Abstract
The container loading problem (CLP) is a real-world driven, combinatorial optimisation problem that addresses the maximisation of space usage in cargo transport units. The research conducted on this problem failed to fulfill the real needs of the transportation industry, owing to the inadequate representation of practical-relevant constraints. The dynamic stability of cargo is one of the most important practical constraints. It has been addressed in the literature in an over-simplified way which does not translate to real-world stability. This paper proposes a physics simulation tool based on a physics engine, which can be used to translate real-world stability into the CLP. To validate the tool, a set of benchmark tests is proposed and the results obtained with the physics simulation tool are compared to the state-of-the-art simulation engineering software Abaqus Unified FEA. Analytical calculations have been also conducted, and it was also possible to conclude that the tool proposed is a valid alternative. Copyright © 2017 Inderscience Enterprises Ltd.

Abstract
A good representation of a simple polygon, with a desired degree of approximation and complexity, is critical in many applications. This paper presents a method to achieve a complete Circle Covering Representation of a simple polygon, through a topological skeleton, the Medial Axis. The aim is to produce an efficient circle representation of irregular pieces, while considering the approximation error and the resulting complexity, i.e. the number of circles. This will help to address limitations of current approaches to some problems, such as Irregular Placement problems, which will, in turn, provide a positive economic and environmental impact where similar problems arise. © 2013 IFAC.

Abstract
Cutting and Packing problems are hard Combinatorial Optimization problems that naturally arise in all industries and services where raw-materials or space must be divided into smaller non-overlapping items, so that waste is minimized. All the Cutting and Packing problems have in common the existence of a geometric sub-problem, originated by the natural item non-overlapping constraints. An important class of Cutting and Packing problems are the Irregular Packing problems that occur when raw materials have to be cut into items with irregular shapes. Irregular Packing problems, also known as Nesting problems, naturally arises in the garment, footwear, tools manufacturing and shipbuilding industries, among others. Each industrial application has its owns particular issues mainly related to the raw material's specific characteristics. Several challenges remain open in the Irregular Packing problems field. Some are due to the combinatorial nature of these problems. Others are of geometric nature, due to the non-convex and non-regular geometry of the items involved. Moreover these geometric challenges do not allow the combinatorial ones being properly tackled. This paper is mainly focused on presenting and discussing efficient tools and representations to tackle the geometric layer of nesting algorithms that capture the needs of the real-world applications of Irregular Packing problems. © 2013 IFAC.

Abstract
In the Container Loading Problem literature, the cargo dynamic stability constraint has been evaluated by the percentage of boxes with insufficient lateral support. This metric has been used as a proxy for the real-world dynamic stability constraint and has conditioned the algorithms developed for this problem. It has the advantage of not being expensive from a computation perspective. However, guaranteeing that at least three sides of a box are in contact with another box or with the container wall does not necessarily ensure stability during transportation. In this paper we propose a physics simulation tool based on a physics engine that will be used in the evaluation of the dynamic stability constraint. We compare the results of our physics simulation tool with the state-of-the-art simulation engineering software Abaqus Unified FEA, and conclude that our tool is a promising alternative.

Abstract
Irregular nesting is a subgroup of cutting and packing problems in which a set of irregular items must be inserted in a rectangular container with a variable width. It is often found ill industries such as textile, wood and shipbuilding and an efficient solution usually renders an economical and environmental positive impact. Due to the complex geometry of items, the no overlapping rule is hard to guarantee and, therefore, geometric tools are usually employed. In this work, a raster method is proposed to solve the overlap minimization problem, which can be adapted to solve the irregular nesting problem. A map of overlap values is created and is employed to find the minimum overlap placement for each item A multiresolution approach is used to reduce the size of the map and, consequently, accelerate the search process. The results from tests performed using 4 benchmark tests indicates that more compact layouts can be obtained using multiple resolutions. Moreover, the results are competitive when compared to other solutions in the literature. Copyright (C)2015 IFAC.

Abstract
This paper analyses distinct methods to represent a polygon through circle covering, which satisfy specific requirements, that impact primarily the feasibility and the quality of the layout of final solution. The trade-off between the quality of the polygonal representation and its derived number of circles is also discussed, showing the impact on the resolution of the problem, in terms of computational efficiency. The approach used to tackle the Nesting problem in strip packing uses a Non-Linear Programming model. Addressing these problems allows to tackle real world problems with continuous rotations. © IFAC.