Rotational placement of irregular polygons over containers with fixed dimensions using simulated annealing and no-fit polygons

Martins, Thiago de Castro; Tsuzuki, Marcos de Sales Guerra

doi:10.1590/s1678-58782008000300005

Cited by 18 publications

(5 citation statements)

References 13 publications

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“…The translation parameter corresponds to an uniform mapping of the perimeter of the collision-free region to the interval [0; 1[. When the collisionfree region is determined for a given item (by removing all no-fit polygons), a point is selected on its perimeter using the translation parameter to place the item [20]. The translation parameter uniquely determines on which point of the no-fit polygon where the item will be translated to.…”

Section: The Proposed Algorithmmentioning

confidence: 99%

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Placement over containers with fixed dimensions solved with adaptive neighborhood simulated annealing

Martins¹,

Tsuzuki²

2009

Bulletin of the Polish Academy of Sciences: Technical Sciences

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Abstract. This work deals with the problem of minimizing the waste of space that occurs on a rotational placement of a set of irregular bi-dimensional items inside a bi-dimensional container. This problem is approached with a heuristic based on Simulated Annealing (SA) with adaptive neighborhood. The objective function is evaluated in a constructive approach, where the items are placed sequentially. The placement is governed by three different types of parameters: sequence of placement, the rotation angle and the translation. The rotation applied and the translation of the polygon are cyclic continuous parameters, and the sequence of placement defines a combinatorial problem. This way, it is necessary to control cyclic continuous and discrete parameters. The approaches described in the literature deal with only type of parameter (sequence of placement or translation). In the proposed SA algorithm, the sensibility of each continuous parameter is evaluated at each iteration increasing the number of accepted solutions. The sensibility of each parameter is associated to its probability distribution in the definition of the next candidate.

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Section: The Proposed Algorithmmentioning

confidence: 99%

“…2.1). For every non-fitted shape, a fixed-depth binary search is performed in order to determinate the largest scale-factor that, applied to it, would allow its placement inside the container with its current rotation [20]. Then, the area of the shape with the largest obtained scalefactor is used to modify the wasted space.…”

Section: 2mentioning

confidence: 99%

Placement over containers with fixed dimensions solved with adaptive neighborhood simulated annealing

Martins¹,

Tsuzuki²

2009

Bulletin of the Polish Academy of Sciences: Technical Sciences

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“…SA with the crystallization heuristic uses feedback to control the parameter named the crystallization factor, which represents the parameter sensibility [9]. SA with the crystallization heuristic was successfully applied to problems with discrete cost functions [10][11][12]. This research improves the crystallization heuristic by combining the Bates and Gaussian distributions.…”

Section: Introductionmentioning

confidence: 99%

Using Feedback Strategies in Simulated Annealing with Crystallization Heuristic and Applications

et al. 2021

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This paper represents how typical advanced engineering design can be structured using a set of parameters and objective functions corresponding to the nature of the problem. The set of parameters can be in different types, including integer, real, cyclic, combinatorial, interval, etc. Similarly, the objective function can be presented in various types including integer (discrete), float, and interval. The simulated annealing with crystallization heuristic can deal with all these combinations of parameters and objective functions when the crystallization heuristic presents a sensibility for real parameters. Herein, simulated annealing with the crystallization heuristic is enhanced by combining Bates and Gaussian distributions and by incorporating feedback strategies to emphasize exploration or refinement, or a combination of the two. The problems that are studied include solving an electrical impedance tomography problem with float parameters and a partially evaluated objective function represented by an interval requiring the solution of 32 sparse linear systems defined by the finite element method, as well as an airplane design problem with several parameters and constraints used to reduce the explored domain. The combination of the proposed feedback strategies and simulated annealing with the crystallization heuristic is compared with existing simulated annealing algorithms and their benchmark results are shown. The enhanced simulated annealing approach proposed herein showed better results for the majority of the studied cases.

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“…But as packing items rectangles that can be rotated only through 901 are used. Martins and Tsuzuki (2008) consider heuristic approach based on simulated annealing for solving rotational placement problems of irregular polygons. Kallrath (2009) considers a problem of packing a set of circles, rectangles and convex polygons into rectangular of minimal area.…”

Section: Introductionmentioning

confidence: 99%

Solving an optimization packing problem of circles and non-convex polygons with rotations into a multiply connected region

Stoyan

Zlotnik

Chugay

2012

Journal of the Operational Research Society

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This paper deals with the packing problem of circles and non-convex polygons, which can be both translated and rotated into a strip with prohibited regions. Using the F-function technique, a mathematical model of the problem is constructed and its characteristics are investigated. Based on the characteristics, a solution approach to the problem is offered. The approach includes the following methods: an optimization method by groups of variables to construct starting points, a modification of the Zoutendijk feasible direction method to search for local minima and a special non-exhaustive search of local minima to find an approximation to a global minimum. A number of numerical results are given. The numerical results are compared with the best known ones.

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Rotational placement of irregular polygons over containers with fixed dimensions using simulated annealing and no-fit polygons

Cited by 18 publications

References 13 publications

Placement over containers with fixed dimensions solved with adaptive neighborhood simulated annealing

Placement over containers with fixed dimensions solved with adaptive neighborhood simulated annealing

Using Feedback Strategies in Simulated Annealing with Crystallization Heuristic and Applications

Solving an optimization packing problem of circles and non-convex polygons with rotations into a multiply connected region

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