validate the solution and the effectiveness of the approach.
An efficient hyperheuristic for strip-packing problems
2008
In this paper we introduce a hyperheuristic to solve hard strip packing problems. The hyperheuristic manages a sequence of greedy low-level heuristics, each element of the sequence placing a given number of objects. A low-level solution is built by placing the objects following the sequence of low-level heuristics. The hyperheuristic performs a hill-climbing algorithm on this sequence by testing different moves (adding, removing, replacing a low-level heuristic). The results we obtained are very encouraging and improve the results from the single heuristics tests. Thus, we conclude that the collaboration among heuristics is an interesting approach to solve hard strip packing problems.