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Exact approaches to late work scheduling on unrelated machines

Liu Xinbo, Wang Wen, Chen Xin, Sterna Malgorzata, Blazewicz Jacek

International Journal of Applied Mathematics and Computer Science

2023

Vol. 33, no. 2

285--295

We consider the scheduling problem on unrelated parallel machines in order to minimize the total late work. Since the problem is NP-hard, we propose a mathematical model and two dedicated exact approaches for solving it, based on the branching and bounding strategy and on enumerating combined with a dynamic programming algorithm. The time efficiencies of all three approaches are evaluated through computational experiments.

Sekwencjonowanie DNA z błędami negatywnymi oraz informacją o powtórzeniach

Kwarciak K., Radom M., Formanowicz P.

Zeszyty Naukowe. Automatyka / Politechnika Śląska

2008

z. 151

215-222

W pracy przedstawiony jest algorytm typu podziału i ograniczeń dla problemu sekwencjonowania przez hybrydyzację z błędami negatywnymi oraz częściową informacją o powtórzeniach. Uwzględnienie tego rodzaju informacji możliwe jest ze względu na rozwój technologii stosowanej w eksperymencie hybrydyzacyjnym. Prowadzi ono do rozszerzenia standardowej wersji metody sekwencjonowania przez hybrydyzację oraz do polepszenia jakości uzyskiwanych rozwiązań.

In this paper a branch and bound algorithm for sequencing by hybridization problem with negative errors and partial information about repetitions is presented. Taking into account information of this type is possible because of the development of the technology used in the hybridization experiment. It leads to an extension of the standard sequencing by hybridization method and to an improvement of the quality of the obtained results.

The branch and bound algorithm for a backup virtual path assignment in survivable atm networks

Walkowiak K.

International Journal of Applied Mathematics and Computer Science

2002

Vol. 12, no 2

257-267

Issues of network survivability are important, since users of computer networks should be provided with some guarantees of data delivery. A large amount of data may be lost in high-speed Asynchronous Transfer Mode (ATM) due to a network failure and cause significant economic loses. This paper addresses problems of network survivability. The characteristics of virtual paths and their influence on network restoration are examined. A new problem of Backup Virtual Path Routing is presented for the local-destination rerouting strategy. The function of the flow lost due to a failure of a single link is chosen as the performance index. The problem of finding the optimal virtual path assignment is NP-complete. Therefore we develop an exact algorithm based on the branch and bound approach. Moreover, two heuristic algorithms are proposed. Numerical results are presented.