An adaptive jellyfish search algorithm for packing items with conflict

The bin packing problem (BPP) is a classic combinatorial optimization problem with several variations. The BPP with conflicts (BPPCs) is not a well-investigated variation. In the BPPC, there are conditions that prevent packing some items together in the same bin. There are very limited efforts utilizing metaheuristic methods to address the BPPC. The current methods only pack the conflict items only and then start a new normal BPP for the non-conflict items; thus, there are two stages to address the BPPC. In this work, an adaption of the jellyfish metaheuristic has been proposed to solve the BPPC in one stage (i.e., packing the conflict and non-conflict items together) by defining the jellyfish operations in the context of the BPPC by proposing two solution representations. These representations frame the BPPC problem on two different levels: item-wise and bin-wise. In the item-wise solution representation, the adapted jellyfish metaheuristic updates the solutions through a set of item swaps without any preference for the bins. In the bin-wise solution representation, the metaheuristic method selects a set of bins, and then it performs the item swaps from these selected bins only. The proposed method was thoroughly benchmarked on a standard dataset and compared against the well-known PSO, Jaya, and heuristics. The obtained results revealed that the proposed methods outperformed the other comparison methods in terms of the number of bins and the average bin utilization. In addition, the proposed method achieved the lowest deviation rate from the lowest bound of the standard dataset relative to the other methods of comparison

QAL-BP: An Augmented Lagrangian Quantum Approach for Bin Packing Problem

The bin packing is a well-known NP-Hard problem in the domain of artificial intelligence, posing significant challenges in finding efficient solutions. Conversely, recent advancements in quantum technologies have shown promising potential for achieving substantial computational speedup, particularly in certain problem classes, such as combinatorial optimization. In this study, we introduce QAL-BP, a novel Quadratic Unconstrained Binary Optimization (QUBO) formulation designed specifically for bin packing and suitable for quantum computation. QAL-BP utilizes the augmented Lagrangian method to incorporate the bin packing constraints into the objective function while also facilitating an analytical estimation of heuristic, but empirically robust, penalty multipliers. This approach leads to a more versatile and generalizable model that eliminates the need for empirically calculating instance-dependent Lagrangian coefficients, a requirement commonly encountered in alternative QUBO formulations for similar problems. To assess the effectiveness of our proposed approach, we conduct experiments on a set of bin-packing instances using a real Quantum Annealing device. Additionally, we compare the results with those obtained from two different classical solvers, namely simulated annealing and Gurobi. The experimental findings not only confirm the correctness of the proposed formulation but also demonstrate the potential of quantum computation in effectively solving the bin-packing problem, particularly as more reliable quantum technology becomes available.Comment: 14 pages, 4 figures, 1 tabl

CHAMP: Creating Heuristics via Many Parameters for online bin packing

The online bin packing problem is a well-known bin packing variant which requires immediate decisions to be made for the placement of a lengthy sequence of arriving items of various sizes one at a time into fixed capacity bins without any overflow. The overall goal is maximising the average bin fullness. We investigate a ‘policy matrix’ representation which assigns a score for each decision option independently and the option with the highest value is chosen for one dimensional online bin packing. A policy matrix might also be considered as a heuristic with many parameters, where each parameter value is a score. We hence investigate a framework which can be used for creating heuristics via many parameters. The proposed framework combines a Genetic Algorithm optimiser, which searches the space of heuristics in policy matrix form, and an online bin packing simulator, which acts as the evaluation function. The empirical results indicate the success of the proposed approach, providing the best solutions for almost all item sequence generators used during the experiments. We also present a novel fitness landscape analysis on the search space of policies. This study hence gives evidence of the potential for automated discovery by intelligent systems of powerful heuristics for online problems; reducing the need for expensive use of human expertise

Functional optimization of a Persian lime packing using TRIZ and multi-objective genetic algorithms

This article proposes a novel approach that uses a mathematical model optimized by Genetic Algorithms harmonized with the Russian theory of problem solving and invention (TRIZ) to design an export packing of Persian Lime. The mathematical model (with functional elements of non-spatial type) optimizes the spaces of the Persian Lime Packing, maximizes the Resistance to Vertical Compression and minimizes the Amount of Material Used, according to the operation restrictions of the packing during the transport of the merchandise. This approach is developed in four phases: the identification of the solution space; the optimization of the conceptual design; the application of TRIZ; and the generation of the final proposal solution. The results show the proposed packing (with 28% less cardboard) supports at least the same vertical load with respect to the nearest competitor packing. However, with the same number of packings per pallet and pallets per container, the space used by the packing assembled and deployed in the container is greater by 10% and 38% respectively. Besides, TRIZ includes innovative non-spatial elements such as the airflow and the friction of the product inside the packing. The contribution of this approach can be replicable for the packing design of other horticultural products of the agri-food chai

Multi-Level Filling Heuristic and an Instance Generator for the Multi-Objective 3D Packing Problem.

