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About 10,000 papers for “Optimization and Packing Problems”

Integrating packing and distribution problems and optimization through mathematical programming

Fábio Miguel, Mariano Frutos, Fernando Tohmé et al. · Decision Science Letters · 2015

This paper analyzes the integration of two combinatorial problems that frequently arise in production and distribution systems. One is the Bin Packing Problem (BPP) problem, which involves finding an ordering of some objects of different volumes to be packed into the minimal number of containers of the same or different size. An optimal solution to this NP-Hard problem can be approximated by means of meta-heuristic methods. On the other hand, we consider the Capacitated Vehicle Routing Problem with Time Windows (CVRPTW), which is a variant of the Travelling Salesman Problem (again a NP-Hard problem) with extra constraints. Here we model those two problems in a single framework and use an evolutionary meta-heuristics to solve them jointly. Furthermore, we use data from a real world company as a test-bed for the method introduced here.

Cited by 2Open access

Optimization Problems and Algorithms in Double-layered Food Packing Systems

Yoshiyuki Karuno, Hiroshi Nagamochi, Xiaoming Wang · Journal of Advanced Mechanical Design Systems and Manufacturing · 2010

In this paper, we discuss lexicographic bi-criteria combinatorial optimization problems arising in two types of double-layered food packing systems, which we call upright and diagonal types. Such food packing systems are known as so-called automatic combination weighers. The first and second layers in a double-layered food packing system consist of n weighing hoppers and n booster hoppers, respectively. Some amount of food such as a green pepper and a handful of potato chips is thrown into each hopper, and it is called an item. The food packing system performs an operation of choosing a subset I' from the set I of the current 2n items to produce a package of the food. Then, the resulting empty hoppers are supplied with next items, and the set I is updated. By repeating the packing operation, a large number of packages are produced one by one. The boosters are just hoppers without weighing function, but the weights of items in the boosters can be known since each type of double-layered food packing systems has its own constructional feature such that they receive next items from the weighing hoppers. The primary objective of lexicographic bi-criteria food packing problems is to minimize the the total weight of chosen items for each package, making the total weight no less than a specified target weight T. The second objective is to maximize the total priority of chosen items for each package so that items with longer durations in hoppers are preferably chosen. The priority of an item is given as its duration in hopper. In this paper, we prove that the lexicographic bi-criteria food packing problems can be solved in O(nT) time by dynamic programming if all input data are integral. We also show the executive efficiency of the pseudo-polynomial dynamic programming algorithms by conducting numerical experiments.

Cited by 26Open access

Matching and packing problems – optimization under uncertainty in theory and practice

Nölke, Lukas · Media (https://www.suub.uni-bremen.de/) · 2023

When solving optimization problems that arise from real-world decision-making processes, uncertainty is a ubiquitous phenomenon that poses a significant obstacle. More often than not, lack of (full) knowledge about certain input parameters requires us to make decisions without knowing what their full effects will be. This thesis investigates how to algorithmically deal with such uncertainties when solving matching and packing problems. Both matching and packing problems are well-studied and among the most fundamental problems in combinatorial optimization. In matching problems, the task is to find a set of disjoint pairs of items, a matching, while in packing problems, items need to be assigned to containers with limited capacities. Additionally, there is an optimization objective, such as minimizing the cost of the matching or maximizing the value of packed items. Both problems have numerous practical applications in which uncertainty plays an important role. It may manifest itself, for instance, in the form of unknown items that are revealed only over time. It should come as no surprise that missing information about crucial problem parameters generally prevents us from reaching the same quality as an optimal offline solution. We consider several matching and packing problems and design algorithms that compute provably good solutions despite uncertainty in the input. Specifically, we consider the following models of uncertainty: online, recourse, and dynamic.

Cited by 0Open access

Nonlinear Optimization and Adaptive Heuristics for Solving Irregular Object Packing Problems

János D. Pintér, Ignacio Castillo, F. J. Kampas · Algorithms · 2024

We review and present several challenging model classes arising in the context of finding optimized object packings (OP). Except for the smallest and/or simplest general OP model instances, it is not possible to find their exact (closed-form) solution. Most OP problem instances become increasingly difficult to handle even numerically, as the number of packed objects increases. Specifically, here we consider classes of general OP problems that can be formulated in the framework of nonlinear optimization. Research experience demonstrates that—in addition to utilizing general-purpose nonlinear optimization solver engines—the insightful exploitation of problem-specific heuristics can improve the quality of numerical solutions. We discuss scalable OP problem classes aimed at packing general circles, spheres, ellipses, and ovals, with numerical (conjectured) solutions of non-trivial model instances. In addition to their practical relevance, these models and their various extensions can also serve as constrained global optimization test challenges.

