New ideas in Lagrangian relaxation for a scheduling problem with the weighted tardiness criterion

• Autorzy: Rudy Jarosław , Idzikowski Radosław , Smutnicki Czesław , Banaszak Zbigniew , Bocewicz Grzegorz

Identyfikatory

DOI

10.61822/amcs-2024-0017

• Języki publikacji: EN

Abstrakty

EN

We consider an extension of Lagrangian relaxation methods for solving the total weighted tardiness scheduling problem on a single machine. First, we investigate a straightforward relaxation method and decompose it into upper and lower subproblems. For the upper subproblem we propose an alternative solving method in the form of a local search metaheuristic. We also introduce a scaling technique by arbitrary numbers to reduce the complexity of the problem and confront it with greatest common divisor scaling. Next, we propose a novel alternative relaxation approach based on aggregating constraints. We discuss the properties and implementation of this new approach and a technique to further reduce its computational complexity. We perform a number of computer experiments on instances based on the OR-Library generation scheme to illustrate and ascertain the numerical properties of the proposed methods. The results indicate that for larger instances the proposed alternative relaxation and scaling approaches have a much better convergence rate with little to no decrease in solution quality. The results also show that the proposed local-search metaheuristic is a viable alternative to the existing solving methods.

Słowa kluczowe

EN

Lagrangian relaxation; scheduling problem; total weighted tardiness; metaheuristics

PL

relaksacja Lagrange'a; problem harmonogramowania; metaheurystyka

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2024
• Tom: Vol. 34, no. 2
• Strony: 235--251
• Opis fizyczny: Bibliogr. 38 poz., rys., tab., wykr.

Twórcy

autor

Rudy Jarosław

• Department of Control Systems and Mechatronics, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

autor

Idzikowski Radosław

• Department of Control Systems and Mechatronics, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

autor

Smutnicki Czesław

• Department of Computer Engineering, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

autor

Banaszak Zbigniew

• Department of Computer Science and Management, Koszalin University of Technology, Śniadeckich 2, 75-453 Koszalin, Poland

autor

Bocewicz Grzegorz

• Department of Computer Science and Management, Koszalin University of Technology, Śniadeckich 2, 75-453 Koszalin, Poland

Bibliografia

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