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Design of production networks for the production of floating substructures for offshore wind turbines
Published in C. Guedes Soares, Developments in Renewable Energies Offshore, 2020
B. Illgen, J. Sender, H. Herholz, W. Flügge
As already indicated by Figure 5, the available quantitative capacity of a certain resource of a production site can be idealized as a kind of container or bin. Therefore, the employment of Bin Packing algorithms seems to be applicable if the capacity demand on this resource is described as the filling of the respective container/bin. Bin Packing problems are defined as n objects, each of a certain but variable size that are to be assigned to a non-defined number of bins of equal capacity/size. Thereby, as few bins as possible should be used and certainly the total size of the objects assigned to a bin must not exceed its capacity (Korte & Vygen 2018). Depending on the task to be performed, a distinction is made between one-, two-, three- or even four-dimensional Bin Packing algorithms (Eliiyi & Türsel Eliiyi 2009). Since the present approach is not based on a task with geometric properties of the objects, further discussions will focus on one-dimensional Bin Packing.
Introduction and Background
Published in Ossama Abdelkhalik, Algorithms for Variable-Size Optimization, 2021
Optimal grouping problems have received a great deal of interest. Examples include the optimal bin packing problems [44], where a set of boxes of different sizes should be packed in containers of a given size, in order to minimize the number of containers. Reference [45] points out that standard FSDS global optimization algorithms are inefficient in handling this type of problem. A Grouping Genetic Algorithm (GGA) was developed to handle this type of problem, see, e.g., reference [43]. The GGA is group oriented, and hence is characterized by a VSDS (one solution may have two groups while another may have three groups). Tailored new definitions for genetic operations had to be introduced in the GGA theory in order to handle the resulting VSDS optimization problem.
Heuristics for Two-Dimensional Bin-Packing Problems
Published in Bogdan M. Wilamowski, J. David Irwin, Intelligent Systems, 2018
Tak Ming Chan, Filipe Alvelos, Elsa Silva, J.M. Valério de Carvalho
Bin-packing problems are well-known combinatorial optimization problems. They are closely related to cutting stock problems and these two problem types are conceptually equal (Wäscher et al. 2007). Thus, some terminologies borrowed from cutting stock problems will be used in the following discussion. The common objective of two-dimensional bin-packing problems is to pack a given set of rectangular items to an unlimited number of identical rectangular bins such that the total number of used bins is minimized and subject to three limitations: (1) all items must be packed to bins, (2) all items cannot overlap, and (3) the edges of items are parallel to those of the bins. Nowadays, these problems are always faced by wood, glass, paper, steel, and cloth industries.
Sparsest packing of two-dimensional objects
Published in International Journal of Production Research, 2021
Tatiana Romanova, Alexander Pankratov, Igor Litvinchev, Sergiy Plankovskyy, Yevgen Tsegelnyk, Olga Shypul
Two-dimensional packing problems consist in allocating a set of two-dimensional objects to a larger container. The objects must be placed completely into the container without overlapping and optimising a certain criterion (i.e. minimising waste or maximising the number of packed objects). Packing is called regular if simple shapes (e.g. circles, ellipses, rectangles or convex polygons) are considered for the objects and the container. Irregular packing (also known as nesting) corresponds to more general shapes, such as convex and non-convex polygons, shapes bounded by arcs and line segments, etc. Packing problems arise in many logistic and industrial applications and are NP-hard (Chazelle, Edelsbrunner, and Guibas 1989).
Aggregation of clans to speed-up solving linear systems on parallel architectures
Published in International Journal of Parallel, Emergent and Distributed Systems, 2022
Dmitry A. Zaitsev, Tatiana R. Shmeleva, Piotr Luszczek
The multi-way number partitioning problem [43] consists of dividing a given multi-set of n integers into a given number k of subsets, minimising the difference between the smallest and the largest subset sums. A specific variant called a bin packing perfectly suits our problem best. In the bin packing problem [6], objects of different volumes are packed into a finite number of bins or containers, each one of a given volume in a way that minimises the number of bins used. Both problems are known to be NP-complete though a series of fast and relatively good quality heuristic techniques are available.
A bi-level optimisation approach for assembly line design using a nested genetic algorithm
Published in International Journal of Production Research, 2021
Daria Leiber, Gunther Reinhart
The ALB problem can be viewed as a special type of bin packing problem. The bin packing problem is a well-studied optimisation problem, where a given number of objects with fixed sizes are arranged into bins and the goal is to minimise the number of bins needed. The assignment of process steps to stations is analogous to this problem statement, with the added constraint of precedence relations (Falkenauer and Delchambre 1992).