Cited by 3Open access

Ant colony optimization and local search for bin packing and cutting stock problems

Joshua A. Levine, Frederick Ducatelle · Journal of the Operational Research Society · 2004

The Bin Packing Problem and the Cutting Stock Problem are two related classes of NP-hard combinatorial optimization problems. Exact solution methods can only be used for very small instances, so for real-world problems, we have to rely on heuristic methods. In recent years, researchers have started to apply evolutionary approaches to these problems, including Genetic Algorithms and Evolutionary Programming. In the work presented here, we used an ant colony optimization (ACO) approach to solve both Bin Packing and Cutting Stock Problems. We present a pure ACO approach, as well as an ACO approach augmented with a simple but very effective local search algorithm. It is shown that the pure ACO approach can compete with existing evolutionary methods, whereas the hybrid approach can outperform the best-known hybrid evolutionary solution methods for certain problem classes. The hybrid ACO approach is also shown to require different parameter values from the pure ACO approach and to give a more robust performance across different problems with a single set of parameter values. The local search algorithm is also run with random restarts and shown to perform significantly worse than when combined with ACO.

Cited by 208

Metaheuristics, Artificial Intelligence, Quantum Computing in Vehicle Routing and Bin Packing Problems optimization

Piotr Nowak · 2025

This article presents current state of knowledge about the optimization of the last stages of the supply chain. Two main problem types with corresponding variants are presented and the most common optimization methods are introduced. The analysis of literature presents current shortage of articles considering simultaneous optimization of multiple stages of supply chain - most articles consider optimization of only one stage with the consideration of just few problem variants. This situation is a mighty lack, which should be filled. Simultaneous optimization of multiple stages of supply chain is a promising path for further reduction of transportation costs, which can significantly improve quality of life of people around the world.

Cited by 0

Weight annealing heuristics for solving bin packing and other combinatorial optimization problems: concepts, algorithms, and computational results

Bruce Golden, Kok-Hua Loh · 2006

The application of weight annealing to combinatorial optimization problems is relatively new, compared to applications of well-known optimization techniques such as simulated annealing and tabu search. The weight annealing approach seeks to expand a neighborhood search by creating distortions in different parts of the search space. Distortion is controlled through weight assignment based on insights gained from one iteration of the search procedure to the next with a view towards focusing computational efforts on the poorly solved regions of the search space. The search for the global optimum should be accelerated and the solution quality should be improved with weight annealing. In this dissertation, we present key ideas behind weight annealing and develop algorithms that solve combinatorial optimization problems. Our weight annealing-based heuristics solve the one-dimensional bin packing problem and the two-dimensional bin packing problem with and without guillotine cutting and item orientation constraints. We also solve the maximum cardinality bin packing problem and the multidimensional multiple knapsack problem with our heuristics.

Cited by 2

Weight Annealing Heuristics for Solving Bin Packing and other Combinatorial Optimization Problems: Concepts, Algorithms and Computational Results

Loh, Kok-Hua · Digital Repository at the University of Maryland (University of Maryland College Park) · 2006

The application of weight annealing to combinatorial optimization problems is relatively new, compared to applications of well-known optimization techniques such as simulated annealing and tabu search. The weight annealing approach seeks to expand a neighborhood search by creating distortions in different parts of the search space. Distortion is controlled through weight assignment based on insights gained from one iteration of the search procedure to the next with a view towards focusing computational efforts on the poorly solved regions of the search space. The search for the global optimum should be accelerated and the solution quality should be improved with weight annealing. In this dissertation, we present key ideas behind weight annealing and develop algorithms that solve combinatorial optimization problems. Our weight annealing-based heuristics solve the one-dimensional bin packing problem and the two-dimensional bin packing problem with and without guillotine cutting and item orientation constraints. We also solve the maximum cardinality bin packing problem and the multidimensional multiple knapsack problem with our heuristics.

Cited by 0Open access

Multiperiod, stochastic and dynamic problems in transportation (network design with temporary contract and disruption optimization in picking-packing)

Pironet, Thierry, Leloup, Emeline · Open Repository and Bibliography (University of Liège) · 2025

We will present some past and on-going researches addressing “stochastic and/or dynamic problems”, closer to real-life contexts. The challenges reside in generating and evaluating the performances of a sequence of decisions related to either a multiperiod framework (days-months) or an on-going daily plan facing several disruptions. Firstly, a general introduction will be performed on the values of information in a multi-period stochastic and dynamic problem. Then, a network design problem with temporary capacity commitment contracts with projected demands will be described. Finally, a time-dependent vehicle routing problem focusing on picking and 3D packing operations will be described within a context of disruptions. We will mainly focus on the problem descriptions and managerial insights drawn by the results. This talk aims to give some insights in order to face these kinds of real-life problems instead of their mono-period deterministic version leading to disconnected one-time decision.

