NDLI: An improved lagrangian relaxation method for discrete optimization applications

Content Provider	IEEE Xplore Digital Library
Author	Weihua Wang Luh, P.B. Yan, J.H. Stern, G.A.
Copyright Year	2008
Description	Author affiliation: Dept. of Electr. & Comput. Eng., Univ. of Connecticut, Storrs, CT (Weihua Wang; Luh, P.B.)
Abstract	Lagrangian relaxation has been a powerful methodology to solve discrete and mixed integer optimization problems such as planning, scheduling, coordination, and unit commitment. The subgradient method is frequently used within Lagrangian relaxation to update multipliers, where a subgradient direction is obtained by fully minimizing the relaxed problem. A dual value is a lower bound to the optimal feasible cost, and can be used to evaluate solution quality. Because full minimization of the relaxed problem is time-consuming and even impossible when the problem is complex, surrogate optimization has been developed where a proper direction can be obtained by only approximate optimization of the relaxed problem. However, the lower bound property of the ldquosurrogate dualrdquo is lost and the convergence of the algorithm cannot be guaranteed. This paper presents a new algorithm based on the surrogate Lagrangian relaxation method to resolve the lower bound issue with convergence guaranteed. The key idea is to examine the different behaviors of the algorithm when the optimal dual value is overestimated or underestimated, and to adjust the estimate accordingly. Theoretical proof on the different behaviors and the convergence of the algorithm are provided. Testing results on manufacturing scheduling problems show the effectiveness of the algorithm.
Starting Page	359
Ending Page	364
File Size	143965
Page Count	6
File Format	PDF
ISBN	9781424420223
DOI	10.1109/COASE.2008.4626544
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2008-08-23
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Bridges USA Councils Automation Conferences
Content Type	Text
Resource Type	Article

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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