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• MODERN APPROACHES TO SOLVING THE 3D BIN PACKING PROBLEM

  М.М. Sorokin , L. А. Gladkov , N. V. Gladkova

  131-150

  2026-09-10

  Abstract ▼

  The article is devoted to the consideration of current trends and approaches to solving the urgent optimization problem of three-dimensional bin packing problem. The importance of building effective methods for solving this problem is due to the rapid growth of e-commerce, where achieving even incremental improvements in container filling density can lead to significant reductions in freight transportation and storage costs. The article provides an analysis of various types of problems and suggests a classification of bin packing problems according to various criteria, including: offline and online packing, by dimension, by type and quantity of containers and cargo. The formulation of the classical optimization knapsack problem is given and various options for constraints due to the specifics of the tasks being solved are considered. A brief overview of the main approaches to solving the problem is given. The analysis and generalization of the characteristic features of the application of metaheuristic approaches based on the use of evolutionary and bioinspired algorithms and machine learning methods is carried out, their advantages and disadvantages are noted. Due to the complexity of the problem under consideration, it is proposed to actively use known and develop new modifications of metaheuristic algorithms that make it possible to find quasi-optimal solutions in polynomial time. The analysis of known machine learning methods and bioinspired algorithms is given, the principles of their operation are described, their main features, advantages and disadvantages are highlighted, and the prospects for their development and application to solve NP-complete combinatorial optimization problems are noted. A generalized principle of operation of metaheuristic algorithms is given. A comparative analysis of the application of various optimization methods has shown the effectiveness of using metaheuristic methods to solve the problem of three-dimensional packaging.

• A BIOINSPIRED APPROACH TO SOLVING THE PROBLEM OF 3D PACKAGING

  V.I. Danilchenko , V.V. Bova , М. М. Semenova , S.V. Ignateva , М. B. Shayliev

  2026-02-27

  Abstract ▼

  This article examines one of the most important combinatorial optimization problems – three-dimensional packaging. Optimizing three-dimensional packaging reduces costs and improves logistics efficiency, making it relevant for industry. This paper analyzes classical approaches such as greedy algorithms and dynamic programming, as well as widely used methods, including evolutionary algorithms and local search. An analysis of existing methods, including greedy search, dynamic programming, evolutionary algorithms, and local search, revealed their key characteristics and identified suitable areas of application. In the context of this analysis, an overview of the key methods that dominated during certain historical periods is presented. The analysis includes consideration of the application conditions of various methods, their effectiveness for specific types of problems, as well as their advantages and limitations.
  A multi-level search algorithm is presented that combines the advantages of traditional and modern optimization methods. This multi-level algorithm improves the accuracy of the packaging problem solution through dynamic parameter adjustment. A software package for solving the three-dimensional packaging optimization problem using bioinspired algorithms has been developed. A computational experiment was conducted on test examples (benchmarks). The packing quality obtained using the developed combined bioinspired algorithm is, on average, 7% higher than the packing results obtained using known algorithms, while the solution time is 7% to 25% shorter, demonstrating the effectiveness of the proposed approach. A series of tests and experiments allowed us to refine theoretical estimates of the time complexity of packing algorithms. In the best case, the time complexity of the algorithms is O(n²), and in the worst case, O(n³).

• MULTILEVEL APPROACH FOR HIGH DIMENSIONAL 3D PACKING PROBLEM

  V. V. Kureichik, А. Е. Glushchenko

  2020-07-20

  Abstract ▼

  The article considers one of the important combinatorial optimization problems, the problem
  of 3D packing of different elements in a fixed volume. It belongs to the class of NP-complex and difficult
  optimization problems. The paper presents and describes the formulation of the 3D packing
  problem, introduces a combined objective function that takes into account all the restrictions. Due to
  the complexity of this task, a multilevel approach is proposed. It is consisting in dividing the 3D packing
  problem into 3 subtasks and solving each subtask in a strict order. Moreover, for each of the
  subtasks a unique set of objects is defined that are not repeated in the remaining subtasks. To implement
  a multi-level approach, the authors developed a combined bio-inspired algorithm based onevolutionary and genetic search. This approach can significantly reduce the time to obtain the result,
  partially solve the problem of preliminary convergence of the algorithms and obtain sets of quasioptimal
  solutions in polynomial time. A software package was developed and computer-based algorithms
  for automated 3D packaging based on a combined bio-inspired search were implemented.
  A computational experiment was conducted on test examples (benchmarks). The packaging quality
  obtained on the basis of the developed combined bio-inspired algorithm is on average 5 % higher
  than the packaging results obtained using known algorithms, and the solution time is less than 5 % to
  20 %, which indicates the effectiveness of the proposed approach. The series of tests and experiments
  carried out made it possible to refine the theoretical estimates of the time complexity of the packaging
  algorithms. In the best case the time complexity of the O (n2) algorithms; in the worst, O (n3).