Cited by 0

An improved parallel genetic algorithm based on particle swarm optimization and its application to packing layout problems

Fengqiang Zhao, Guangqiang Li, Jialu Du et al. · 2012

Packing layout problems belong to NP-Complete problems theoretically. They are concerned more and more in recent years and arise in a variety of application fields such as the layout design of spacecraft modules, plant equipments, platforms of marine drilling well, shipping, vehicle and robots. The algorithms based on swarm intelligence are relatively effective to solve this kind of problems. But usually there still exist two main defects of them, i.e. premature convergence and slow convergence rate. To overcome them, an improved parallel genetic algorithm based on particle swarm optimization (PSO-PGA) is proposed on the basis of traditional parallel genetic algorithms (PGA). In this algorithm, parallel evolution of multiple subpopulations based on improved adaptive crossover and mutation is adopted. And more importantly, in accordance with characteristics of different classes of subpopulations, different modes of PSO update operators are introduced. It aims at making full use of the fast convergence property of particle swarm optimization (PSO). The proposed arithmetic-progression rank-based selection with pressure can prevent the algorithm from premature in the early stage and benefit accelerating convergence in the late stage as well. An example of packing layout problems shows the proposed PSO-PGA is feasible and effective.

Cited by 0

Decoupling Geometry from Optimization in 2D Irregular Cutting and Packing Problems: An Open-Source Collision Detection Engine

Jeroen Gardeyn, Greet Vanden Berghe, Tony Wauters · INFORMS journal on computing · 2025

Addressing irregular cutting and packing (C&P) optimization problems poses two distinct challenges: the geometric challenge of determining whether an item can be feasibly placed at a certain position and the optimization challenge of finding a good solution according to some objective function. Until now, those tackling such problems have had to address both challenges simultaneously, requiring two distinct sets of expertise and a lot of research and development effort. One way to lower this barrier is to decouple the two challenges. In this paper, we introduce a powerful collision detection engine (CDE) for two-dimensional (2D) irregular C&P problems, which assumes full responsibility for the geometric challenge. The CDE (i) allows users to focus with full confidence on their optimization challenge by abstracting geometry away, and (ii) enables independent advances to propagate to all optimization algorithms built atop it. We present a set of core principles and design philosophies to model a general and adaptable CDE focused on maximizing performance, accuracy, and robustness. These principles are accompanied by a concrete open-source implementation called jagua-rs. This paper, together with its implementation, serves as a catalyst for future advances in irregular C&P problems by providing a solid foundation that can either be used as it currently exists or further improved upon. History: Accepted by Ted Ralphs, Area Editor for Software Tools. Funding: This work was supported by Research Foundation – Flanders (FWO) [Grants 1S71222N and K804824N]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.1025 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.1025 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Cited by 0Open access

PSO-Augmented NSGA-III Algorithm: A Combined Optimization Approach to Heterogeneous Vehicle Routing and Bin Packing Problems

Yi Liu, Wenchao Chen, Xiaoyun Jiang · IEEE Access · 2024

This study presents an Integrated Particle Swarm Optimization and Nondominated Sorting Genetic Algorithm III (IPSO-NSGA-III) to address the combined optimization challenges in logistics enterprises of heterogeneous vehicle routing and bin packing. The algorithm is designed to optimize four critical performance metrics: travel distance, time penalty costs, vehicle loading efficiency, and fixed vehicle costs. By enhancing vehicle routing and bin packing strategies, the approach targets the reduction of logistics distribution costs and increases in vehicle loading rates, ultimately enhancing the cost-effectiveness of distribution operations. The performance of IPSO-NSGA-III is rigorously evaluated through multi-objective function testing and a detailed case study, where it is compared against other state-of-the-art algorithms. The case study results show that, the IPSO-NSGA-III outperforms the NSGA-III by delivering more effective solutions that consider the interplay between vehicle routing and bin packing. The optimized solutions facilitate a decrease in operational expenses and an improvement in logistics efficiency, which translates to higher customer satisfaction and stronger competitiveness for logistics companies.

Cited by 2Open access

Surrogate-Assisted Multi-Objective Optimization for Simultaneous Three-Dimensional Packing and Motion Planning Problems Using the Sequence-Triple Representation

Liu, Ziang, Kawabe, Tomoya, Nishi, Tatsushi et al. · Figshare · 2024

Packing problems are classical optimization problems with wide-ranging applications. With the advancement of robotic manipulation, there are growing demands for the automation of packing tasks. However, the simultaneous optimization of packing and the robot’s motion planning is challenging because these two decisions are interconnected, and no previous study has addressed this optimization problem. This paper presents a framework to simultaneously determine the robot’s motion planning and packing decision to minimize the robot’s processing time and the container’s volume. This framework comprises three key components: solution encoding, surrogate modeling, and evolutionary computation. The sequence-triple representation encodes complex packing solutions by a sequence of integers. A surrogate model is trained to predict the processing time for a given packing solution to reduce the computational burden. Training data is generated by solving the motion planning problem for a set of packing solutions using the rapidly exploring random tree algorithm. The Non-Dominated Sorting Genetic Algorithm II searches for the Pareto solutions. Experimental evaluations are conducted using a 6-DOF robot manipulator. The experimental results suggest that implementing the surrogate model can reduce the computational time by 91.1%. The proposed surrogate-assisted optimization method can obtain significantly better solutions than the joint angular velocity-based estimation method.

