A two-stage packing problem procedure

This paper deals with a two-stage packing problem that has to be solved in the daily distribution process of a Portuguese trading company. In the first stage, boxes including goods are to be packed on pallets, while in the second stage these pallets are loaded into one or more trucks. The boxes have to be transported to different customers, and the main goal is to guarantee a sufficient utilization of the truck loading space. A two-stage packing procedure is proposed to cover both problem stages. First, boxes are loaded onto pallets by means of a well-known container loading algorithm. Then, trucks are filled with loaded pallets by a tree search algorithm. The performance of the two-stage approach was evaluated using a set of instances that are based on actual company data.publishe

A two-stage packing procedure for a Portuguese trading company

This case study deals with a two-stage packing problem that has to be solved in the daily distribution process of a Portuguese trading company. At the first stage boxes including goods are to be packed on pallets while at the second stage these pallets are loaded into one or more trucks. The boxes have to be transported to different customers and the actual goal is to guarantee a sufficient utilization of the truck loading spaces. A two-stage packing procedure is proposed to cover both problem stages. First boxes are loaded onto pallets using a well-known container loading algorithm. Then trucks are filled with loaded pallets by means of a new tree search algorithm. The applicability and performance of the two-stage approach was evaluated with a set of instances that are based on actual company data

Greedy seeding procedure for GAs solving a strip packing problem

In this paper, the two-dimensional strip packing problem with 3-stage level patterns is tackled using genetic algorithms (GAs). We evaluate the usefulness of a greedy seeding procedure for creating the initial population, incorporating problem knowledge. This is motivated by the expectation that the seeding will speed up the GA by starting the search in promising regions of the search space. An analysis of the impact of the seeded initial population is offered, together with a complete study of the influence of these modifications on the genetic search. The results show that the use of an appropriate seeding of the initial population outperforms existing GA approaches on all the used problem instances, for all the metrics used, and in fact it represents the new state of the art for this problem.Red de Universidades con Carreras en Informática (RedUNCI

Greedy seeding procedure for GAs solving a strip packing problem

In this paper, the two-dimensional strip packing problem with 3-stage level patterns is tackled using genetic algorithms (GAs). We evaluate the usefulness of a greedy seeding procedure for creating the initial population, incorporating problem knowledge. This is motivated by the expectation that the seeding will speed up the GA by starting the search in promising regions of the search space. An analysis of the impact of the seeded initial population is offered, together with a complete study of the influence of these modifications on the genetic search. The results show that the use of an appropriate seeding of the initial population outperforms existing GA approaches on all the used problem instances, for all the metrics used, and in fact it represents the new state of the art for this problem.Red de Universidades con Carreras en Informática (RedUNCI

Exact solutions for the agricultural and the two-dimensional packing problems

Objectives and study method: The objective of this study is to develop exact algorithms that can be used as management tools for the agricultural production planning and to obtain exact solutions for two of the most well known twodimensional packing problems: the strip packing problem and the bin packing problem. For the agricultural production planning problem we propose a new hierarchical scheme of three stages to improve the current agricultural practices. The objective of the first stage is to delineate rectangular and homogeneous management zones into the farmer’s plots considering the physical and chemical soil properties. This is an important task because the soil properties directly affect the agricultural production planning. The methodology for this stage is based on a new method called “Positions and Covering” that first generates all the possible positions in which the plot can be delineated. Then, we use a mathematical model of linear programming to obtain the optimal physical and chemical management zone delineation of the plot. In the second stage the objective is to determine the optimal crop pattern that maximizes the farmer’s profit taken into account the previous management zones delineation. In this case, the crop pattern is affected by both management zones delineation, physical and chemical. A mixed integer linear programming is used to solve this stage. The objective of the last stage is to determine in real-time the amount of water to irrigate in each crop. This stage takes as input the solution of the crop planning stage, the atmospheric conditions (temperature, radiation, etc.), the humidity level in plots, and the physical management zones of plots, just to name a few. This procedure is made in real-time during each irrigation period. A linear programming is used to solve this problem. A breakthrough happen when we realize that we could propose some adaptations of the P&C methodology to obtain optimal solutions for the two-dimensional packing problem and the strip packing. We empirically show that our methodologies are efficient on instances based on real data for both problems: agricultural and two-dimensional packing problems. Contributions and conclusions: The exact algorithms showed in this study can be used in the making-decision support for agricultural planning and twodimensional packing problems. For the agricultural planning problem, we show that the implementation of the new hierarchical approach can improve the farmer profit between 5.27% until 8.21% through the optimization of the natural resources. An important characteristic of this problem is that the soil properties (physical and chemical) and the real-time factors (climate, humidity level, evapotranspiration, etc.) are incorporated. With respect to the two-dimensional packing problems, one of the main contributions of this study is the fact that we have demonstrate that many of the best solutions founded in literature by others approaches (heuristics approaches) are the optimal solutions. This is very important because some of these solutions were up to now not guarantee to be the optimal solutions

TS2PACK: A Two-Level Tabu Search for the Three-dimensional Bin Packing Problem

Three-dimensional orthogonal bin packing is a problem NP-hard in the strong sense where a set of boxes must be orthogonally packed into the minimum number of three-dimensional bins. We present a two-level tabu search for this problem. The first-level aims to reduce the number of bins. The second optimizes the packing of the bins. This latter procedure is based on the Interval Graph representation of the packing, proposed by Fekete and Schepers, which reduces the size of the search space. We also introduce a general method to increase the size of the associated neighborhoods, and thus the quality of the search, without increasing the overall complexity of the algorithm. Extensive computational results on benchmark problem instances show the effectiveness of the proposed approach, obtaining better results compared to the existing one