Algorithms and data structures for three-dimensional packing

Cutting and packing problems are increasingly prevalent in industry. A well utilised freight vehicle will save a business money when delivering goods, as well as reducing the environmental impact, when compared to sending out two lesser-utilised freight vehicles. A cutting machine that generates less wasted material will have a similar effect. Industry reliance on automating these processes and improving productivity is increasing year-on-year. This thesis presents a number of methods for generating high quality solutions for these cutting and packing challenges. It does so in a number of ways. A fast, efficient framework for heuristically generating solutions to large problems is presented, and a method of incrementally improving these solutions over time is implemented and shown to produce even higher packing utilisations. The results from these findings provide the best known results for 28 out of 35 problems from the literature. This framework is analysed and its effectiveness shown over a number of datasets, along with a discussion of its theoretical suitability for higher-dimensional packing problems. A way of automatically generating new heuristics for this framework that can be problem specific, and therefore highly tuned to a given dataset, is then demonstrated and shown to perform well when compared to the expert-designed packing heuristics. Finally some mathematical models which can guarantee the optimality of packings for small datasets are given, and the (in)effectiveness of these techniques discussed. The models are then strengthened and a novel model presented which can handle much larger problems under certain conditions. The thesis finishes with a discussion about the applicability of the different approaches taken to the real-world problems that motivate them

A Multi-Start Algorithm for Solving the Capacitated Vehicle Routing Problem with Two-Dimensional Loading Constraints

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Applying computational intelligence to a real-world container loading problem in a warehouse environment

One of the problems presented in the day-to-day running of a warehouse is that of optimally selecting and loading groups of heavy rectangular palletised goods into larger rectangular containers while satisfying a number of practical constraints. The research presented in this thesis was commissioned by the logistics department in NSK Europe Ltd, for the purpose of providing feasible solutions to this problem. The problem is a version of the Container Loading Problem in the literature, and it is an active research area with many practical applications in industry. Most of the advances made in this area focus more on the optimisation of container utility i.e. volume or weight capacity, with very few focusing on the practical feasibility of the loading layout or pattern produced. Much of the work done also addresses only a few practical constraints at a time, leaving out a number of constraints that are of importance in real-world container loading. As this problem is well known to be a combinatorial NPhard problem, the exact mathematical methods that exist for solving it are computationally feasible for only problem instances with small sizes. For these reasons, this thesis investigates the use of computational intelligence techniques for solving and providing near-optimum solutions to this problem while simultaneously satisfying a number of practical constraints that must be considered for the solutions provided to be feasible. In proposing a solution to this problem and dealing with all the constraints considered, an algorithmic framework that decomposes the CLPs into sub-problems is presented. Each subproblem is solved using an appropriate algorithm, and a combination of constraints particular to each problem is satisfied. The resulting hybrid algorithm solves the entire problem as a whole and satisfies all the considered constraints. In order to identify and select feasible container layouts that are practical and easy to load, a measure of disorder, based on the concept of entropy in physics and information theory, is derived. Finally, a novel method of directing a Monte-Carlo tree search process using the derived entropy measure is employed, to generate loading layouts that are comparable to those produced by expert human loaders. In summary, this thesis presents a new approach for dealing with real-world container loading in a warehouse environment, particularly in instances where layout complexity is of major importance; such as the loading of heavy palletised goods using forklift trucks. The approach can be used to deal with a number of relevant practical constraints that need to be satisfied simultaneously, including those encountered when the heavy goods are arranged and physically packed into a container using forklift trucks

Evolutionary algorithms and hyper-heuristics for orthogonal packing problems

This thesis investigates two major classes of Evolutionary Algorithms, Genetic Algorithms (GAs) and Evolution Strategies (ESs), and their application to the Orthogonal Packing Problems (OPP). OPP are canonical models for NP-hard problems, the class of problems widely conceived to be unsolvable on a polynomial deterministic Turing machine, although they underlie many optimisation problems in the real world. With the increasing power of modern computers, GAs and ESs have been developed in the past decades to provide high quality solutions for a wide range of optimisation and learning problems. These algorithms are inspired by Darwinian nature selection mechanism that iteratively select better solutions in populations derived from recombining and mutating existing solutions. The algorithms have gained huge success in many areas, however, being stochastic processes, the algorithms' behaviour on different problems is still far from being fully understood. The work of this thesis provides insights to better understand both the algorithms and the problems. The thesis begins with an investigation of hyper-heuristics as a more general search paradigm based on standard EAs. Hyper-heuristics are shown to be able to overcome the difficulty of many standard approaches which only search in partial solution space. The thesis also looks into the fundamental theory of GAs, the schemata theorem and the building block hypothesis, by developing the Grouping Genetic Algorithms (GGA) for high dimensional problems and providing supportive yet qualified empirical evidences for the hypothesis. Realising the difficulties of genetic encoding over combinatorial search domains, the thesis proposes a phenotype representation together with Evolution Strategies that operates on such representation. ESs were previously applied mainly to continuous numerical optimisation, therefore being less understood when searching in combinatorial domains. The work in this thesis develops highly competent ES algorithms for OPP and opens the door for future research in this area

Evolutionary algorithms and hyper-heuristics for orthogonal packing problems

This thesis investigates two major classes of Evolutionary Algorithms, Genetic Algorithms (GAs) and Evolution Strategies (ESs), and their application to the Orthogonal Packing Problems (OPP). OPP are canonical models for NP-hard problems, the class of problems widely conceived to be unsolvable on a polynomial deterministic Turing machine, although they underlie many optimisation problems in the real world. With the increasing power of modern computers, GAs and ESs have been developed in the past decades to provide high quality solutions for a wide range of optimisation and learning problems. These algorithms are inspired by Darwinian nature selection mechanism that iteratively select better solutions in populations derived from recombining and mutating existing solutions. The algorithms have gained huge success in many areas, however, being stochastic processes, the algorithms' behaviour on different problems is still far from being fully understood. The work of this thesis provides insights to better understand both the algorithms and the problems. The thesis begins with an investigation of hyper-heuristics as a more general search paradigm based on standard EAs. Hyper-heuristics are shown to be able to overcome the difficulty of many standard approaches which only search in partial solution space. The thesis also looks into the fundamental theory of GAs, the schemata theorem and the building block hypothesis, by developing the Grouping Genetic Algorithms (GGA) for high dimensional problems and providing supportive yet qualified empirical evidences for the hypothesis. Realising the difficulties of genetic encoding over combinatorial search domains, the thesis proposes a phenotype representation together with Evolution Strategies that operates on such representation. ESs were previously applied mainly to continuous numerical optimisation, therefore being less understood when searching in combinatorial domains. The work in this thesis develops highly competent ES algorithms for OPP and opens the door for future research in this area