Microarray technology produces gene expression data on a genomic scale for an endless variety of ... more Microarray technology produces gene expression data on a genomic scale for an endless variety of organisms and conditions. However, this vast amount of information needs to be extracted in a reasonable way and funneled into manageable and functionally meaningful patterns. Genes may be reasonably combined using knowledge about their interaction behaviour. On a proteomic level, biochemical research has elucidated an increasingly complete image of the metabolic architecture, especially for less complex organisms like the well studied bacterium Escherichia coli. We sought to discover central components of the metabolic network, regulated by the expression of associated genes under changing conditions. We mapped gene expression data from E. coli under aerobic and anaerobic conditions onto the enzymatic reaction nodes of its metabolic network. An adjacency matrix of the metabolites was created from this graph. A consecutive ones clustering method was used to obtain network clusters in the...
In 1982, Padberg and Rao gave a polynomial-time separation algorithm for b-matching polyhedra. Th... more In 1982, Padberg and Rao gave a polynomial-time separation algorithm for b-matching polyhedra. The current best known implementations of their separation algorithm run in O(|V | 2 |E| log(|V | 2 /|E|)) time when there are no edge capacities, but in O(|V ||E| 2 log(|V | 2 /|E|)) time when capacities are present. We propose a new exact separation algorithm for the capacitated case which has the same running time as for the uncapacitated case. For the sake of brevity, however, we will restrict our introduction to the case of perfect 1-capacitated b-matchings, which includes, for example, the separation problem for perfect 2-matchings. As well as being faster than the Padberg-Rao approach, our new algorithm is simpler and easier to implement.
Computing Best Transition Pathways in High-Dimensional Dynamical Systems: Application to the Alpha L \leftrightharpoons Beta \leftrightharpoons Alpha R Transitions in Octaalanine
Multiscale Modeling & Simulation, 2006
The Energy Citations Database (ECD) provides access to historical and current research (1948 to t... more The Energy Citations Database (ECD) provides access to historical and current research (1948 to the present) from the Department of Energy (DOE) and predecessor agencies.
Crew pairing problems are often solved using column generation in a branch-and-price framework. T... more Crew pairing problems are often solved using column generation in a branch-and-price framework. The oscillation of dual points is the main reason which leads to instability in the standard implementation of this method. One device to deal with the problem is to use the trust-region idea to stabilize the path of dual points. Therefore, a so-called stabilized column generation with
Fast heuristics for large geometric traveling salesman problems
ORSA Journal on computing, 1992
Very frequently in practical applications we are faced with large or very large scale traveling s... more Very frequently in practical applications we are faced with large or very large scale traveling salesman problems where the number of cities may range from several hundreds or thousands up to even millions. Due to timing restrictions in the production process there ...
Many practical optimal control problems include discrete decisions. These may be either time-inde... more Many practical optimal control problems include discrete decisions. These may be either time-independent parameters or time-dependent control functions as gears or valves that can only take discrete values at any given time. While great progress has been achieved in the solution of optimization problems involving integer variables, in particular mixed-integer linear programs, as well as in continuous optimal control problems, the combination of the two is yet an open field of research. We consider the question of lower bounds that can be obtained by a relaxation of the integer requirements. For general nonlinear mixed-integer programs such lower bounds typically suffer from a huge integer gap. We convexify (with respect to binary controls) and relax the original problem and prove that the optimal solution of this continuous control problem yields the best lower bound for the nonlinear integer problem. Building on this theoretical result we present a novel algorithm to solve mixed-integer optimal control problems, with a focus on discrete-valued control functions. Our algorithm is based on the direct multiple shooting method, an adaptive refinement of the underlying control discretization grid and tailored heuristic integer methods. Its applicability is shown by a challenging application, the energy optimal control of a subway train with discrete gears and velocity limits.
In this paper we study the Windy Postman Problem. This is a well known Arc Routing Problem which ... more In this paper we study the Windy Postman Problem. This is a well known Arc Routing Problem which contains the Mixed Chinese Postman Problem as a special case. We present here a full description of the polyhedron associated to the Windy Postman Problem over graphs with up to 4 vertices and 10 edges. We introduce two new families of facet-inducing inequalities and we prove that these inequalities and the already known Odd Zigzag inequalities are mod-2 cut inequalities. Moreover, a Branch & Cut (B&C) algorithm that incorporates two new separation algorithms for all the previously mentioned inequalities and a new heuristic procedure to obtain upper bounds are presented. Finally, the performance of the B&C algorithm over several sets of large WPP and MCPP instances, with up to 3000 nodes and 9000 links, shows that up to our knowledge this is the best algorithm for the exact resolution of the WPP and the MCPP. and proposed a cutting plane algorithm for the WPP based on a previous polyhedral study that, as far as we know, is the first polyhedral approach that has been applied to the resolution of a NP-hard Arc Routing Problem. They proved that the Odd-cut inequalities and the k-wheel inequalities are facet-inducing, although only the separation of the first ones was implemented in their cutting plane algorithm. More recently, Corberán, Plana & Sanchis (2006) present a new family of facet-inducing inequalities for the Windy General Routing Problem, the Odd Zigzag inequalities, which also applies to the WPP. These inequalities generalize the 3-wheel inequalities proposed by for the WPP.
