7,835 research outputs found
An improved multi-parametric programming algorithm for flux balance analysis of metabolic networks
Flux balance analysis has proven an effective tool for analyzing metabolic
networks. In flux balance analysis, reaction rates and optimal pathways are
ascertained by solving a linear program, in which the growth rate is maximized
subject to mass-balance constraints. A variety of cell functions in response to
environmental stimuli can be quantified using flux balance analysis by
parameterizing the linear program with respect to extracellular conditions.
However, for most large, genome-scale metabolic networks of practical interest,
the resulting parametric problem has multiple and highly degenerate optimal
solutions, which are computationally challenging to handle. An improved
multi-parametric programming algorithm based on active-set methods is
introduced in this paper to overcome these computational difficulties.
Degeneracy and multiplicity are handled, respectively, by introducing
generalized inverses and auxiliary objective functions into the formulation of
the optimality conditions. These improvements are especially effective for
metabolic networks because their stoichiometry matrices are generally sparse;
thus, fast and efficient algorithms from sparse linear algebra can be leveraged
to compute generalized inverses and null-space bases. We illustrate the
application of our algorithm to flux balance analysis of metabolic networks by
studying a reduced metabolic model of Corynebacterium glutamicum and a
genome-scale model of Escherichia coli. We then demonstrate how the critical
regions resulting from these studies can be associated with optimal metabolic
modes and discuss the physical relevance of optimal pathways arising from
various auxiliary objective functions. Achieving more than five-fold
improvement in computational speed over existing multi-parametric programming
tools, the proposed algorithm proves promising in handling genome-scale
metabolic models.Comment: Accepted in J. Optim. Theory Appl. First draft was submitted on
August 4th, 201
Learning the LMP-Load Coupling From Data: A Support Vector Machine Based Approach
This paper investigates the fundamental coupling between loads and locational
marginal prices (LMPs) in security-constrained economic dispatch (SCED).
Theoretical analysis based on multi-parametric programming theory points out
the unique one-to-one mapping between load and LMP vectors. Such one-to-one
mapping is depicted by the concept of system pattern region (SPR) and
identifying SPRs is the key to understanding the LMP-load coupling. Built upon
the characteristics of SPRs, the SPR identification problem is modeled as a
classification problem from a market participant's viewpoint, and a Support
Vector Machine based data-driven approach is proposed. It is shown that even
without the knowledge of system topology and parameters, the SPRs can be
estimated by learning from historical load and price data. Visualization and
illustration of the proposed data-driven approach are performed on a 3-bus
system as well as the IEEE 118-bus system
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