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[popis_en] => The scheduling of manufacturing processes aims to find sequences of jobs on given machines optimal by a selected criterion such as minimal completion time of all operations, minimal losses caused by exceeding the required completion times, minimal sum of machine idle times, etc. In the paper, a mathematical model of the job shop scheduling problem is derived and suitable representations are mentioned for solving it by heuristic methods, due to the fact that this combinatorial problem is NP-complete and exact solutions can only be gained in a reasonable time for small instances.
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[popis] => The task of planning trajectories plays an important role in transportation, robotics, information systems, etc. In robot motion planning, the robot should pass around obstacles from a given starting position to a given target position, touching none of them, i.e. the goal is to find a collision-free path from the starting to the target position. Research on path planning has yielded many fundamentally different approaches to the solution of this problem that can be classified as roadmap methods (visibility graph method, Voronoi diagram) and methods based on cell decomposition. Assuming movements only in a restricted number of directions (eight directional or horizontal/vertical) the task, with respect to its combinatorial nature, can be solved by decomposition methods using heuristic techniques. The cell decomposition methods may include a case-based reasoning procedure. Robot motion planning algorithms can be modified by considering a robot as a point and enlarging the obstacles in the workspace accordingly. In order to avoid the explicit construction of the obstacle region, sampling-based motion planning algorithms have been proposed such as probabilistic roadmap methods or rapidly exploring random trees. We present drawbacks of these approaches Then, using the Voronoi diagrams, we need only polynomial time for finding a solution and, choosing a Euclidean or rectilinear metric, it can be adapted to tasks with general or directional-constrained movements
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[citace_html] => ŠEDA, M. A Comparison of Roadmap and Cell Decomposition Methods in Robot Motion Planning. WSEAS TRANSACTIONS on SYSTEMS and CONTROL, 2007, vol. 2, no. 2, p. 101-108. ISSN: 1991-8763.
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[popis] => In this paper, mathematical models for permutation flow shop scheduling and job shop scheduling problems are proposed. The first problem is based on a mixed integer programming model. As the problem is NP-complete, this model can only be used for smaller instances where an optimal solution can be computed. For large instances, another model is proposed which is suitable for solving the problem by stochastic heuristic methods. For the job shop scheduling problem, a mathematical model and its main representation schemes are presented.
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[citace_text] => HOUŠKA, P., SINGULE, V., BŘEZINA, T., EHRENBERGER, Z. Control of dynamic stability of the four-legged walking robot movement. Elektronika, 2004, roč. 2004, č. 8-9, 3 s. ISSN: 0033-2089.
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