Integer Linear Optimization Problem Research Articles

Improving Strand Pairing Prediction through Exploring Folding Cooperativity

The topology of beta-sheets is defined by the pattern of hydrogen-bonded strand pairing. Therefore, predicting hydrogen bonded strand partners is a fundamental step towards predicting beta-sheet topology. At the same time, finding the correct partners is very difficult due to long range interactions involved in strand pairing. Additionally, patterns of amino acids involved, in beta-sheet formations are very general and therefore difficult to use for computational recognition of specific contacts between strands. In this work, we report a new strand pairing algorithm. To address above mentioned difficulties, our algorithm attempts to mimic elements of the folding process. Namely, in addition to ensuring that the predicted hydrogen bonded strand pairs satisfy basic global consistency constraints, it takes into account hypothetical folding pathways. Consistently with this view, introducing hydrogen bonds between a pair of strands changes the probabilities of forming hydrogen bonds between other pairs of strand. We demonstrate that this approach provides an improvement over previously proposed algorithms. We also compare the performance of this method to that of a global optimization algorithm that poses the problem as integer linear programming optimization problem and solves it using ILOG CPLEX package.

Combinatorial influence of environmental parameters on transcription factor activity

Motivation: Cells receive a wide variety of environmental signals, which are often processed combinatorially to generate specific genetic responses. Changes in transcript levels, as observed across different environmental conditions, can, to a large extent, be attributed to changes in the activity of transcription factors (TFs). However, in unraveling these transcription regulation networks, the actual environmental signals are often not incorporated into the model, simply because they have not been measured. The unquantified heterogeneity of the environmental parameters across microarray experiments frustrates regulatory network inference.Results: We propose an inference algorithm that models the influence of environmental parameters on gene expression. The approach is based on a yeast microarray compendium of chemostat steady-state experiments. Chemostat cultivation enables the accurate control and measurement of many of the key cultivation parameters, such as nutrient concentrations, growth rate and temperature. The observed transcript levels are explained by inferring the activity of TFs in response to combinations of cultivation parameters. The interplay between activated enhancers and repressors that bind a gene promoter determine the possible up- or downregulation of the gene. The model is translated into a linear integer optimization problem. The resulting regulatory network identifies the combinatorial effects of environmental parameters on TF activity and gene expression.Availability: The Matlab code is available from the authors upon request.Contact: t.a.knijnenburg@tudelft.nlSupplementary information: Supplementary data are available at Bioinformatics online.

Locating Satellite Booster Disinfectant Stations

Booster disinfectant is introduced within a distribution system to maintain disinfectant residuals and avoid high dosages near water sources. Assuming that first order reaction kinetics apply to chlorine decay, an integer linear programming optimization problem is posed to determine booster locations and their injection rates. The formulation avoids long water quality simulations by adding constraints requiring the concentrations at the beginning and end of the design period to be the same. The optimization problem is divided into two levels. The upper level selects the booster locations using a genetic algorithm, if more than a few boosters are included, or enumeration, if the number of boosters and/or potential locations is relatively small. Given a set of boosters from the upper level, the lower level minimizes the chlorine mass to be injected to maintain required residuals. The approach is applied to the Brushy Plains system for alternative numbers of allowable boosters.

A multiobjective optimization model for processing and distributing biosolids to reuse fields

Advanced wastewater treatment plants remove deleterious nutrients, chemicals, and microorganisms from wastewater and produce biosolids products to be reused at farms and other sites. These biosolids are carefully regulated by environmental restrictions but still may be malodorous to the local populations. In this paper, we develop a multiobjective optimization model to simultaneously minimize the biosolids odours as well as processing and distribution costs. The model employs a linear odour function and bilinear costs; the latter being approximated via Schur's decomposition and special ordered set (SOS) type 2 variables resulting in a mixed integer linear multiobjective optimization problem. Such a model can be used proactively by these plants to produce the least malodorous product at minimal costs. We demonstrate use of the model with a case study for the Blue Plains advanced wastewater treatment plant run by the DC Water and Sewer Authority in Washington, DC.

Including metabolite concentrations into flux balance analysis: thermodynamic realizability as a constraint on flux distributions in metabolic networks.

