Multi‐Objective Hyper‐Heuristics

Multi‐objective hyper‐heuristics is a search method or learning mechanism that operates over a fixed set of low‐level heuristics to solve multi‐objective optimization problems by controlling and combining the strengths of those heuristics. Although numerous papers on hyper‐heuristics have been published and several studies are still underway, most research has focused on single‐objective optimization. Work on hyper‐heuristics for multi‐objective optimization remains limited. This chapter draws attention to this area of research to help researchers and PhD students understand and reuse these methods. It also provides the basic concepts of multi‐objective optimization and hyper‐heuristics to facilitate a better understanding of the related research areas, in addition to exploring hyper‐heuristic methodologies that address multi‐objective optimization. Some design issues related to the development of hyper‐heuristic framework for multi‐objective optimization are discussed. The chapter concludes with a case study of multi‐objective selection hyper‐heuristics and its application on a real‐world problem

Problemas de corte: métodos exactos y aproximados para formulaciones mono y multi-objetivo

Los problemas de corte y empaquetado son una familia de problemas de optimización combinatoria que han sido ampliamente estudiados en numerosas áreas de la industria y la investigación, debido a su relevancia en una enorme variedad de aplicaciones reales. Son problemas que surgen en muchas industrias de producción donde se debe realizar la subdivisión de un material o espacio disponible en partes más pequeñas. Existe una gran variedad de métodos para resolver este tipo de problemas de optimización. A la hora de proponer un método de resolución para un problema de optimización, es recomendable tener en cuenta el enfoque y las necesidades que se tienen en relación al problema y su solución. Las aproximaciones exactas encuentran la solución óptima, pero sólo es viable aplicarlas a instancias del problema muy pequeñas. Las heurísticas manejan conocimiento específico del problema para obtener soluciones de alta calidad sin necesitar un excesivo esfuerzo computacional. Por otra parte, las metaheurísticas van un paso más allá, ya que son capaces de resolver una clase muy general de problemas computacionales. Finalmente, las hiperheurísticas tratan de automatizar, normalmente incorporando técnicas de aprendizaje, el proceso de selección, combinación, generación o adaptación de heurísticas más simples para resolver eficientemente problemas de optimización. Para obtener lo mejor de estos métodos se requiere conocer, además del tipo de optimización (mono o multi-objetivo) y el tamaño del problema, los medios computacionales de los que se dispone, puesto que el uso de máquinas e implementaciones paralelas puede reducir considerablemente los tiempos para obtener una solución. En las aplicaciones reales de los problemas de corte y empaquetado en la industria, la diferencia entre usar una solución obtenida rápidamente y usar propuestas más sofisticadas para encontrar la solución óptima puede determinar la supervivencia de la empresa. Sin embargo, el desarrollo de propuestas más sofisticadas y efectivas normalmente involucra un gran esfuerzo computacional, que en las aplicaciones reales puede provocar una reducción de la velocidad del proceso de producción. Por lo tanto, el diseño de propuestas efectivas y, al mismo tiempo, eficientes es fundamental. Por esta razón, el principal objetivo de este trabajo consiste en el diseño e implementación de métodos efectivos y eficientes para resolver distintos problemas de corte y empaquetado. Además, si estos métodos se definen como esquemas lo más generales posible, se podrán aplicar a diferentes problemas de corte y empaquetado sin realizar demasiados cambios para adaptarlos a cada uno. Así, teniendo en cuenta el amplio rango de metodologías de resolución de problemas de optimización y las técnicas disponibles para incrementar su eficiencia, se han diseñado e implementado diversos métodos para resolver varios problemas de corte y empaquetado, tratando de mejorar las propuestas existentes en la literatura. Los problemas que se han abordado han sido: el Two-Dimensional Cutting Stock Problem, el Two-Dimensional Strip Packing Problem, y el Container Loading Problem. Para cada uno de estos problemas se ha realizado una amplia y minuciosa revisión bibliográfica, y se ha obtenido la solución de las distintas variantes escogidas aplicando diferentes métodos de resolución: métodos exactos mono-objetivo y paralelizaciones de los mismos, y métodos aproximados multi-objetivo y paralelizaciones de los mismos. Los métodos exactos mono-objetivo aplicados se han basado en técnicas de búsqueda en árbol. Por otra parte, como métodos aproximados multi-objetivo se han seleccionado unas metaheurísticas multi-objetivo, los MOEAs. Además, para la representación de los individuos utilizados por estos métodos se han empleado codificaciones directas mediante una notación postfija, y codificaciones que usan heurísticas de colocación e hiperheurísticas. Algunas de estas metodologías se han mejorado utilizando esquemas paralelos haciendo uso de las herramientas de programación OpenMP y MPI. En el caso d

Choice function based hyper-heuristics for multi-objective optimization

A selection hyper-heuristic is a high level search methodology which operates over a fixed set of low level heuristics. During the iterative search process, a heuristic is selected and applied to a candidate solution in hand, producing a new solution which is then accepted or rejected at each step. Selection hyper-heuristics have been increasingly, and successfully, applied to single-objective optimization problems, while work on multi-objective selection hyper-heuristics is limited. This work presents one of the initial studies on selection hyper-heuristics combining a choice function heuristic selection methodology with great deluge and late acceptance as non-deterministic move acceptance methods for multi-objective optimization. A well-known hypervolume metric is integrated into the move acceptance methods to enable the approaches to deal with multi-objective problems. The performance of the proposed hyper-heuristics is investigated on the Walking Fish Group test suite which is a common benchmark for multi-objective optimization. Additionally, they are applied to the vehicle crashworthiness design problem as a real-world multi-objective problem. The experimental results demonstrate the effectiveness of the non-deterministic move acceptance, particularly great deluge when used as a component of a choice function based selection hyper-heuristic

