Microbes may maximize the number of daughter cells per time or per amount of nutrients consumed. These two strategies correspond, respectively, to the use of enzyme-efficient or substrate-efficient metabolic pathways. In reality, fast growth is often associated with wasteful, yield-inefficient metabolism, and a general thermodynamic trade-off between growth rate and biomass yield has been proposed to explain this. We studied growth rate/yield trade-offs by using a novel modeling framework, Enzyme-Flux Cost Minimization (EFCM) and by assuming that the growth rate depends directly on the enzyme investment per rate of biomass production. In a comprehensive mathematical model of core metabolism in E. coli, we screened all elementary flux modes leading to cell synthesis, characterized them by the growth rates and yields they provide, and studied the shape of the resulting rate/yield Pareto front. By varying the model parameters, we found that the rate/yield trade-off is not universal, but depends on metabolic kinetics and environmental conditions. A prominent trade-off emerges under oxygen-limited growth, where yield-inefficient pathways support a 2-to-3 times higher growth rate than yield-efficient pathways. EFCM can be widely used to predict optimal metabolic states and growth rates under varying nutrient levels, perturbations of enzyme parameters, and single or multiple gene knockouts.

We investigate new class of congestion games, called Totally Unimodular (TU) Congestion Games, where the players’ strategies are binary vectors inside polyhedra defined by totally unimodular constraint matrices. Network congestion games belong to this class. In the symmetric case, when all players have the same strategy set, we design an algorithm that finds an optimal aggregated strategy and then decomposes it into the single players’ strategies. This approach yields strongly polynomial-time algorithms to (i) find a pure Nash equilibrium, and (ii) compute a socially optimal state, if the delay functions are weakly convex. We also show how this technique can be extended to matroid congestion games. We then introduce some combinatorial TU congestion games, where the players'strategies are matchings, vertex covers, edge covers, and stable sets of a given bipartite graph. In the asymmetric case, we show that for these games (i) it is PLS-complete to find a pure Nash equilibrium even in case of linear delay functions, and (ii) it is NP-hard to compute a socially optimal state, even in case of weakly convex delay functions.

We model three on-chip network design problems—memory controller placement, resource allocation in heterogeneous on-chip networks, and their combination—as mathematical optimization problems. We model the first two problems as mixed integer linear programs. We model the third problem as a mixed integer nonlinear program, which we then linearize exactly. Sophisticated optimization algorithms enable solutions to be obtained much more efficiently. Detailed simulations using synthetic traffic and benchmark applications validate that our designs provide better performance than solutions proposed previously. Our work provides further evidence toward suitability of optimization models in searching/pruning architectural design space.

Systematic, genome-wide loss-of-function experiments can be used to identify host factors that directly or indirectly facilitate or inhibit the replication of a virus in a host cell. We present an approach that combines an integer linear program and a diffusion kernel method to infer the pathways through which those host factors modulate viral replication. The inputs to the method are a set of viral phenotypes observed in single-host-gene mutants and a background network consisting of a variety of host intracellular interactions. The output is an ensemble of subnetworks that provides a consistent explanation for the measured phenotypes, predicts which unassayed host factors modulate the virus, and predicts which host factors are the most direct interfaces with the virus. We infer host-virus interaction subnetworks using data from experiments screening the yeast genome for genes modulating the replication of two RNA viruses. Because a gold-standard network is unavailable, we assess the predicted subnetworks using both computational and qualitative analyses. We conduct a cross-validation experiment in which we predict whether held-aside test genes have an effect on viral replication. Our approach is able to make high-confidence predictions more accurately than several baselines, and about as well as the best baseline, which does not infer mechanistic pathways. We also examine two kinds of predictions made by our method: which host factors are nearest to a direct interaction with a viral component, and which unassayed host genes are likely to be involved in viral replication. Multiple predictions are supported by recent independent experimental data, or are components or functional partners of confirmed relevant complexes or pathways. Integer program code, background network data, and inferred host-virus subnetworks are available at http://www.biostat.wisc.edu/~craven/chasman_host_virus/.

We describe a framework for modeling optimization problems for solution on a grid computer. The framework is easy to adapt to multiple grid engines and can seamlessly integrate evolving mechanisms from particular computing platforms. It facilitates the widely used master-worker model of computing and is shown to be flexible and powerful enough for a large variety of optimization applications. In particular, we summarize a number of new features of the GAMS modeling system that provide a lightweight, portable, and powerful framework for optimization on a grid. We provide downloadable examples of its use for embarrasingly parallel financial applications, decomposition of complementarity problems, and for solving very difficult mixed-integer programs to optimality. Computational results are provided for a number of different grid engines, including multicore machines, a pool of machines controlled by the Condor resource manager, and the grid engine from Sun Microsystems.

