pARMS: a parallel version of the algebraic recursive multilevel solver

Zhongze Li; Yousef Saad; Masha Sosonkina

doi:10.1002/nla.325

pARMS: a parallel version of the algebraic recursive multilevel solver

Numerical Linear Algebra with Applications ◽

10.1002/nla.325 ◽

2003 ◽

Vol 10 (5-6) ◽

pp. 485-509 ◽

Cited By ~ 51

Author(s):

Zhongze Li ◽

Yousef Saad ◽

Masha Sosonkina

Keyword(s):

Parallel Version ◽

Multilevel Solver

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Exploiting Soft Constraints within Decomposition and Coordination Methods for Sub-hourly Unit Commitment

10.36227/techrxiv.12950414.v1 ◽

2020 ◽

Author(s):

Niranjan Raghunathan ◽

Mikhail Bragin ◽

Bing Yan ◽

Peter Luh ◽

Khosrow Moslehi ◽

...

Keyword(s):

Unit Commitment ◽

Daily Basis ◽

Time Limit ◽

Soft Constraints ◽

Problem Complexity ◽

Surrogate Optimization ◽

Parallel Version ◽

Improved Performance ◽

Coordination Methods ◽

Relaxed Problem

Unit commitment (UC) is an important problem solved on a daily basis within a strict time limit. While hourly UC problems are currently considered, they may not be flexible enough with the fast-changing demand and the increased penetration of intermittent renewables. Sub-hourly UC is therefore recommended. This, however, will significantly increase problem complexity even under the deterministic setting, and current methods may not be able to obtain good solutions within the time limit. In this paper, deterministic sub-hourly UC is considered, with the innovative exploitation of soft constraints – constraints that do not need to be strictly satisfied, but with predetermined penalty coefficients for their violations. The key idea is the “surrogate optimization” concept that ensures multiplier convergence within “surrogate” Lagrangian relaxation as long as the “surrogate optimality condition” is satisfied without the need to optimally solve the “relaxed problem.” Consequently, subproblems can still be formed and optimized when soft constraints are not relaxed, leading to a drastically reduced number of multipliers and improved performance. To further enhance the method, a parallel version is developed. Testing results on the Polish system demonstrate the effectiveness and robustness of both the sequential and parallel versions at finding high-quality solutions within the time limit.

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