Constraint programming methods in three-dimensional container packing

Cutting and packing problems are present in many, at first glance unconnected, areas, therefore it's beneficial to have a good understanding of their underlying structure, to select proper techniques for finding solutions. Cutting and packing problems are a class of combinatorial problems in which there are specified two classes of objects: big and small items and the task is to place the small items within big items. Even in the 1-dimensional case, bin-packing is strongly NP-hard (Garey 1978), which suggests, that exact solutions may not be found in a reasonable time for bigger instances. In the literature, there are presented many various approaches to packing problems, e.g. mixed-integer programming, approximation algorithms, heuristic solutions, and local search algorithms, including metaheuristic approaches like Tabu Search or Simulated Annealing. The main goal of this work is to review existing solutions, survey the variants arising from the industry applications, present a solution based on constraint programming and compare its performance with the results in the literature. Optimization with constraint programming is a method searching for the global optima, hence it may require a higher workload compared to the heuristic and local search approaches, which may finish in a local optimum. The performance of the presented model will be measured on test data used in the literature, which were used in many articles presenting a variety of approaches to three-dimensional container packing, which will allow us to compare the efficiency of the constraint programming model with other methods used in the operational research

Volumetric Techniques for Product Routing and Loading Optimisation in Industry 4.0: A Review

Industry 4.0 has become a crucial part in the majority of processes, components, and related modelling, as well as predictive tools that allow a more efficient, automated and sustainable approach to industry. The availability of large quantities of data, and the advances in IoT, AI, and data-driven frameworks, have led to an enhanced data gathering, assessment, and extraction of actionable information, resulting in a better decision-making process. Product picking and its subsequent packing is an important area, and has drawn increasing attention for the research community. However, depending of the context, some of the related approaches tend to be either highly mathematical, or applied to a specific context. This article aims to provide a survey on the main methods, techniques, and frameworks relevant to product packing and to highlight the main properties and features that should be further investigated to ensure a more efficient and optimised approach

Analysis on the less flexibility first (LFF) algorithm and its application to the container loading problem.

Wu Yuen-Ting.Thesis (M.Phil.)--Chinese University of Hong Kong, 2005.Includes bibliographical references (leaves 88-90).Abstracts in English and Chinese.Chapter 1. --- Introduction --- p.1Chapter 1.1 --- Background --- p.1Chapter 1.2 --- Research Objective --- p.4Chapter 1.3 --- Contribution --- p.5Chapter 1.4 --- Structure of this thesis --- p.6Chapter 2. --- Literature Review --- p.7Chapter 2.1 --- Genetic Algorithms --- p.7Chapter 2.1.1 --- Pre-processing step --- p.8Chapter 2.1.2 --- Generation of initial population --- p.10Chapter 2.1.3 --- Crossover --- p.11Chapter 2.1.4 --- Mutation --- p.12Chapter 2.1.5 --- Selection --- p.12Chapter 2.1.6 --- Results of GA on Container Loading Algorithm --- p.13Chapter 2.2 --- Layering Approach --- p.13Chapter 2.3 --- Mixed Integer Programming --- p.14Chapter 2.4 --- Tabu Search Algorithm --- p.15Chapter 2.5 --- Other approaches --- p.16Chapter 2.5.1 --- Block arrangement --- p.17Chapter 2.5.2 --- Multi-Directional Building Growing algorithm --- p.17Chapter 2.6 --- Comparisons of different container loading algorithms --- p.18Chapter 3. --- Principle of LFF Algorithm --- p.8Chapter 3.1 --- Definition of Flexibility --- p.8Chapter 3.2 --- The Less Flexibility First Principle (LFFP) --- p.23Chapter 3.3 --- The 2D LFF Algorithm --- p.25Chapter 3.3.1 --- Generation of Corner-Occupying Packing Move (COPM) --- p.26Chapter 3.3.2 --- Pseudo-packing and the Greedy Approach --- p.27Chapter 3.3.3 --- Real-packing --- p.30Chapter 3.4 --- Achievement of 2D LFF --- p.31Chapter 4. --- Error Bound Analysis on 2D LFF --- p.21Chapter 4.1 --- Definition of Error Bound --- p.21Chapter 4.2 --- Cause and Analysis on Unsatisfactory Results by LFF --- p.33Chapter 4.3 --- Formal Proof on Error Bound --- p.39Chapter 5. --- LFF for Container Loading Problem --- p.33Chapter 5.1 --- Problem Formulation and Term Definitions --- p.48Chapter 5.2 --- Possible Problems to be solved --- p.53Chapter 5.3 --- Implementation in Container Loading --- p.54Chapter 5.3.1 --- The Basic Algorithm --- p.56Chapter 5.4 --- A Sample Packing Scenario --- p.62Chapter 5.4.1 --- Generation of COPM list --- p.63Chapter 5.4.2 --- Pseudo-packing and the greedy approach --- p.66Chapter 5.4.3 --- Update of corner list --- p.69Chapter 5.4.4 --- Real-Packing --- p.70Chapter 5.5 --- Ratio Approach: A Modification to LFF --- p.70Chapter 5.6 --- LFF with Tightness Measure: CPU time Cut-down --- p.75Chapter 5.7 --- Experimental Results --- p.77Chapter 5.7.1 --- Comparison between LFF and LFFR --- p.77Chapter 5.7.2 --- "Comparison between LFFR, LFFT and other algorithms" --- p.78Chapter 5.7.3 --- Computational Time for different algorithms --- p.81Chapter 5.7.4 --- Conclusion of the experimental results --- p.83Chapter 6. --- Conclusion --- p.85Bibiography --- p.8

