Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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

Version 1 : Received: 6 November 2021 / Approved: 9 November 2021 / Online: 9 November 2021 (13:24:19 CET)

How to cite: Lazarev, A.A.; Lemtyuzhnikova, D.V.; Tyunyatkin, A.A. An Interpolation-Based Polynomial Method of Estimating the Objective Function Value in Scheduling Problems of Minimizing the Maximum Lateness. Preprints 2021, 2021110169 (doi: 10.20944/preprints202111.0169.v1). Lazarev, A.A.; Lemtyuzhnikova, D.V.; Tyunyatkin, A.A. An Interpolation-Based Polynomial Method of Estimating the Objective Function Value in Scheduling Problems of Minimizing the Maximum Lateness. Preprints 2021, 2021110169 (doi: 10.20944/preprints202111.0169.v1).

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.

Keywords

discrete mathematics; scheduling; optimization; interpolation; approximation; objective function.

Subject

MATHEMATICS & COMPUTER SCIENCE, Numerical Analysis & Optimization

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