Computing finest mincut partitions of a graph and application to routing problems
Discrete Applied Mathematics, 2008
Let G=(V,E,w) be an n-vertex graph with edge weights w&am... more Let G=(V,E,w) be an n-vertex graph with edge weights w>0. We propose an algorithm computing all partitions of V into mincuts of G such that the mincuts in the partitions cannot be partitioned further into mincuts. There are O(n) such finest mincut partitions. A mincut is a non-empty proper subset of V such that the total weight of edges with
Motivation: Gene expression profiling by microarrays or transcript sequencing enables observing t... more Motivation: Gene expression profiling by microarrays or transcript sequencing enables observing the pathogenic function of tumors on a mesoscopic level. Results: We investigated neuroblastoma tumors that clinically exhibit a very heterogeneous course ranging from rapid growth with fatal outcome to spontaneous regression and detected regulatory oncogenetic shifts in their metabolic networks. In contrast to common enrichment tests, we took network topology into account by applying adjusted wavelet transforms on an elaborated and new 2D grid representation of curated pathway maps from the Kyoto Enzyclopedia of Genes and Genomes. The aggressive form of the tumors showed regulatory shifts for purine and pyrimidine biosynthesis as well as folate-mediated metabolism of the onecarbon pool in respect to increased nucleotide production. We spotted an oncogentic regulatory switch in glutamate metabolism for which we provided experimental validation, being the first steps towards new possible drug therapy. The pattern recognition method we used complements normal enrichment tests to detect such functionally related regulation patterns. Availability and Implementation: PathWave is implemented in a package for R (www.r-project.org) version 2.6.0 or higher. It is freely available from
Microarray technology produces gene expression data on a genomic scale for an endless variety of ... more Microarray technology produces gene expression data on a genomic scale for an endless variety of organisms and conditions. However, this vast amount of information needs to be extracted in a reasonable way and funneled into manageable and functionally meaningful patterns. Genes may be reasonably combined using knowledge about their interaction behaviour. On a proteomic level, biochemical research has elucidated an increasingly complete image of the metabolic architecture, especially for less complex organisms like the well studied bacterium Escherichia coli. We sought to discover central components of the metabolic network, regulated by the expression of associated genes under changing conditions. We mapped gene expression data from E. coli under aerobic and anaerobic conditions onto the enzymatic reaction nodes of its metabolic network. An adjacency matrix of the metabolites was created from this graph. A consecutive ones clustering method was used to obtain network clusters in the...
In 1982, Padberg and Rao gave a polynomial-time separation algorithm for b-matching polyhedra. Th... more In 1982, Padberg and Rao gave a polynomial-time separation algorithm for b-matching polyhedra. The current best known implementations of their separation algorithm run in O(|V | 2 |E| log(|V | 2 /|E|)) time when there are no edge capacities, but in O(|V ||E| 2 log(|V | 2 /|E|)) time when capacities are present. We propose a new exact separation algorithm for the capacitated case which has the same running time as for the uncapacitated case. For the sake of brevity, however, we will restrict our introduction to the case of perfect 1-capacitated b-matchings, which includes, for example, the separation problem for perfect 2-matchings. As well as being faster than the Padberg-Rao approach, our new algorithm is simpler and easier to implement.
Computing Best Transition Pathways in High-Dimensional Dynamical Systems: Application to the Alpha L \leftrightharpoons Beta \leftrightharpoons Alpha R Transitions in Octaalanine
Multiscale Modeling & Simulation, 2006
The Energy Citations Database (ECD) provides access to historical and current research (1948 to t... more The Energy Citations Database (ECD) provides access to historical and current research (1948 to the present) from the Department of Energy (DOE) and predecessor agencies.