Magnetic Resonance Elastography of the Brain: from Phantom to Mouse to Man

The overall objective of this study is to develop magnetic resonance elastography: MRE) imaging to better understand brain deformation, brain tissue mechanical properties, and brain-skull interaction in vivo. The findings of this study provide parameters for numerical models of human head biomechanics, as well as data for validation of these models. Numerical simulations offer enormous potential to the study of traumatic brain injury: TBI) and may also contribute to the development of prophylactic devices for high-risk subjects: e.g., military personnel, first-responders, and athletes). Current numerical models have not been adequately parameterized or validated and their predictions remain controversial. This dissertation describes three kinds of MRE experiments, conducted in phantom: physical model), mouse, and man. Phantom studies provide a means to experimentally confirm the accuracy of MRE estimates of viscoelastic parameters in relatively simple materials and geometries. Studies in the mouse provide insight into the dispersive nature of brain tissue mechanical properties at frequencies beyond those that can be measured in humans. Studies in human subjects provide direct measurements of the human brain\u27s response to dynamic extracranial loads, including skull-brain energy transmission and viscoelastic properties

Application of general semi-infinite Programming to Lapidary Cutting Problems

We consider a volume maximization problem arising in gemstone cutting industry. The problem is formulated as a general semi-infinite program (GSIP) and solved using an interiorpoint method developed by Stein. It is shown, that the convexity assumption needed for the convergence of the algorithm can be satisfied by appropriate modelling. Clustering techniques are used to reduce the number of container constraints, which is necessary to make the subproblems practically tractable. An iterative process consisting of GSIP optimization and adaptive refinement steps is then employed to obtain an optimal solution which is also feasible for the original problem. Some numerical results based on realworld data are also presented

Agent-Based System for Mobile Service Adaptation Using Online Machine Learning and Mobile Cloud Computing Paradigm

An important aspect of modern computer systems is their ability to adapt. This is particularly important in the context of the use of mobile devices, which have limited resources and are able to work longer and more efficiently through adaptation. One possibility for the adaptation of mobile service execution is the use of the Mobile Cloud Computing (MCC) paradigm, which allows such services to run in computational clouds and only return the result to the mobile device. At the same time, the importance of machine learning used to optimize various computer systems is increasing. The novel concept proposed by the authors extends the MCC paradigm to add the ability to run services on a PC (e.g. at home). The solution proposed utilizes agent-based concepts in order to create a system that operates in a heterogeneous environment. Machine learning algorithms are used to optimize the performance of mobile services online on mobile devices. This guarantees scalability and privacy. As a result, the solution makes it possible to reduce service execution time and power consumption by mobile devices. In order to evaluate the proposed concept, an agent-based system for mobile service adaptation was implemented and experiments were performed. The solution developed demonstrates that extending the MCC paradigm with the simultaneous use of machine learning and agent-based concepts allows for the effective adaptation and optimization of mobile services

Discrete Modeling of Heat Conduction in Granular Media

This thesis addresses heat conduction in granular systems both under static and slow flow conditions with and without the presence of astagnant interstitial fluid. A novel discrete simulation technique for granular heat transfer, the Thermal Particle Dynamics (TPD) method hasbeen developed. By modeling particle-particle interactions, bed heterogeneities -- e.g., mechanical and thermal -- are directly accountedfor and transient temperature distribution are obtained at the particle level. This technique, based on the Discrete Element Method, not onlysheds light on fundamental issues in heat conduction in particulate systems, but also provides a valuable test-bench for existingcontinuous theories. Computational results, as well as supporting experiments coupled with existing theoretical models are used to probethe validity of the proposed simulation technique. Studies on heat conduction through static beds of particles indicate that stress and contact heterogeneities -- due primarily to theexistence of localized ``chains' of particles which support the majority of an imposed load (stress chains) -- may cause dramaticchanges in the way that heat is transported by conduction. It is found that by matching the microstructure of an experimental system onlyqualitatively, quantitatively accurate estimates of effective properties are possible, without requiring adjustable parameters. Onekey result in this study reveals that an important consideration has been missing from previous granular conduction studies -- the stressdistribution in the particle bed. Extensions of TPD to incorporate the ability to model heat transfer in particulate systems in the presenceof an interstitial fluid indicate that a good qualitative and quantitative agreement between measured and calculated values of theeffective thermal conductivity for a wide variety of materials in the presence of both liquid and/or gas are possible. Simulation results for slow granular flows -- e.g., simple shear cell and a rotating drum -- indicate that in both cases there is anenhancement of the effective thermal conductivity with increase in the shear rate due to enhanced mixing of the particles. These results arein agreement with previous theoretical and experimental investigations. In contrast to the behavior found at high shear rates, where the thermal conductivity is proportional to the shear rate, a complex non-linear relation is found for the effective conductivity in granular flows at low shear rates. This observation has not beenpreviously reported. It is argued that a balance between heat conduction and convection is necessary to explain these observations