TS2PACK: A Two-Level Tabu Search for the Three-dimensional Bin Packing Problem

Three-dimensional orthogonal bin packing is a problem NP-hard in the strong sense where a set of boxes must be orthogonally packed into the minimum number of three-dimensional bins. We present a two-level tabu search for this problem. The first-level aims to reduce the number of bins. The second optimizes the packing of the bins. This latter procedure is based on the Interval Graph representation of the packing, proposed by Fekete and Schepers, which reduces the size of the search space. We also introduce a general method to increase the size of the associated neighborhoods, and thus the quality of the search, without increasing the overall complexity of the algorithm. Extensive computational results on benchmark problem instances show the effectiveness of the proposed approach, obtaining better results compared to the existing one

Automating the packing heuristic design process with genetic programming

The literature shows that one-, two-, and three-dimensional bin packing and knapsack packing are difficult problems in operational research. Many techniques, including exact, heuristic, and metaheuristic approaches, have been investigated to solve these problems and it is often not clear which method to use when presented with a new instance. This paper presents an approach which is motivated by the goal of building computer systems which can design heuristic methods. The overall aim is to explore the possibilities for automating the heuristic design process. We present a genetic programming system to automatically generate a good quality heuristic for each instance. It is not necessary to change the methodology depending on the problem type (one-, two-, or three-dimensional knapsack and bin packing problems), and it therefore has a level of generality unmatched by other systems in the literature. We carry out an extensive suite of experiments and compare with the best human designed heuristics in the literature. Note that our heuristic design methodology uses the same parameters for all the experiments. The contribution of this paper is to present a more general packing methodology than those currently available, and to show that, by using this methodology, it is possible for a computer system to design heuristics which are competitive with the human designed heuristics from the literature. This represents the first packing algorithm in the literature able to claim human competitive results in such a wide variety of packing domains

An online packing heuristic for the three-dimensional container loading problem in dynamic environments and the Physical Internet

In this paper, we consider the online three-dimensional container loading problem. We develop a novel online packing algorithm to solve the three-dimensional bin packing problem in the online case where items are not know well in advance and they have to be packed in real-time when they ar-rive. This is relevant in many real-world scenarios such as automated cargo loading in warehouses. This is also relevant in the new logistics model of Physical Internet. The effectiveness of the online packing heuristic is evalu-ated on a set of generated data. The experimental results show that the algo-rithm could solve the 3D container loading problems in online fashion and is competitive against other algorithms both in the terms of running time, space utilization and number of bins

Online dynamic bin packing

In this thesis we study online algorithms for dynamic bin packing. An online algorithm is presented with input throughout time and must make irrevocable decisions without knowledge of future input. The classical bin packing problem is a combinatorial optimization problem in which a set of items must be packed into a minimum number of uniform-sized bins without exceeding their capacities. The problem has been studied since the early 1970s and many variants continue to attract researchers’ attention today. The dynamic version of the bin packing problem was introduced by Coffman, Garey and Johnson in 1983. The problem is a generalization of the bin packing problem in which items may arrive and depart dynamically. In this setting, an online algorithm for bin packing is presented with one item at a time, without knowledge of its departure time, nor arrival and departure times of future items, and must decide in which bin the item should be packed. Migration of items between bins is not allowed, however rearrangement of items within a bin is permitted. The objective of problem is to minimize the maximum number of bins used over all time. In multi-dimensional generalizations of the problem, multi-dimensional items must be packed without overlap in multi-dimensional bins of uniform size in each dimension. In this work, we study the setting where items are oriented and cannot be rotated. We first consider online one-dimensional dynamic bin packing and present a lower bound of 8/3 ∼ 2.666 on the achievable competitive ratio of any deterministic online algorithm, improving the best known 2.5-lower bound. Since the introduction of the problem by Coffman, Garey and Johnson, the progress on the problem has focused on improving the original lower bound of 2.388 to 2.428, and to the best known 2.5-lower bound. Our improvement from 2.5 to 8/3 ∼ 2.666 makes a big step forward in closing the gap between the lower bound and the upper bound, which currently stands at 2.788. Secondly we study the online two- and three-dimensional dynamic bin packing problem by designing and analyzing algorithms for special types of input. Bar-Noy et al. initiated the study of the one-dimensional unit fraction bin packing problem, a restricted version where all sizes of items are of the form 1/k, for some integer k > 0. Another related problem is for power fraction items, where sizes are of the form 1/2k, for some integer k ≥ 0. We initiate the study of online multi-dimensional dynamic bin packing of unit fraction items and power fraction items, where items have lengths unit fraction and power fraction in each dimension, respectively. While algorithms for general input are suitable for unit fraction and power fraction items, their worst-case performance guarantees are the same for special types of input. For unit fraction and power fraction items, we design and analyze online algorithms that achieve better worst-case performance guarantees compared to their classical counterparts. Our algorithms give careful consideration to unit and power fraction items, which allows us to reduce the competitive ratios for these types of inputs. Lastly we focus on obtaining lower bounds on the performance of the family of Any- Fit algorithms (Any-Fit, Best-Fit, First-Fit, Worst-Fit) for online multi-dimensional dynamic bin packing. Any-Fit algorithms are classical online algorithms initially studied for the one-dimensional version of the bin packing problem. The common rule that the algorithms use is to never pack a new item to a new bin if the item can be packed in any of the existing bins. While the family of Any-Fit algorithms is always O(1)-competitive for one-dimensional dynamic bin packing, we show that this is no longer the case for multi-dimensional dynamic bin packing when using Best-Fit and Worst-Fit, even if the input consists of power fraction items or unit fraction items. For these restricted inputs, we prove that Best-Fit and Worst-Fit have unbounded competitive ratios, while for First-Fit we provide lower bounds that are higher than the lower bounds for any online algorithm. Furthermore, for general input we show that all classical Any-Fit algorithms are not competitive for online multi-dimensional dynamic bin packing

