268 research outputs found
Solving Assembly Line Balancing Problems by Combining IP and CP
Assembly line balancing problems consist in partitioning the work necessary
to assemble a number of products among different stations of an assembly line.
We present a hybrid approach for solving such problems, which combines
constraint programming and integer programming.Comment: 10 pages, Sixth Annual Workshop of the ERCIM Working Group on
Constraints, Prague, June 200
Dynamic optimization of metabolic networks coupled with gene expression
The regulation of metabolic activity by tuning enzyme expression levels is
crucial to sustain cellular growth in changing environments. Metabolic networks
are often studied at steady state using constraint-based models and
optimization techniques. However, metabolic adaptations driven by changes in
gene expression cannot be analyzed by steady state models, as these do not
account for temporal changes in biomass composition. Here we present a dynamic
optimization framework that integrates the metabolic network with the dynamics
of biomass production and composition, explicitly taking into account enzyme
production costs and enzymatic capacity. In contrast to the established dynamic
flux balance analysis, our approach allows predicting dynamic changes in both
the metabolic fluxes and the biomass composition during metabolic adaptations.
We applied our algorithm in two case studies: a minimal nutrient uptake
network, and an abstraction of core metabolic processes in bacteria. In the
minimal model, we show that the optimized uptake rates reproduce the empirical
Monod growth for bacterial cultures. For the network of core metabolic
processes, the dynamic optimization algorithm predicted commonly observed
metabolic adaptations, such as a diauxic switch with a preference ranking for
different nutrients, re-utilization of waste products after depletion of the
original substrate, and metabolic adaptation to an impending nutrient
depletion. These examples illustrate how dynamic adaptations of enzyme
expression can be predicted solely from an optimization principle
Logic programming with pseudo-Boolean constraints
Boolean constraints play an important role in various constraint logic programming languages. In this paper we consider pseudo-Boolean constraints, that is equations and inequalities between pseudo-Boolean functions. A pseudo-Boolean function is an integer-valued function of Boolean variables and thus a generalization of a Boolean function. Pseudo-Boolean functions occur in many application areas, in particular in problems from operations research. An interesting connection to logic is that inference problems in propositional logic can be translated into linear pseudo-Boolean optimization problems. More generally, pseudo-Boolean constraints can be seen as a particular way of combining two of the most important domains in constraint logic programming: arithmetic and Boolean algebra. In this paper we define a new constraint logic programming language {\em CLP(PB)} for logic progamming with pseudo-Boolean constraints. The language is an instance of the general constraint logic programming language scheme {\em CLP(X)} and inherits all the typical semantic properties. We show that any pseudo-Boolean constraint has a most general solution and give variable elimination algorithms for pseudo-Boolean unification and unconstrained pseudo-Boolean optimization. Both algorithms subsume the well-known Boolean unification algorithm of B\"uttner and Simonis
Cutting planes and the elementary closure in fixed dimension
The elementary closure of a polyhedron is the intersection of with all its Gomory-Chvátal cutting planes. is a rational polyhedron provided that is rational. The known bounds for the number of inequalities defining are exponential, even in fixed dimension. We show that the number of inequalities needed to describe the elementary closure of a rational polyhedron is polynomially bounded in fixed dimension. If is a simplicial cone, we construct a polytope , whose integral elements correspond to cutting planes of . The vertices of the integer hull include the facets of . A polynomial upper bound on their number can be obtained by applying a result of Cook et al. Finally, we present a polynomial algorithm in varying dimension, which computes cutting planes for a simplicial cone that correspond to vertices of
A mixed-integer linear programming approach to the reduction of genome-scale metabolic networks
Constraint-based analysis has become a widely used method to study metabolic
networks. While some of the associated algorithms can be applied to genome-
scale network reconstructions with several thousands of reactions, others are
limited to small or medium-sized models. In 2015, Erdrich et al. introduced a
method called NetworkReducer, which reduces large metabolic networks to
smaller subnetworks, while preserving a set of biological requirements that
can be specified by the user. Already in 2001, Burgard et al. developed a
mixed-integer linear programming (MILP) approach for computing minimal
reaction sets under a given growth requirement
Narrowing strategies for arbitrary canonical rewrite systems
Narrowing is a universal unification procedure for equational theories defined by a canonical term rewriting system. In its original form it is extremely inefficient. Therefore, many optimizations have been proposed during the last years. In this paper, we present the narrowing strategies for arbitrary canonical systems in a uniform framework and introduce the new narrowing strategy LSE narrowing. LSE narrowing is complete and improves all other strategies which are complete for arbitrary canonical systems. It is optimal in the sense that two different LSE narrowing derivations cannot generate the same narrowing substitution. Moreover, LSE narrowing computes only normalized narrowing substitutions
On the geometry of elementary flux modes
Elementary flux modes (EFMs) play a prominent role in the constraint-based analysis of metabolic networks. They correspond to minimal functional units of the metabolic network at steady-state and as such have been studied for almost 30 years. The set of all EFMs in a metabolic network tends to be very large and may have exponential size in the number of reactions. Hence, there is a need to elucidate the structure of this set. Here we focus on geometric properties of EFMs. We analyze the distribution of EFMs in the face lattice of the steady-state flux cone of the metabolic network and show that EFMs in the relative interior of the cone occur only in very special cases. We introduce the concept of degree of an EFM as a measure how elementary it is and study the decomposition of flux vectors and EFMs depending on their degree. Geometric analysis can help to better understand the structure of the set of EFMs, which is important from both the mathematical and the biological viewpoint
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