A massively parallel interior-point solver for LPs with generalized arrowhead structure, and applications to energy system models

Research output: Contribution to journalResearch articleContributedpeer-review



Linear energy system models are a crucial component of energy system design and operations, as well as energy policy consulting. If detailed enough, such models lead to large-scale linear programs, which can be intractable even for the best state-of-the-art solvers. This article introduces an interior-point solver that exploits common structures of energy system models to efficiently run in parallel on distributed-memory systems. The solver is designed for linear programs with doubly-bordered block-diagonal constraint matrix and makes use of a Schur complement based decomposition. In order to handle the large number of linking constraints and variables commonly observed in energy system models, a distributed Schur complement preconditioner is used. In addition, the solver features a number of more generic techniques such as parallel matrix scaling and structure-preserving presolving. The implementation is based on the solver PIPS-IPM. We evaluate the computational performance on energy system models with up to four billion nonzero entries in the constraint matrix—and up to one billion columns and one billion rows. This article mainly concentrates on the energy system model ELMOD, which is a linear optimization model representing the European electricity markets by the use of a nodal pricing market-clearing. It has been widely applied in the literature on energy system analyses in recent years. However, it will be demonstrated that the new solver is also applicable to other energy system models.


Original languageEnglish
Article number1
Pages (from-to)60-71
Number of pages12
JournalEuropean Journal of Operational Research
Issue number1
Publication statusPublished - 1 Jan 2022

External IDs

Scopus 85111550318
unpaywall 10.1016/j.ejor.2021.06.063
Mendeley a19e950a-0ee8-38c5-8e1c-a2f53f4abed6
WOS 000691200300005
dblp journals/eor/RehfeldtHSKMG22
ORCID /0000-0002-9416-6786/work/141544855
ORCID /0000-0001-7170-3596/work/142241569


DFG Classification of Subject Areas according to Review Boards

Sustainable Development Goals


  • Energiewirtschaft, energie economics, Block structured LP, Energy systems, Large scale optimization, Linear programming, OR in energy

Library keywords