Iterated tabu search for the circular open dimension problem

Abstract

This paper mainly investigates the circular open dimension problem (CODP), which consists of packing a set of circles of known radii into a strip of fixed width and unlimited length without overlapping. The objective is to minimize the length of the strip. An iterated tabu search approach, named ITS, is proposed. ITS starts from a randomly generated solution and attempts to gain improvements by a tabu search procedure. After that, if the obtained solution is not feasible, a perturbation operator is subsequently employed to reconstruct the incumbent solution and an acceptance criterion is implemented to determine whether or not accept the perturbed solution. This process is repeated until a feasible solution has been found or the allowed computation time has been elapsed. Computational experiments based on well-known benchmark instances show that ITS produces quite competitive results with respect to the best known results. For 18 representative CODP instances taken from the literature, ITS succeeds in improving 13 best known results within reasonable time. In addition, for another challenging related variant: the problem of packing arbitrary sized circles into a circular container, ITS also succeeds in improving many best known results. Supplementary experiments are also provided to analyze the influence of the perturbation operator, as well as the acceptance criterion.

Аспекты Использования Алгоритма Силовой Укладки Графа В Промышленной Технологии Укладки Кабелей В Судостроении

“…На практике нередко выбирается «жадные» стратегии [4] упаковки. Много работ посвящено применению итерационных методов и рандомизированным стратегиям, направленным на преодоление локальных экстремумов [4,5], таких как имитации отжига [6], запретных направлений и многократного рестарта [7], генетических алгоритмов [8,9] и других. Отдельный практический интерес имеют так называемые многоуровневые алгоритмы [10], основанные на последовательной редукции исходных данных, переходу к более простой задаче, ее решении и восстановлении решения в терминах исходной задачи.…”

Adaptive Simulated Annealing with Greedy Search for the Circle Bin Packing Problem

“…The quasi-physical methods are based on a physical gradient or human-intuitive behavior to enhance the solutions obtained by problem-oriented heuristics (Wang, Huang, Zhang and Xu, 2002;Lubachevsky and Graham, 1997), while meta-heuristic optimizations usually have an evaluation function devised to employ a trade-off between randomization and local search, with the goal of directing and remodeling basic heuristics to generate feasible solutions. Typical algorithms include a simulated annealing approach (SA) (Hifi, Paschos and Zissimopoulos, 2004), monotonic basin hopping approach (MBH) (Grosso, Jamali, Locatelli and Schoen, 2010), iterated tabu search(ITS) (Fu, Huang and Lü, 2013), action-space-based global optimization algorithm (ASGO) (He, Huang and Yang, 2015), formulation space search (FSS) (López and Beasley, 2016), adaptive tabu search and variable neighborhood descent (ATS-VND) (Zhizhong, Xinguo, Kun and Zhanghua, 2018), etc.…”

Optimized Packing Clusters of Objects in a Rectangular Container

“…Various shapes of objects were studied. In particular, cutting and packing problems for ellipses are presented in [3][4][5][6], circular packing problems are investigated in [7][8][9][10][11][12][13], and packing problems for convex polygons are considered in [11][12][13][14][15][16]. Papers [17][18][19][20][21] are devoted to irregular packing involving arbitrary shaped objects.…”