Real-polarized genetic algorithm for the three-dimensional bin packing problem

This article presents a non-deterministic approach to the Three-Dimensional Bin Packing Problem, using a genetic algorithm. To perform the packing, an algorithm was developed considering rotations, size constraints of objects and better utilization of previous free spaces (flexible width). Genetic operators have been implemented based on existing operators, but the highlight is the Real-Polarized crossover operator that produces new solutions with a certain disturbance near the best parent. The proposal presented here has been tested on instances already known in the literature and real instances. A visual comparison using boxplot was done and, in some situations, it was possible to say that the obtained results are statistically superior than the ones presented in the literature. In a given instance class, the presented Genetic Algorithm found solutions reaching up to 70% less bins

Modified genetic algorithm as a new approach for solving the problem of 3d packaging

In this paper, we proposed one of the options for developing a new evolutionary heuristic approach for solving the three-dimensional packing problem called BPP (Bin packing problem), as applied to the variation of this problem with a single container and a set of boxes of various dimensions, called the SKP (Single knapsack problem), and The comparison of 11 basic evolutionary heuristic approaches to solving the problem of three-dimensional packing of BPP (Bin packing problem) variations SKP (Single knapsack problem) with the developed new evolutionary heuristic approach to solving BPP using modi cited genetic algorithm (MGA). By performing correlation and statistical analysis using 10 randomly created sets of input data for solving BPP, the effectiveness of MGAs was proved in comparison with 11 basic evolutionary algorithms for solving BPP. Thus, it was confirmed that MGA and similar algorithms can be effectively used to solve such logistic NP-difficult problems

An anytime tree search algorithm for two-dimensional two- and three-staged guillotine packing problems

[libralesso_anytime_2020] proposed an anytime tree search algorithm for the 2018 ROADEF/EURO challenge glass cutting problem (https://www.roadef.org/challenge/2018/en/index.php). The resulting program was ranked first among 64 participants. In this article, we generalize it and show that it is not only effective for the specific problem it was originally designed for, but is also very competitive and even returns state-of-the-art solutions on a large variety of Cutting and Packing problems from the literature. We adapted the algorithm for two-dimensional Bin Packing, Multiple Knapsack, and Strip Packing Problems, with two- or three-staged exact or non-exact guillotine cuts, the orientation of the first cut being imposed or not, and with or without item rotation. The combination of efficiency, ability to provide good solutions fast, simplicity and versatility makes it particularly suited for industrial applications, which require quickly developing algorithms implementing several business-specific constraints. The algorithm is implemented in a new software package called PackingSolver

A genetic programming hyper-heuristic approach to automated packing

This thesis presents a programme of research which investigated a genetic programming hyper-heuristic methodology to automate the heuristic design process for one, two and three dimensional packing problems. Traditionally, heuristic search methodologies operate on a space of potential solutions to a problem. In contrast, a hyper-heuristic is a heuristic which searches a space of heuristics, rather than a solution space directly. The majority of hyper-heuristic research papers, so far, have involved selecting a heuristic, or sequence of heuristics, from a set pre-defined by the practitioner. Less well studied are hyper-heuristics which can create new heuristics, from a set of potential components. This thesis presents a genetic programming hyper-heuristic which makes it possible to automatically generate heuristics for a wide variety of packing problems. The genetic programming algorithm creates heuristics by intelligently combining components. The evolved heuristics are shown to be highly competitive with human created heuristics. The methodology is first applied to one dimensional bin packing, where the evolved heuristics are analysed to determine their quality, specialisation, robustness, and scalability. Importantly, it is shown that these heuristics are able to be reused on unseen problems. The methodology is then applied to the two dimensional packing problem to determine if automatic heuristic generation is possible for this domain. The three dimensional bin packing and knapsack problems are then addressed. It is shown that the genetic programming hyper-heuristic methodology can evolve human competitive heuristics, for the one, two, and three dimensional cases of both of these problems. No change of parameters or code is required between runs. This represents the first packing algorithm in the literature able to claim human competitive results in such a wide variety of packing domains