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
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Simulated annealing (statistical cooling) is applied to bin packing problems. Different cooling strategies are compared empirically and for a particular 100 item problem a solution is given which is most likely the best known so far. This paper presents a tabu search and best-fit decreasing (BFD) algorithms to address a real-world steel cutting problem from a retail steel distributor. It consists of cutting large steel blocks in order to obtain smaller tailored blocks ordered by clients. The problem is addressed as a cutting & packing problem, formulated as a 3-dimensional residual bin packing problem for minimization of stock variation. The performance of the proposed approaches is compared to an heuristic and ant colony optimization (ACO) algorithms. The proposed algorithms were able to reduce the stock variation by up to 179 . The comparison of results between the tabu search and BFD algorithm shows that a multiple order joint analysis benefits the optimization of the addressed objective. 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. In this paper, we describe two heuristics for the Single Vehicle Loading Problem (SVLP), which can handle practical constraints that are frequently encountered in the freight transportation industry, such as the servicing order of clients; item fragility; and the stability of the goods. The two heuristics, Deepest-Bottom-Left-Fill and Maximum Touching Area, are 3D extensions of natural heuristics that have previously only been applied to 2D packing problems. We employ these heuristics as part of a two-phase tabu search algorithm for the Three-Dimensional Loading Capacitated Vehicle Routing Problem (3L-CVRP), where the task is to serve all customers using a homogeneous fleet of vehicles at minimum traveling cost. The resultant algorithm produces mostly superior solutions to existing approaches, and appears to scale better with problem size. The three-dimensional bin-packing problem is the problem of orthogonally packing a set of boxes into a minimum number of three-dimensional bins. In this paper we present a heuristic algorithm based on guided local search. Starting with an upper bound on the number of bins obtained by a greedy heuristic, the presented algorithm iteratively decreases the number of bins, each time searching for a feasible packing of the boxes. The process terminates when a given time limit has been reached or the upper bound matches a precomputed lower bound. The algorithm can also be applied to two-dimensional bin-packing problems by having a constant depth for all boxes and bins. Computational experiments are reported for two- and three-dimensional instances with up to 200 boxes, showing that the algorithm on average finds better solutions than do heuristics from the literature.