Solving Irregular Strip Packing Problems With Free Rotations Using Separation Lines

Solving nesting problems or irregular strip packing problems is to position polygons in a fixed width and unlimited length strip, obeying polygon integrity containment constraints and non-overlapping constraints, in order to minimize the used length of the strip. To ensure non-overlapping, we used separation lines. A straight line is a separation line if given two polygons, all vertices of one of the polygons are on one side of the line or on the line, and all vertices of the other polygon are on the other side of the line or on the line. Since we are considering free rotations of the polygons and separation lines, the mathematical model of the studied problem is nonlinear. Therefore, we use the nonlinear programming solver IPOPT (an algorithm of interior points type), which is part of COIN-OR. Computational tests were run using established benchmark instances and the results were compared with the ones obtained with other methodologies in the literature that use free rotation

Incorporating chemical signalling factors into cell-based models of growing epithelial tissues

In this paper we present a comprehensive computational framework within which the effects of chemical signalling factors on growing epithelial tissues can be studied. The method incorporates a vertex-based cell model, in conjunction with a solver for the governing chemical equations. The vertex model provides a natural mesh for the finite element method (FEM), with node movements determined by force laws. The arbitrary Lagrangian–Eulerian formulation is adopted to account for domain movement between iterations. The effects of cell proliferation and junctional rearrangements on the mesh are also examined. By implementing refinements of the mesh we show that the finite element (FE) approximation converges towards an accurate numerical solution. The potential utility of the system is demonstrated in the context of Decapentaplegic (Dpp), a morphogen which plays a crucial role in development of the Drosophila imaginal wing disc. Despite the presence of a Dpp gradient, growth is uniform across the wing disc. We make the growth rate of cells dependent on Dpp concentration and show that the number of proliferation events increases in regions of high concentration. This allows hypotheses regarding mechanisms of growth control to be rigorously tested. The method we describe may be adapted to a range of potential application areas, and to other cell-based models with designated node movements, to accurately probe the role of morphogens in epithelial tissues

Simulation studies of a phenomenological model for elongated virus capsid formation

We study a phenomenological model in which the simulated packing of hard, attractive spheres on a prolate spheroid surface with convexity constraints produces structures identical to those of prolate virus capsid structures. Our simulation approach combines the traditional Monte Carlo method with a modified method of random sampling on an ellipsoidal surface and a convex hull searching algorithm. Using this approach we identify the minimum physical requirements for non-icosahedral, elongated virus capsids, such as two aberrant flock house virus (FHV) particles and the prolate prohead of bacteriophage $\phi_{29}$, and discuss the implication of our simulation results in the context of recent experimental findings. Our predicted structures may also be experimentally realized by evaporation-driven assembly of colloidal spheres

Novel approaches to container loading: from heuristics to hybrid tabu search

A thesis submitted for the degree of Doctor of Philosophy of the University ofBedford shireThis work investigates new approaches to the container loading problem which address the issue of how to load three-dimensional, rectangular items (e.g. boxes) into the container in such a way that maximum utilisation is made of the container space. This problem occurs in several industry sectors where the loading approach places cargo effectively into aeroplanes, ships, trailers or trucks in order to save considerable cost. In carrying out this work, the investigation starts by developing a new heuristic approach to the two-dimensional bin packing problem, which has lower complexity than container loading in the aspects of constraints and geometry. A novel approach, including the heuristic strategies and handling method for remaining areas, is developed that can produce good results when testing with benchmark and real world data. Based on the research for two-dimensional bin packing, a novel heuristic approach is developed to deal with the container loading problem with some practical constraints. The heuristic approach to container loading also includes heuristic strategies and the handling of remaining spaces. The heuristic strategies construct effective loading arrangements where combinations of identical or different box types are loaded in blocks. The handling method for remaining spaces further improves the loading arrangements through the representation, partitioning and merging of remaining spaces. The heuristic approach obtains better volume utilisation and the highest stability compared with other published heuristic approaches. However, it does not achieve as high a volume utilisation as metaheuristic approaches, e.g. genetic algorithms and tabu search.To improve volume utilisation, a new hybrid heuristic approach to the container loading problem is further developed based on the tabu search technique which covers the encoding, evaluation criterion and configuration of neighbourhood and candidate solutions. The heuristic strategies as well as the handling method for remaining spaces developed in the heuristic approach are used in this new hybrid tabu search approach. It is shown that the hybrid approach has better volume utilisation than the published approaches under the condition that all loaded boxes with one hundred per cent support from below. In addition, the experimental results show that both the heuristic and hybrid tabu search approaches can also be applied to the multiple container loading problem