A heuristic for the container loading problem: A tertiary-tree-based dynamic space decomposition approach

Increasing fuel costs, post-911 security concerns, and economic globalization provide a strong incentive for container carriers to use available container space more efficiently, thereby minimizing the number of container trips and reducing socio-economic vulnerability. A heuristic algorithm based on a tertiary tree model is proposed to handle the container loading problem (CLP) with weakly heterogeneous boxes. A dynamic space decomposition method based on the tertiary tree structure is developed to partition the remaining container space after a block of homogeneous rectangular boxes is loaded into a container. This decomposition approach, together with an optimal-fitting sequencing and an inner-right-corner-occupying placement rule, permits a holistic loading strategy to pack a container. Comparative studies with existing algorithms and an illustrative example demonstrate the efficiency of this algorithm

PackIt: A Virtual Environment for Geometric Planning

The ability to jointly understand the geometry of objects and plan actions for manipulating them is crucial for intelligent agents. We refer to this ability as geometric planning. Recently, many interactive environments have been proposed to evaluate intelligent agents on various skills, however, none of them cater to the needs of geometric planning. We present PackIt, a virtual environment to evaluate and potentially learn the ability to do geometric planning, where an agent needs to take a sequence of actions to pack a set of objects into a box with limited space. We also construct a set of challenging packing tasks using an evolutionary algorithm. Further, we study various baselines for the task that include model-free learning-based and heuristic-based methods, as well as search-based optimization methods that assume access to the model of the environment. Code and data are available at https://github.com/princeton-vl/PackIt.Comment: Accepted to ICML 202

Online 3D Bin Packing with Constrained Deep Reinforcement Learning

We solve a challenging yet practically useful variant of 3D Bin Packing Problem (3D-BPP). In our problem, the agent has limited information about the items to be packed into the bin, and an item must be packed immediately after its arrival without buffering or readjusting. The item's placement also subjects to the constraints of collision avoidance and physical stability. We formulate this online 3D-BPP as a constrained Markov decision process. To solve the problem, we propose an effective and easy-to-implement constrained deep reinforcement learning (DRL) method under the actor-critic framework. In particular, we introduce a feasibility predictor to predict the feasibility mask for the placement actions and use it to modulate the action probabilities output by the actor during training. Such supervisions and transformations to DRL facilitate the agent to learn feasible policies efficiently. Our method can also be generalized e.g., with the ability to handle lookahead or items with different orientations. We have conducted extensive evaluation showing that the learned policy significantly outperforms the state-of-the-art methods. A user study suggests that our method attains a human-level performance

Learning Physically Realizable Skills for Online Packing of General 3D Shapes

We study the problem of learning online packing skills for irregular 3D shapes, which is arguably the most challenging setting of bin packing problems. The goal is to consecutively move a sequence of 3D objects with arbitrary shapes into a designated container with only partial observations of the object sequence. Meanwhile, we take physical realizability into account, involving physics dynamics and constraints of a placement. The packing policy should understand the 3D geometry of the object to be packed and make effective decisions to accommodate it in the container in a physically realizable way. We propose a Reinforcement Learning (RL) pipeline to learn the policy. The complex irregular geometry and imperfect object placement together lead to huge solution space. Direct training in such space is prohibitively data intensive. We instead propose a theoretically-provable method for candidate action generation to reduce the action space of RL and the learning burden. A parameterized policy is then learned to select the best placement from the candidates. Equipped with an efficient method of asynchronous RL acceleration and a data preparation process of simulation-ready training sequences, a mature packing policy can be trained in a physics-based environment within 48 hours. Through extensive evaluation on a variety of real-life shape datasets and comparisons with state-of-the-art baselines, we demonstrate that our method outperforms the best-performing baseline on all datasets by at least 12.8% in terms of packing utility.Comment: ACM Transactions on Graphics (TOG

Container Loading Problems: A State-of-the-Art Review

Container loading is a pivotal function for operating supply chains efficiently. Underperformance results in unnecessary costs (e.g. cost of additional containers to be shipped) and in an unsatisfactory customer service (e.g. violation of deadlines agreed to or set by clients). Thus, it is not surprising that container loading problems have been dealt with frequently in the operations research literature. It has been claimed though that the proposed approaches are of limited practical value since they do not pay enough attention to constraints encountered in practice.In this paper, a review of the state-of-the-art in the field of container loading will be given. We will identify factors which - from a practical point of view - need to be considered when dealing with container loading problems and we will analyze whether and how these factors are represented in methods for the solution of such problems. Modeling approaches, as well as exact and heuristic algorithms will be reviewed. This will allow for assessing the practical relevance of the research which has been carried out in the field. We will also mention several issues which have not been dealt with satisfactorily so far and give an outlook on future research opportunities

Optimal Packing of Irregular 3D Objects For Transportation and Disposal

This research developed algorithms, platforms, and workflows that can optimize the packing of 3D irregular objects while guaranteeing an acceptable processing time for real-life problems, including but not limited to nuclear waste packing optimization. Many nuclear power plants (NPPs) are approaching their end of intended design life, and approximately half of existing NPPs will be shut down in the next two decades. Since decommissioning and demolition of these NPPs will lead to a significant increase in waste inventory, there is an escalating demand for technologies and processes that can efficiently manage the decommissioning and demolition (D&D) activities, especially optimal packing of NPP waste. To minimize the packing volume of NPP waste, the objective is to arrange irregular-shaped waste objects into one or a set of containers such that container volume utilization is maximized, or container size is minimized. Constraints also include weight and radiation limits per container imposed by transportation requirements and the waste acceptance requirements of storage facilities and repositories. This problem falls under the theoretical realm of cutting and packing problems, precisely, the 3D irregular packing problem. Despite its broad applications and substantial potential, research on 3D irregular cutting and packing problems is still nascent, and largely absent in construction and civil engineering. Finding good solutions for real-life problems, such as the one mentioned above, through current approaches is computationally expensive and time-consuming. New algorithms and technologies, and processes are required. This research adopted 3D scanning as a means of geometry acquisition of as-is 3D irregular objects (e.g., nuclear waste generated from decommissioning and demolition of nuclear power plants), and a metaheuristics-based packing algorithm is implemented to find good packing configurations. Given the inefficiency of fully autonomous packing algorithms, a virtual reality (VR) interactive platform allowing human intervention in the packing process was developed to decrease the time and computation power required, while potentially achieving better outcomes. The VR platform was created using the Unity® game engine and its physics engine to mimic real-world physics (e.g., gravity and collision). Validation in terms of feasibility, efficiency, and rationality of the presented algorithms and the VR platform is achieved through functional demonstration with case studies. Different optimal packing workflows were simulated and evaluated in the VR platform. Together, these algorithms, the VR platform, and workflows form a rational and systematic framework to tackle the optimal packing of 3D irregular objects in civil engineering and construction. The overall framework presented in this research has been demonstrated to effectively provide packing configurations with higher packing efficiency in an adequate amount of time compared to conventional methods. The findings from this research can be applied to numerous construction and manufacturing activities, such as optimal packing of prefabricated construction assemblies, facility waste management, and 3D printing