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    Recent advances and applications of surrogate models for finite element method computations: a review
    (Springer, 2022-07-17) Kůdela, Jakub; Matoušek, Radomil
    The utilization of surrogate models to approximate complex systems has recently gained increased popularity. Because of their capability to deal with black-box problems and lower computational requirements, surrogates were successfully utilized by researchers in various engineering and scientific fields. An efficient use of surrogates can bring considerable savings in computational resources and time. Since literature on surrogate modelling encompasses a large variety of approaches, the appropriate choice of a surrogate remains a challenging task. This review discusses significant publications where surrogate modelling for finite element method-based computations was utilized. We familiarize the reader with the subject, explain the function of surrogate modelling, sampling and model validation procedures, and give a description of the different surrogate types. We then discuss main categories where surrogate models are used: prediction, sensitivity analysis, uncertainty quantification, and surrogate-assisted optimization, and give detailed account of recent advances and applications. We review the most widely used and recently developed software tools that are used to apply the discussed techniques with ease. Based on a literature review of 180 papers related to surrogate modelling, we discuss major research trends, gaps, and practical recommendations. As the utilization of surrogate models grows in popularity, this review can function as a guide that makes surrogate modelling more accessible.
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    Optimal control of combined heat and power station operation
    (Springer Nature, 2023-09-13) Kůdela, Jakub; Suja, Jerguš; Šomplák, Radovan; Pluskal, Jaroslav; Hrabec, Dušan
    Combined heat and power stations have become one of the most utilized units of district heating systems. These stations usually contain several boilers for burning fossil fuels and renewable resources used for heating up steam, which can be used either for residential and commercial heating or electricity generation. To ensure efficiency, a boiler should either run continuously (for at least a given period) on a power output higher than a given threshold or switch off. The optimal control of the plant operations should combine an efficient setup for the turbine and boilers in operation, reflecting the demand for steam and the price of electricity, and a schedule that describes which boilers should be in operation at a given time. This paper proposes a method for optimal control of combined heat and power station operation for a given time horizon. The method is based on a two-level approach. The lower-level models correspond to finding the optimal setup of the combined heat and power station parameters for an hourly demand for different kinds of steam. The upper-level model corresponds to the optimal schedule of the operations of the individual boilers, which is planned for the entire time horizon. The lower-level model is modeled as a mixed-integer linear programming problem and is solved using parametric programming. A dynamic programming algorithm solves the upper-level model with a rolling horizon. The validity of the proposed method and its computational complexity for different granularity of the time horizon, different ranges of the parameters, varying demand for various kinds of steam, and varying electricity prices are investigated in a case study. The presented approach can be readily applied to other control problems with a similar structure.
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    Evolutionary Computation Techniques for Path Planning Problems in Industrial Robotics: A State-of-the-Art Review
    (MDPI, 2023-12-04) Juříček, Martin; Parák, Roman; Kůdela, Jakub
    The significance of robot manipulators in engineering applications and scientific research has increased substantially in recent years. The utilization of robot manipulators to save labor and increase production accuracy is becoming a common practice in industry. Evolutionary computation (EC) techniques are optimization methods that have found their use in diverse engineering fields. This state-of-the-art review focuses on recent developments and progress in their applications for industrial robotics, especially for path planning problems that need to satisfy various constraints that are implied by both the geometry of the robot and its surroundings. We discuss the most-used EC method and the modifications that suit this particular purpose, as well as the different simulation environments that are used for their development. Lastly, we outline the possible research gaps and the expected directions future research in this area will entail.
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    Chance-Constrained Optimization Formulation for Ship Conceptual Design: A Comparison of Metaheuristic Algorithms
    (MDPI, 2023-11-03) Kůdela, Jakub
    This paper presents a new chance-constrained optimization (CCO) formulation for the bulk carrier conceptual design. The CCO problem is modeled through the scenario design approach. We conducted extensive numerical experiments comparing the convergence of both canonical and state-of-the-art metaheuristic algorithms on the original and CCO formulations and showed that the CCO formulation is substantially more difficult to solve. The two best-performing methods were both found to be differential evolution-based algorithms. We then provide an analysis of the resulting solutions in terms of the dependence of the distribution functions of the unit transportation costs and annual cargo capacity of the ship design on the probability of violating the chance constraints.
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    The Maximum Clique Problem and Integer Programming Models, Their Modifications, Complexity and Implementation
    (MDPI, 2023-10-26) Šeda, Miloš
    The maximum clique problem is a problem that takes many forms in optimization and related graph theory problems, and also has many applications. Because of its NP-completeness (nondeterministic polynomial time), the question arises of its solvability for larger instances. Instead of the traditional approaches based on the use of approximate or stochastic heuristic methods, we focus here on the use of integer programming models in the GAMS (General Algebraic Modelling System) environment, which is based on exact methods and sophisticated deterministic heuristics incorporated in it. We propose modifications of integer models, derive their time complexities and show their direct use in GAMS. GAMS makes it possible to find optimal solutions to the maximum clique problem for instances with hundreds of vertices and thousands of edges within minutes at most. For extremely large instances, good approximations of the optimum are given in a reasonable amount of time. A great advantage of this approach over all the mentioned algorithms is that even if GAMS does not find the best known solution within the chosen time limit, it displays its value at the end of the calculation as a reachable bound.