ISSN:
1436-3259
Keywords:
Stochastic optimization
;
linear programming
;
simplex method
;
Karmarkar's method
Source:
Springer Online Journal Archives 1860-2000
Topics:
Architecture, Civil Engineering, Surveying
,
Energy, Environment Protection, Nuclear Power Engineering
,
Geography
,
Geosciences
Notes:
Abstract Optimization of multi-reservoir systems operations is typically a very large scale optimization problem. The following are the three types of optimization problems solved using linear programming (LP): (i) deterministic optimization for multiple periods involving fine stage intervals, for example, from an hour to a week (ii) implicit stochastic optimization using multiple years of inflow data, and (iii) explicit stochastic optimization using probability distributions of inflow data. Until recently, the revised simplex method has been the most efficient solution method available for solving large scale LP problems. In this paper, we show that an implementation of the Karmarkar's interior-point LP algorithm with a newly developed stopping criterion solves optimization problems of large multi-reservoir operations more efficiently than the simplex method. For example, using a Micro VAX II minicomputer, a 40 year, monthly stage, two-reservoir system optimization problem is solved 7.8 times faster than the advanced simplex code in MINOS 5.0. The advantage of this method is expected to be greater as the size of the problem grows from two reservoirs to multiples of reservoirs. This paper presents the details of the implementation and testing and in addition, some other features of the Karmarkar's algorithm which makes it a valuable optimization tool are illuminated.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01543425
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