A multi-objective hyper-heuristic based on choice function

Hyper-heuristics are emerging methodologies that perform a search over the space of heuristics in an attempt to solve difficult computational optimization problems. We present a learning selection choice function based hyper-heuristic to solve multi-objective optimization problems. This high level approach controls and combines the strengths of three well-known multi-objective evolutionary algorithms (i.e. NSGAII, SPEA2 and MOGA), utilizing them as the low level heuristics. The performance of the proposed learning hyper-heuristic is investigated on the Walking Fish Group test suite which is a common benchmark for multi-objective optimization. Additionally, the proposed hyper-heuristic is applied to the vehicle crashworthiness design problem as a real-world multi-objective problem. The experimental results demonstrate the effectiveness of the hyper-heuristic approach when compared to the performance of each low level heuristic run on its own, as well as being compared to other approaches including an adaptive multi-method search, namely AMALGAM

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

A genetic programming hyper-heuristic approach to automated packing

This thesis presents a programme of research which investigated a genetic programming hyper-heuristic methodology to automate the heuristic design process for one, two and three dimensional packing problems. Traditionally, heuristic search methodologies operate on a space of potential solutions to a problem. In contrast, a hyper-heuristic is a heuristic which searches a space of heuristics, rather than a solution space directly. The majority of hyper-heuristic research papers, so far, have involved selecting a heuristic, or sequence of heuristics, from a set pre-defined by the practitioner. Less well studied are hyper-heuristics which can create new heuristics, from a set of potential components. This thesis presents a genetic programming hyper-heuristic which makes it possible to automatically generate heuristics for a wide variety of packing problems. The genetic programming algorithm creates heuristics by intelligently combining components. The evolved heuristics are shown to be highly competitive with human created heuristics. The methodology is first applied to one dimensional bin packing, where the evolved heuristics are analysed to determine their quality, specialisation, robustness, and scalability. Importantly, it is shown that these heuristics are able to be reused on unseen problems. The methodology is then applied to the two dimensional packing problem to determine if automatic heuristic generation is possible for this domain. The three dimensional bin packing and knapsack problems are then addressed. It is shown that the genetic programming hyper-heuristic methodology can evolve human competitive heuristics, for the one, two, and three dimensional cases of both of these problems. No change of parameters or code is required between runs. This represents the first packing algorithm in the literature able to claim human competitive results in such a wide variety of packing domains

Moldable Items Packing Optimization

This research has led to the development of two mathematical models to optimize the problem of packing a hybrid mix of rigid and moldable items within a three-dimensional volume. These two developed packing models characterize moldable items from two perspectives: (1) when limited discrete configurations represent the moldable items and (2) when all continuous configurations are available to the model. This optimization scheme is a component of a lean effort that attempts to reduce the lead-time associated with the implementation of dynamic product modifications that imply packing changes. To test the developed models, they are applied to the dynamic packing changes of Meals, Ready-to-Eat (MREs) at two different levels: packing MRE food items in the menu bags and packing menu bags in the boxes. These models optimize the packing volume utilization and provide information for MRE assemblers, enabling them to preplan for packing changes in a short lead-time. The optimization results are validated by running the solutions multiple times to access the consistency of solutions. Autodesk Inventor helps visualize the solutions to communicate the optimized packing solutions with the MRE assemblers for training purposes

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

The three-dimensional single-bin-size bin packing problem: combining metaheuristic and machine learning approaches

The Three-Dimensional Single-Bin-Size Bin Packing Problem is one of the most studied problem in the Cutting & Packing category. From a strictly mathematical point of view, it consists of packing a finite set of strongly heterogeneous “small” boxes, called items, into a finite set of identical “large” rectangles, called bins, minimizing the unused volume and requiring that the items are packed without overlapping. The great interest is mainly due to the number of real-world applications in which it arises, such as pallet and container loading, cutting objects out of a piece of material and packaging design. Depending on these real-world applications, more objective functions and more practical constraints could be needed. After a brief discussion about the real-world applications of the problem and a exhaustive literature review, the design of a two-stage algorithm to solve the aforementioned problem is presented. The algorithm must be able to provide the spatial coordinates of the placed boxes vertices and also the optimal boxes input sequence, while guaranteeing geometric, stability, fragility constraints and a reduced computational time. Due to NP-hard complexity of this type of combinatorial problems, a fusion of metaheuristic and machine learning techniques is adopted. In particular, a hybrid genetic algorithm coupled with a feedforward neural network is used. In the first stage, a rich dataset is created starting from a set of real input instances provided by an industrial company and the feedforward neural network is trained on it. After its training, given a new input instance, the hybrid genetic algorithm is able to run using the neural network output as input parameter vector, providing as output the optimal solution. The effectiveness of the proposed works is confirmed via several experimental tests