Scheduling problems arise in many applications in process industries. However, despite various efforts to develop efficient scheduling methods, current approaches cannot be used to solve instances of industrial importance in reasonable time frames. The goal of this paper is the development of a dynamic decomposition framework that exploits the structure of the problem and is well suited for grid computing. The problem we study is the simultaneous batching and scheduling of multistage batch processes for which the binary decision variables are batch selection, batch-unit assignment, and batch sequencing on units. We present methods to decompose the original problem into a number of subproblems in a dynamic fashion. First, we discuss the generation of subproblems based on fixing the batch-selection variables. Second, we generate subproblems by fixing the batch-unit assignment variables in a bottlenecking stage. Third, we generate subproblems by fixing the last batch in the sequence on each unit of the bottlenecking stage. Furthermore, the second and third methods can be carried out in various combinations. Alternatively, a problem can be decomposed into a number of promising subproblems using an automatic strong branching scheme. Our results show that the proposed method can be used on a grid computer to solve large problems to optimality in a reasonable computational time.

An optimization framework for three-dimensional conformal radiation therapy is presented. In conformal therapy, beams of radiation are applied to a patient from different directions, where the aperture through which the beam is delivered from each direction is chosen to match the shape of the tumor, as viewed from that direction. Wedge filters may be used to produce a gradient in beam intensity across the aperture. Given a set of equispaced beam angles, a mixed-integer linear program can be solved to determine the most effective angles to be used in a treatment plan, the weight (exposure time) to be used for each beam, and the type and orientation of wedges to be used. Practical solution techniques for this problem are described; they include strengthening of the formulation and solution of smaller approximate problems obtained by a reduced parametrization of the treatment region. In addition, techniques for controlling the dose-volume histogram implicitly for various parts of the treatment region using hot- and cold-spot control parameters are presented. Computational results are given that show the effectiveness of the proposed approach on practical data sets.

This paper develops simple cost models for provisioning content distribution networks that use the simple and highly scalable bandwidth skimming protocol for streaming. New insight is obtained into: (1) how cost-effective proxy servers are in multicast streaming systems; (2) the most effective streaming protocol; and (3) the optimal proxy content, as a function of the system configuration and workload. A key result is that proxy servers are only cost effective if: (a) the origin server does not have a multicast capability; or (b) the file request rate is low, and thus multicast is not highly effective; or (c) the cost of a proxy server stream is a very small fraction (i.e., approximately 1/P) of the cost of an origin server stream, where P is the number of proxy servers and the cost of either type of stream includes both the server and network resource costs. For cases where proxy servers are cost effective, results in the paper provide the optimal proxy content and the most effective streaming protocol, as a function of a wide range of system configuration and workload parameters. In contrast to previous work, full file caching outperforms prefix caching over a significant region of this system design space, due to more efficient multicast streaming protocols as well as a more complete exploration of the practical system configuration space.

Complementarity solvers are continually being challenged by modelers demanding improved reliability and scalability. Building upon a strong theoretical background, the semismooth algorithm has the potential to meet both of these requirements. We discuss relevant theory associated with the algorithm and then describe a sophisticated implementation in detail. Particular emphasis is given to the use of preconditioned iterative methods to solve the (nonsymmetric) systems of linear equations generated at each iteration and robust methods for dealing with singularity. Results on the MCPLIB test suite indicate that the code is reliable and efficient and scales well to very large problems.

The problem of adaptive routing in a network with failures is considered. The network may be in one of finitely many states characterized by different travel times along the arcs, and transitions between the states occur according to a continuous-time Markov chain. The objective was to develop a routing strategy that minimizes the total expected travel time. Dynamic programming models and flow-oriented models were developed and analyzed in the uncapacitated and the capacitated case. It is shown that the robust plan can be found from a special two-stage stochastic programming problem in which the second-stage models the rerouting problem after the state transition in the network. The models are illustrated on an example of the Sioux Falls transportation network. The computational results reveal striking properties of different routing policies and show that substantial improvements in both duration and size of jams can be achieved by employing robust strategies. © 2000 John Wiley & Sons, Inc.

We discuss the use of Condor, a distributed resource management system, as a provider of computational resources for NEOS, an environment for solving optimization problems over the Internet. We also describe how problems are submitted and processed by NEOS, and then scheduled and solved by Condor on available (idle) workstations

This article applies splitting techniques developed for set-valued maximal monotone operators to monotone affine variational inequalities, including, as a special case, the classical linear complementarity problem. We give a unified presentation of several splitting algorithms for monotone operators, and then apply these results to obtain two classes of algorithms for affine variational inequalities. The second class resembles classical matrix splitting, but has a novel “under-relaxation” step, and converges under more general conditions. In particular, the convergence proofs do not require the affine operator to be symmetric. We specialize our matrix-splitting-like method to discrete-time optimal control problems formulated as extended linear-quadratic programs in the manner advocated by Rockafellar and Wets. The result is a highly parallel algorithm, which we implement and test on the Connection Machine CM-5 computer family.

Genetic algorithms are one example of the use of a random element within an algorithm for combinatorial optimization. We consider the application of the genetic algorithm to a particular problem, the Assembly Line Balancing Problem. A general description of genetic algorithms is given, and their specialized use on our test-bed problems is discussed. We carry out extensive computational testing to find appropriate values for the various parameters associated with this genetic algorithm. These experiments underscore the importance of the correct choice of a scaling parameter and mutation rate to ensure the good performance of a genetic algorithm. We also describe a parallel implementation of the genetic algorithm and give some comparisons between the parallel and serial implementations. Both versions of the algorithm are shown to be effective in producing good solutions for problems of this type (with appropriately chosen parameters). INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.