Cited by 0Open access

Surrogate-Assisted Multi-Objective Optimization for Simultaneous Three-Dimensional Packing and Motion Planning Problems Using the Sequence-Triple Representation

Liu, Ziang, Kawabe, Tomoya, Nishi, Tatsushi et al. · Figshare · 2024

Packing problems are classical optimization problems with wide-ranging applications. With the advancement of robotic manipulation, there are growing demands for the automation of packing tasks. However, the simultaneous optimization of packing and the robot’s motion planning is challenging because these two decisions are interconnected, and no previous study has addressed this optimization problem. This paper presents a framework to simultaneously determine the robot’s motion planning and packing decision to minimize the robot’s processing time and the container’s volume. This framework comprises three key components: solution encoding, surrogate modeling, and evolutionary computation. The sequence-triple representation encodes complex packing solutions by a sequence of integers. A surrogate model is trained to predict the processing time for a given packing solution to reduce the computational burden. Training data is generated by solving the motion planning problem for a set of packing solutions using the rapidly exploring random tree algorithm. The Non-Dominated Sorting Genetic Algorithm II searches for the Pareto solutions. Experimental evaluations are conducted using a 6-DOF robot manipulator. The experimental results suggest that implementing the surrogate model can reduce the computational time by 91.1%. The proposed surrogate-assisted optimization method can obtain significantly better solutions than the joint angular velocity-based estimation method.

Cited by 0Open access

Research on Genetic Algorithm Optimization with Fusion Tabu Search Strategy and Its Application in Solving Three-Dimensional Packing Problems

Zhenjia Kang, Yong Guan, Jiake Wang et al. · Symmetry · 2024

Symmetry is an important principle and characteristic that is prevalent in nature and artificial environments. In the three-dimensional packing problem, leveraging the inherent symmetry of goods and the symmetry of the packing space can enhance packing efficiency and utilization.The three-dimensional packing problem is an NP-hard combinatorial optimization problem in the field of modern logistics, with high computational complexity. This paper proposes an improved genetic algorithm by incorporating a fusion tabu search strategy to address this problem. The algorithm employs a three-dimensional loading mathematical model and utilizes a wall-building method under residual space constraints for stacking goods. Furthermore, adaptation of fitness variation strategy, chromosome adjustment, and tabu search algorithm are introduced to balance the algorithm’s global and local search capabilities, as well as to enhance population diversity and convergence speed. Through testing on benchmark cases such as Bischoff and Ratcliff, the improved algorithm demonstrates an average increase of over 3% in packing space utilization compared to traditional genetic algorithms and other heuristic algorithms, validating its feasibility and effectiveness. The proposed improved genetic algorithm provides new insights for solving three-dimensional packing problems and optimizing logistics loading schedules, offering promising prospects for various applications.

Cited by 5Open access

Surrogate-Assisted Multi-Objective Optimization for Simultaneous Three-Dimensional Packing and Motion Planning Problems Using the Sequence-Triple Representation

Ziang Liu, Tomoya Kawabe, Tatsushi Nishi et al. · Applied Artificial Intelligence · 2024

Packing problems are classical optimization problems with wide-ranging applications. With the advancement of robotic manipulation, there are growing demands for the automation of packing tasks. However, the simultaneous optimization of packing and the robot’s motion planning is challenging because these two decisions are interconnected, and no previous study has addressed this optimization problem. This paper presents a framework to simultaneously determine the robot’s motion planning and packing decision to minimize the robot’s processing time and the container’s volume. This framework comprises three key components: solution encoding, surrogate modeling, and evolutionary computation. The sequence-triple representation encodes complex packing solutions by a sequence of integers. A surrogate model is trained to predict the processing time for a given packing solution to reduce the computational burden. Training data is generated by solving the motion planning problem for a set of packing solutions using the rapidly exploring random tree algorithm. The Non-Dominated Sorting Genetic Algorithm II searches for the Pareto solutions. Experimental evaluations are conducted using a 6-DOF robot manipulator. The experimental results suggest that implementing the surrogate model can reduce the computational time by 91.1%. The proposed surrogate-assisted optimization method can obtain significantly better solutions than the joint angular velocity-based estimation method.

Cited by 6Open access