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A heuristic approach to optimizing the loading of homogeneous marine cargo

Bernardelli Michał

Operations Research and Decisions

2022

Vol. 32, No. 2

1--15

In this article, the optimal loading of homogeneous marine cargo is considered. A mathematical formulation in terms of a mixed-integer linear program can be given. Still, the level of complexity turns out to be too high to perform full-scale computations. On the one hand, the reasons for this are the multitude of variables and constraints. On the other hand, feasible solutions to such problems may often be economically unacceptable or simply empty. Therefore, a heuristic is presented, according to which the relaxation of the limiting conditions influencing the solution’s feasibility and its economic profitability was parametrized. Under this heuristic, shifting the deadlines of selected orders is allowed. Also, the assignment of orders to vessels is separated from the allocation of vessels to piers in loading and unloading ports. The solution presented can be easily generalized by adding additional restrictions or features like indirect vessels, founding cost, or differentiation between materials.

Dynamic Path Planning with Regular Triangulations

Brož P., Zemek M., Kolingerová I., Szkandera J.

Machine Graphics and Vision

2014

Vol. 23, No. 3/4

119--142

Path planning is a well known problem that has been extensively studied in many scientific disciplines. In general, it defines a task of finding a path between two given spots in an abstract environment so that the path satisfies certain criterion of optimality. Although there are many methods solving this objective, they usually assume the examined space does not change in runtime. Modern applications, however, do not have to meet these requirements, especially in case of virtual reality or computer games. Therefore, we propose a general model for real-time path planning in dynamic environment where the obstacles can nondeterministically appear, disappear, change the position, orientation or even shape. The model uses a triangulation for dynamic space subdivision among bounding spheres of the obstacles and a heuristic algorithm to repair an already found path after any change of the scene. The presented solution is the first one using regular triangulation. At the price of the suboptimal result, it provides an efficient and fast way to plan a path with the maximal clearance among the moving and changing obstacles. In comparison to raster based techniques and methods using the Delaunay triangulation (Voronoi diagram), it requires less time to preprocess and generates paths with a larger clearance.