Adaptive beam search lookahead algorithms for the circular packing problem

Akeb, Hakim; Hifi, Mhand; M’Hallah, Rym

doi:10.1111/j.1475-3995.2009.00745.x

Cited by 10 publications

(2 citation statements)

References 15 publications

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“…COP requests each current packing circle contact with two packed circles or the boundary of the container and does not overlap with other circles, and the MHD function can measure the quality of the candidate action of the circle placement. There are several follow-up works based on COP heuristic and MHD function to either solve other variants or improve the algorithm efficiency: Huang, Li, Akeb and Li (2005) adopt this heuristic for packing circles in a rectangular container; Lü and Huang (2008) apply a Pruned-Enriched-Rosenbluth Method (PERM) to improve the performance on the unequal circle packing problem; Akeb, Hifi and M'Hallah (2009); Akeb, Hifi and M'Hallah (2010) further employ the beam search and adaptive beam search algorithms to improve the performance on unequal circle packing problems, and Chen, Tang, Song, Zeng, Peng and Liu (2018) present a greedy heuristic algorithm for solving the PECC problem. There also exist other circle placement heuristics for solving the packing problems, such as Bottom-Left-Fill (Martello, Monaci and Vigo, 2003;Burke, Hellier, Kendall andWhitwell, 2006) andBest Local Position (Hifi andM'Hallah, 2004;Hifi and M'Hallah, 2007).…”

Section: Related Workmentioning

confidence: 99%

Geometric Batch Optimization for the Packing Equal Circles in a Circle Problem on Large Scale

Zhou¹,

He²,

Zheng³

et al. 2023

Preprint

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The problem of packing equal circles in a circle is a classic and famous packing problem, which is well-studied in academia and has a variety of applications in industry. This problem is computationally challenging, and researchers mainly focus on small-scale instances with the number of circular items less than 320 in the literature. In this work, we aim to solve this problem on large scale. Specifically, we propose a novel geometric batch optimization method that not only can significantly speed up the convergence process of continuous optimization but also reduce the memory requirement during the program's runtime. Then we propose a heuristic search method, called solution-space exploring and descent, that can discover a feasible solution efficiently on large scale. Besides, we propose an adaptive neighbor object maintenance method to maintain the neighbor structure applied in the continuous optimization process. In this way, we can find high-quality solutions on large scale instances within reasonable computational times. Extensive experiments on the benchmark instances sampled from = 300 to 1,000 show that our proposed algorithm outperforms the state-of-the-art algorithms and performs excellently on large scale instances. In particular, our algorithm found 10 improved solutions out of the 21 well-studied moderate scale instances and 95 improved solutions out of the 101 sampled large scale instances. Furthermore, our geometric batch optimization, heuristic search, and adaptive maintenance methods are general and can be adapted to other packing and continuous optimization problems.

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Section: Related Workmentioning

confidence: 99%

Geometric Batch Optimization for the Packing Equal Circles in a Circle Problem on Large Scale

Zhou¹,

He²,

Zheng³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…So, some heuristic methods are generally proposed to solve it. For the circular packing problem in a rectangular container, the solving algorithms include the heuristic tabu search algorithm [1], the heuristic algorithm based on bounded enumeration strategy for evaluating corner placement [2], et al For the problem of packing circles into a larger circular container, some authors have developed various heuristic algorithms to generate approximate solutions, including the quasi-physical quasi-human algorithm [3][4][5], the complete quasi-physical algorithm [6], the Pruned-Enriched Rosenbluth Method (PERM) [7], the dynamic adaptive local search algorithm [8], the simulated annealing (SA) [9] and its improved algorithms [10,11], the beam search algorithm [12] and the adaptive beam search algorithm [13], the energy landscape paving (ELP) method [14,15], the global optimization algorithm based on the quasi-physical method [16], and others.…”

Section: Introductionmentioning

confidence: 99%

A New Heuristic Algorithm for Packing Equal Circles into A Larger Equilateral Triangular Container