Crew pairing problems are often solved using column generation in a branch-and-price framework. T... more Crew pairing problems are often solved using column generation in a branch-and-price framework. The oscillation of dual points is the main reason which leads to instability in the standard implementation of this method. One device to deal with the problem is to use the trust-region idea to stabilize the path of dual points. Therefore, a so-called stabilized column generation with
Fast heuristics for large geometric traveling salesman problems
ORSA Journal on computing, 1992
Very frequently in practical applications we are faced with large or very large scale traveling s... more Very frequently in practical applications we are faced with large or very large scale traveling salesman problems where the number of cities may range from several hundreds or thousands up to even millions. Due to timing restrictions in the production process there ...
Many practical optimal control problems include discrete decisions. These may be either time-inde... more Many practical optimal control problems include discrete decisions. These may be either time-independent parameters or time-dependent control functions as gears or valves that can only take discrete values at any given time. While great progress has been achieved in the solution of optimization problems involving integer variables, in particular mixed-integer linear programs, as well as in continuous optimal control problems, the combination of the two is yet an open field of research. We consider the question of lower bounds that can be obtained by a relaxation of the integer requirements. For general nonlinear mixed-integer programs such lower bounds typically suffer from a huge integer gap. We convexify (with respect to binary controls) and relax the original problem and prove that the optimal solution of this continuous control problem yields the best lower bound for the nonlinear integer problem. Building on this theoretical result we present a novel algorithm to solve mixed-integer optimal control problems, with a focus on discrete-valued control functions. Our algorithm is based on the direct multiple shooting method, an adaptive refinement of the underlying control discretization grid and tailored heuristic integer methods. Its applicability is shown by a challenging application, the energy optimal control of a subway train with discrete gears and velocity limits.
In this paper we study the Windy Postman Problem. This is a well known Arc Routing Problem which ... more In this paper we study the Windy Postman Problem. This is a well known Arc Routing Problem which contains the Mixed Chinese Postman Problem as a special case. We present here a full description of the polyhedron associated to the Windy Postman Problem over graphs with up to 4 vertices and 10 edges. We introduce two new families of facet-inducing inequalities and we prove that these inequalities and the already known Odd Zigzag inequalities are mod-2 cut inequalities. Moreover, a Branch & Cut (B&C) algorithm that incorporates two new separation algorithms for all the previously mentioned inequalities and a new heuristic procedure to obtain upper bounds are presented. Finally, the performance of the B&C algorithm over several sets of large WPP and MCPP instances, with up to 3000 nodes and 9000 links, shows that up to our knowledge this is the best algorithm for the exact resolution of the WPP and the MCPP. and proposed a cutting plane algorithm for the WPP based on a previous polyhedral study that, as far as we know, is the first polyhedral approach that has been applied to the resolution of a NP-hard Arc Routing Problem. They proved that the Odd-cut inequalities and the k-wheel inequalities are facet-inducing, although only the separation of the first ones was implemented in their cutting plane algorithm. More recently, Corberán, Plana & Sanchis (2006) present a new family of facet-inducing inequalities for the Windy General Routing Problem, the Odd Zigzag inequalities, which also applies to the WPP. These inequalities generalize the 3-wheel inequalities proposed by for the WPP.
Computing finest mincut partitions of a graph and application to routing problems
Discrete Applied Mathematics, 2008
Let G=(V,E,w) be an n-vertex graph with edge weights w&am... more Let G=(V,E,w) be an n-vertex graph with edge weights w>0. We propose an algorithm computing all partitions of V into mincuts of G such that the mincuts in the partitions cannot be partitioned further into mincuts. There are O(n) such finest mincut partitions. A mincut is a non-empty proper subset of V such that the total weight of edges with
Motivation: Gene expression profiling by microarrays or transcript sequencing enables observing t... more Motivation: Gene expression profiling by microarrays or transcript sequencing enables observing the pathogenic function of tumors on a mesoscopic level. Results: We investigated neuroblastoma tumors that clinically exhibit a very heterogeneous course ranging from rapid growth with fatal outcome to spontaneous regression and detected regulatory oncogenetic shifts in their metabolic networks. In contrast to common enrichment tests, we took network topology into account by applying adjusted wavelet transforms on an elaborated and new 2D grid representation of curated pathway maps from the Kyoto Enzyclopedia of Genes and Genomes. The aggressive form of the tumors showed regulatory shifts for purine and pyrimidine biosynthesis as well as folate-mediated metabolism of the onecarbon pool in respect to increased nucleotide production. We spotted an oncogentic regulatory switch in glutamate metabolism for which we provided experimental validation, being the first steps towards new possible drug therapy. The pattern recognition method we used complements normal enrichment tests to detect such functionally related regulation patterns. Availability and Implementation: PathWave is implemented in a package for R (www.r-project.org) version 2.6.0 or higher. It is freely available from
Uploads
Papers by G. Reinelt