Cutting and packing problems belong to the family of combinatorial optimisation. When dealing with optimisation problems, the goal is to analyse and identify the alternative that most closely approximates the optimal solution. Finding an optimisation process that yields a truly optimal solution, however, is not a simple task. That is why finding solutions to optimisation problems continues to be a very active and dynamic area of research to this day. The interest in optimisation is closely linked to the search for alternatives to deal with problems in the everyday world, physical or material problems from the real world. Optimisation covers several areas of research in engineering, where a large part of the problems are part of complex systems for which there is no simple and general method for efficiently optimising either the problems or their possible solutions. Hence the need exists to constantly study and improve the optimisation processes. Many interdisciplinary factors are involved in the design of optimisation schemes, but primarily statistics, mathematics and computer science. Therefore, when applying these factors to analysing a specific problem, one has to consider all of the aspects from the field to which the problem belongs. Depending on the number of objectives, optimisation problems can be classified into single-objective or multi-objective. Single-objective problems aim to optimise a single objective to be maximised or minimised. In this type of problem, the possible solutions are easy to compare, since it is just a matter of evaluating which solution is best for the objective in question. In the case of multi-objective optimisation problems, several objectives are optimised at once, which makes comparing the possible solutions an indirect process. This work concerns itself with a study of the 3D Packing Problem, 3DPP. Cutting and packing problems have been studied in depth for numerous areas of industry and research. The 3DPP proposed in this work is of most concern in industry and in the transport of goods due to its relevance to a wide variety of real applications. When solving a problem of this type, the objective is normally to arrange a set of rectangular items (boxes) inside a rectangular object of larger dimensions (container) so as to maximise the volume of the cargo. However, there is one important aspect that the literature normally ignores when dealing with this type of problem, which is the tare limit that each type of container has. For example, the cost of renting lorries to transport goods is calculated based on the total weight that they can transport, independently of the cargo volume. It is thus beneficial to determine the loading pattern that allows maximising the cargo volume while at the same time maximising the value of the accumulated weight. Along these lines, the problem studied in this thesis is proposed as a Multi-Objective Optimization Problem (MOP), whose objective is not just to maximise the cargo volume, but also its weight inside the container. The solution algorithms can be classified into two types: exact and approximate. Exact algorithms guarantee finding the best solution for the problem in question. They have the drawback, however, of being highly time and resource intensive. In contrast, approximate algorithms do not guarantee finding the optimal solution but they do have lower time and resource requirements. Approximate algorithms include heuristics and metaheuristics. Heuristics are ad hoc methods designed to solve a specific problem. They rely on concrete knowledge of the problem to yield high-quality solutions without requiring an excessive computational effort. Metaheuristics are more general methods that can be adapted to different problems and can better utilise the computational resources. These methods offer a good compromise between the effort needed to apply them and the quality of the solutions they yield. Computationally, the 3DPP problem is hard to solve, meaning that an exact solution cannot be obtained in polynomial time. Thus, although there are isolated works that approach it using exact algorithms, most studies focus on providing solutions that rely on heuristics and metaheuristics. The heuristics applied to the 3DPP must be developed taking into account different distributions of specific pieces. Recent years have seen an increase in the evaluation of metaheuristics to solve the 3D Packing Problem, such as genetic algorithms, simulated annealing algorithms, tabu search algorithms and hybrid algorithms. Specifically, the evolutionary algorithms have taken on great significance. They are a type of metaheuristics whose design is inspired by biological evolution and its genetic/molecular basis. Multi-Objective Optimization Evolutionary algorithms (MOEAs) have shown real promise in solving real-world multi-objective problems. In particular, they have yielded competitive solutions for several cutting and packing problems. In this context, the difference between using a solution calculated quickly and using more sophisticated proposals to find the optimal solution can determine the very survival of a company. Developing these sophisticated and effective proposals, however, normally entails a significant computational effort that in real applications can result in reduced production speeds. It is thus essential that we find proposals that are both effective and efficient

A Lifelong Learning Hyper-heuristic Method for Bin Packing.

We describe a novel Hyper-heuristic system which continuously learns over time to solve a combinatorial optimisation problem. The system continuously generates new heuristics and samples problems from its environment; representative problems and heuristics are incorporated into a self-sustaining network of interacting entities in- spired by methods in Artificial Immune Systems.The network is plastic in both its structure and content leading to the following properties: it exploits existing knowl- edge captured in the network to rapidly produce solutions; it can adapt to new prob- lems with widely differing characteristics; it is capable of generalising over the prob- lem space. The system is tested on a large corpus of 3968 new instances of 1D-bin packing problems as well as on 1370 existing problems from the literature; it shows excellent performance in terms of the quality of solutions obtained across the datasets and in adapting to dynamically changing sets of problem instances compared to pre- vious approaches. As the network self-adapts to sustain a minimal repertoire of both problems and heuristics that form a representative map of the problem space, the system is further shown to be computationally efficient and therefore scalable