Liu¹,

Zhang²,

Liu³

et al. 2012

IJACT

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This paper studies the problem of packing equal circles into a larger equilateral triangular container, which is concerned with how to pack these circles into the container without overlapping. Its aim is to minimize the edge length of the container as much as possible. By incorporating some heuristic configuration update strategies, a local search strategy based on the gradient method and the dichotomous search (DS) strategy into the simulated annealing (SA) algorithm, a new heuristic algorithm, the heuristic simulated annealing algorithm based on dichotomous search (HSADS), is put forward for solving this problem. In HSADS, the heuristic configuration update strategies are used to produce new configurations, and the gradient method is used to search for lower-energy minima near newly generated configurations, and the dichotomous search strategy is used to gain the minimal edge length of the equilateral triangular container. By testing six equal circles instances from the literature, the proposed algorithm improves the best known results of them so far. The experimental results show that HSADS is an effective algorithm for the problem of packing equal circles into a larger equilateral triangular container.

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Tabu search algorithm combined with global perturbation for packing arbitrary sized circles into a circular container

Huang

2011

Sci. China Inf. Sci.

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Tabu search algorithm combined with global perturbation for packing arbitrary sized circles into a circular container SCIENTIA SINICA Informationis 42, 843 (2012); Heuristic algorithm based on tabu search for the circular packing problem with equilibrium constraints SCIENTIA SINICA Informationis 41, 1076 (2011); Packing unequal circles into a square container based on the narrow action spaces SCIENCE CHINA Information Sciences 61, 048104 (2018);Abstract The arbitrary sized circle packing problem (ACP) is concerned about how to pack a number of arbitrary sized circles into a smallest possible circular container without overlapping. As a classical NP-hard problem, ACP is theoretically important and is often encountered in practical applications. Based on the already existing Quasi-physical method, this paper proposes a hybrid algorithm named GP-TS which combines tabu search with global perturbation to solve the two-dimensional ACP. The Quasi-physical method is a continuous optimization method which is used to obtain a local optimal configuration from any initial configuration. The tabu search procedure iteratively updates the incumbent configuration with its best neighboring configuration according to some forbidden rule and aspiration criterion. If the configuration obtained by the tabu search procedure does not satisfy the constraints, the global perturbation operator is subsequently applied in order that the search jumps out of the current local optimum without destroying the incumbent configuration too much. After that, the tabu search procedure is launched again. GP-TS is performed by repeating this process until the stop criterion is met. Computational experiments based on 3 sets of representative instances show that GP-TS can improve many best known results within reasonable time.approximate solutions instead of the global optimal one within reasonable time become the only feasible approaches for solving NP-hard problems.This paper studies the two-dimensional arbitrary sized circle packing problem (ACP) as to how to pack a number of arbitrary sized circles into a smallest possible circular container without overlapping in two-dimensional situation. For this problem, almost all the existing approaches are heuristic algorithms, which can be mainly classified into two categories: Constructive approaches and perturbation-based approaches. The frameworks of constructive approaches are very different from those of perturbationbased approaches, just as described as follows.Constructive approaches attempt to pack the circles one by one in sequence into the container according to some constructive rules, until all the circles are packed feasibly. The key points include: (1) How to design the constructive rules? (2) Which circle should be selected to pack at each step? (3) Where to pack the selected circle? (4) Is backtracking necessary? If necessary, how to backtrack? Different ways of tackling these questions lead to different algorithms, such as the corner-occupying algorithm A1.5 [12], the PERM method [13], ...

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Adaptive beam search lookahead algorithms for the circular packing problem

Cited by 10 publications

References 15 publications

Geometric Batch Optimization for the Packing Equal Circles in a Circle Problem on Large Scale

Geometric Batch Optimization for the Packing Equal Circles in a Circle Problem on Large Scale

A New Heuristic Algorithm for Packing Equal Circles into A Larger Equilateral Triangular Container

Tabu search algorithm combined with global perturbation for packing arbitrary sized circles into a circular container

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