@misc{Rudy_Jarosław_New,
 author={Rudy, Jarosław and Idzikowski, Radosław and Smutnicki, Czesław and Banaszak, Zbigniew and Bocewicz, Grzegorz},
 howpublished={online},
 publisher={Zielona Góra: Uniwersytet Zielonogórski},
 language={eng},
 abstract={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.},
 abstract={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.},
 type={artykuł},
 title={New ideas in Lagrangian relaxation for a scheduling problem with the weighted tardiness criterion},
 keywords={Lagrangian relaxation, scheduling, total weighted tardiness, metaheuristics},
}