New Lagrangian Relaxation Based Algorithm for Resource Scheduling with Homogeneous Subproblems

X.H. Guan, Q.Z. Zhai and F. Lai
Additional contact information
X.H. Guan: Xian Jiaotong University
Q.Z. Zhai: Xian Jiaotong University
F. Lai: Xian Jiaotong University

Journal of Optimization Theory and Applications, 2002, vol. 113, issue 1, No 5, 65-82

Abstract: Abstract Solution oscillations, often caused by identical solutions to the homogeneous subproblems, constitute a severe and inherent disadvantage in applying Lagrangian relaxation based methods to resource scheduling problems with discrete decision variables. In this paper, the solution oscillations caused by homogeneous subproblems in the Lagrangian relaxation framework are identified and analyzed. Based on this analysis, the key idea to alleviate the homogeneous oscillations is to differentiate the homogeneous subproblems. A new algorithm is developed to solve the problem under the Lagrangian relaxation framework. The basic idea is to introduce a second-order penalty term in the Lagrangian. Since the dual cost function is no longer decomposable, a surrogate subgradient is used to update the multiplier at the high level. The homogeneous subproblems are not solved simultaneously, and the oscillations can be avoided or at least alleviated. Convergence proofs and properties of the new dual cost function are presented in the paper. Numerical testing for a short-term generation scheduling problem with two groups of identical units demonstrates that solution oscillations are greatly reduced and thus the generation schedule is significantly improved.

Keywords: Resource scheduling; resource allocation; Lagrangian relaxation (search for similar items in EconPapers)
Date: 2002
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1023/A:1014805213554 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:113:y:2002:i:1:d:10.1023_a:1014805213554

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1023/A:1014805213554

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().