Recent progress in the field of robotic manipulation has generated interest in fully automatic object packing in warehouses. This paper proposes a formulation of the packing problem that is tailored to the automated warehousing domain. Besides minimizing waste space inside a container, the problem requires stability of the object pile during packing and the feasibility of the robot motion executing the placement plans. To address this problem, a set of constraints are formulated, and a constructive packing pipeline is proposed to solve for these constraints. The pipeline is able to pack geometrically complex, non-convex objects with stability while satisfying robot constraints. In particular, a new 3D positioning heuristic called Heightmap-Minimization heuristic is proposed, and heightmaps are used to speed up the search. Experimental evaluation of the method is conducted with a realistic physical simulator on a dataset of scanned real-world items, demonstrating stable and high-quality packing plans compared with other 3D packing methods.
On the other hand, irregular shape packing, often referred to as nesting, is a more recent variant of the cutting and packing problem. With non-rectilinear geometries, the search space is infinite, with few guidelines available to narrow it down to finite options. Metaheuristics such as Simulated Annealing (SA) @cite_8 @cite_3 @cite_22 and Guided Local Search (GLS) @cite_25 @cite_7 @cite_15 @cite_1 @cite_19 are the most popular tools for solving a nesting problem. These methods commonly start with an initial placement and iteratively improve the placement by moving the pieces in the neighborhood while minimizing an objective function (e.g., overlap in the system). In addition to metaheuristic methods, recent work has also proposed constructive positioning heuristics for 3D irregular objects, such as Deepest-Bottom-Left-Fill (DBLF), which places items in the deepest, bottom-most, left-most position; and Maximum Touching Area (MTA), which places an item in a position that maximizes the total contact area of its faces with the faces of other items @cite_16 .
@cite_22 @cite_7 @cite_8 @cite_1 @cite_3 @cite_19 @cite_15 @cite_16 @cite_25
1520820726 2161926431 2017565019 2087191078
We propose a new constructive algorithm, called HAPE3D, which is a heuristic algorithm based on the principle of minimum total potential energy for the 3D irregular packing problem, involving packing a set of irregularly shaped polyhedrons into a box-shaped container with fixed width and length but unconstrained height. The objective is to allocate all the polyhedrons in the container, and thus minimize the waste or maximize profit. HAPE3D can deal with arbitrarily shaped polyhedrons, which can be rotated around each coordinate axis at different angles. The most outstanding merit is that HAPE3D does not need to calculate no-fit polyhedron (NFP), which is a huge obstacle for the 3D packing problem. HAPE3D can also be hybridized with a meta-heuristic algorithm such as simulated annealing. Two groups of computational experiments demonstrate the good performance of HAPE3D and prove that it can be hybridized quite well with a meta-heuristic algorithm to further improve the packing quality. One of the main issues in addressing three-dimensional packing problems is finding an efficient and accurate definition of the points at which to place the items inside the bins, because the performance of exact and heuristic solution methods is actually strongly influenced by the choice of a placement rule. We introduce the extreme point concept and present a new extreme point-based rule for packing items inside a three-dimensional container. The extreme point rule is independent from the particular packing problem addressed and can handle additional constraints, such as fixing the position of the items. The new extreme point rule is also used to derive new constructive heuristics for the three-dimensional bin-packing problem. Extensive computational results show the effectiveness of the new heuristics compared to state-of-the-art results. Moreover, the same heuristics, when applied to the two-dimensional bin-packing problem, outperform those specifically designed for the problem. This paper considers a new variant of the two-dimensional bin packing problem where each rectangle is assigned a due date and each bin has a fixed processing time. Hence the objective is not only to minimize the number of bins, but also to minimize the maximum lateness of the rectangles. This problem is motivated by the cutting of stock sheets and the potential increased efficiency that might be gained by drawing on a larger pool of demand pieces by mixing orders, while also aiming to ensure a certain level of customer service. We propose a genetic algorithm for searching the solution space, which uses a new placement heuristic for decoding the gene based on the best fit heuristic designed for the strip packing problems. The genetic algorithm employs an innovative crossover operator that considers several different children from each pair of parents. Further, the dual objective is optimized hierarchically with the primary objective periodically alternating between maximum lateness and number of bins. As a result, the approach produces several non-dominated solutions with different trade-offs. Two further approaches are implemented. One is based on a previous Unified Tabu Search, suitably modified to tackle this revised problem. The other is randomized descent and serves as a benchmark for comparing the results. Comprehensive computational results are presented, which show that the Unified Tabu Search still works well in minimizing the bins, but the genetic algorithm performs slightly better. When also considering maximum lateness, the genetic algorithm is considerably better. We introduce a novel computational method for geometric rearrangement of multiple movable objects on a cluttered surface, where objects can change locations more than once by pick and or push actions. This method consists of four stages: (i) finding tentative collision-free final configurations for all objects (all the new objects together with all other objects in the clutter) while also trying to minimize the number of object relocations, (ii) gridization of the continuous plane for a discrete placement of the initial configurations and the tentative final configurations of objects on the cluttered surface, (iii) finding a sequence of feasible pick and push actions to achieve the final discrete placement for the objects in the clutter from their initial discrete place, while simultaneously minimizing the number of object relocations, and (iv) finding feasible final configurations for all objects according to the optimal task plan calculated in stage (iii). For (i) and (iv), we introduce algorithms that utilize local search with random restarts; for (ii), we introduce a mathematical modeling of the discretization problem and use the state-of-the-art ASP reasoners to solve it; for (iii) we introduce a formal hybrid reasoning framework that allows embedding of geometric reasoning in task planning, and use the expressive formalisms and reasoners of ASP. We illustrate the usefulness of our integrated AI approach with several scenarios that cannot be solved by the existing approaches. We also provide a dynamic simulation for one of the scenarios, as supplementary material.