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2. Application of the Interpolation Approach for Approximating Single-Machine Scheduling Problem with an Unknown Objective Function

Author

Lazarev, Alexander, Barashov, Egor, Lemtyuzhnikova, Darya, Tyunyatkin, Andrey, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Olenev, Nicholas, editor, Evtushenko, Yuri, editor, Jaćimović, Milojica, editor, Khachay, Michael, editor, Malkova, Vlasta, editor, and Pospelov, Igor, editor

Published
2022
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11. An Interpolation-Based Polynomial Method of Estimating the Objective Function Value in Scheduling Problems of Minimizing the Maximum Lateness

Author

Darya V. Lemtyuzhnikova, Alexander A. Lazarev, and Andrey Alexandrovich Tyunyatkin

Subjects
Mathematical optimization, Polynomial method, Scheduling (production processes), Value (mathematics), numerical_analysis_optimization, Mathematics, Interpolation
Abstract

An approach to estimating the objective function value of minimization maximum lateness problem is proposed. It is shown how to use transformed instances to define a new continuous objective function. After that, using this new objective function, the approach itself is formulated. We calculate the objective function value for some polynomially solvable transformed instances and use them as interpolation nodes to estimate the objective function of the initial instance. What is more, two new polynomial cases, that are easy to use in the approach, are proposed. In the end of the paper numeric experiments are described and their results are provided.

Published
2021

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