BackgroundIn recent years, constrained optimization – usually referred to as flux balance analysis (FBA) – has become a widely applied method for the computation of stationary fluxes in large-scale metabolic networks. The striking advantage of FBA as compared to kinetic modeling is that it basically requires only knowledge of the stoichiometry of the network. On the other hand, results of FBA are to a large degree hypothetical because the method relies on plausible but hardly provable optimality principles that are thought to govern metabolic flux distributions.ResultsTo augment the reliability of FBA-based flux calculations we propose an additional side constraint which assures thermodynamic realizability, i.e. that the flux directions are consistent with the corresponding changes of Gibb's free energies. The latter depend on metabolite levels for which plausible ranges can be inferred from experimental data. Computationally, our method results in the solution of a mixed integer linear optimization problem with quadratic scoring function. An optimal flux distribution together with a metabolite profile is determined which assures thermodynamic realizability with minimal deviations of metabolite levels from their expected values. We applied our novel approach to two exemplary metabolic networks of different complexity, the metabolic core network of erythrocytes (30 reactions) and the metabolic network iJR904 of Escherichia coli (931 reactions). Our calculations show that increasing network complexity entails increasing sensitivity of predicted flux distributions to variations of standard Gibb's free energy changes and metabolite concentration ranges. We demonstrate the usefulness of our method for assessing critical concentrations of external metabolites preventing attainment of a metabolic steady state.ConclusionOur method incorporates the thermodynamic link between flux directions and metabolite concentrations into a practical computational algorithm. The weakness of conventional FBA to rely on intuitive assumptions about the reversibility of biochemical reactions is overcome. This enables the computation of reliable flux distributions even under extreme conditions of the network (e.g. enzyme inhibition, depletion of substrates or accumulation of end products) where metabolite concentrations may be drastically altered.

Global pairwise sequence alignment through mixed-integer linear programming: a template-free approach

The problem of protein sequence alignment is the main starting point for biological analysis of genomic information. A new approach to global pairwise sequence alignment is proposed. This approach is formulated in a mathematically rigorous way, as a mixed integer linear optimization (MILP) problem. Not only does the proposed formulation guarantee the identification of the global optimal alignment, but it also allows for a complete rank-ordered list of any number of user specified top ranking pairwise alignments and for the incorporation of restraints based on restrictions necessary to maintain biological function. This approach has been applied to the alignment of transmembrane helices and serine proteases to demonstrate its utility and advantages over other algorithms.

GASUB: finding global optima to discrete location problems by a genetic-like algorithm

In many discrete location problems, a given number s of facility locations must be selected from a set of m potential locations, so as to optimize a predetermined fitness function. Most of such problems can be formulated as integer linear optimization problems, but the standard optimizers only are able to find one global optimum. We propose a new genetic-like algorithm, GASUB, which is able to find a predetermined number of global optima, if they exist, for a variety of discrete location problems. In this paper, a performance evaluation of GASUB in terms of its effectiveness (for finding optimal solutions) and efficiency (computational cost) is carried out. GASUB is also compared to MSH, a multi-start substitution method widely used for location problems. Computational experiments with three types of discrete location problems show that GASUB obtains better solutions than MSH. Furthermore, the proposed algorithm finds global optima in all tested problems, which is shown by solving those problems by Xpress-MP, an integer linear programing optimizer (21). Results from testing GASUB with a set of known test problems are also provided.

A multi-level approach for network design of integrated supply chains

Integrated e-supply chains are distributed manufacturing systems composed of various resources belonging to different companies and integrated with streamlined material, information and financial flow. The configuration of the supply-chain network is essential for business to pursue a competitive advantage and to meet the market demand. This paper proposes a three-level hierarchical methodology for a supply chain network design at the planning-management level. The integrated supply chain network is described as a set of consecutive stages connected by communication and transportation links, and the configuration aim consists in selecting the actors of the stages on the basis of transportation connection and information flow. More precisely, the first level evaluates the performance of the entities candidate to join the network and singles out efficient elements. The second level solves a multi-criteria integer linear optimization problem to configure the network. Finally, the third level is devoted to evaluating and validating the solution proposed in the first two levels. The overall decision process is the result of the interaction of the modules that are dedicated to each decision level. The paper presents some optimization techniques to synthesize the first two levels and illustrates the hierarchical decision process by way of a case study.

Deploying long-lived and cost-effective hybrid sensor networks

In this paper, we consider the problem of network deployment in hybrid sensor networks, consisting of both resource-rich and resource-impoverished sensor devices. The resource-rich devices, called micro-servers, are more expensive but have significantly greater bandwidth and energy capabilities compared to the low-cost, low-powered sensors. Such hybrid sensor networks have the potential to support the higher bandwidth communications of broadband sensor networking applications, as well as the fine-grained sensing that is made possible by smaller sensor devices. However, care must be taken to ensure that such systems are cost-effective to the end user. We investigate some fundamental questions for hybrid sensor network deployment—for a given number of micro-servers, what is the maximum lifetime of a sensor network and the optimal micro-server placement? What benefit can additional micro-servers add to the network, and how financially cost-effective is it to introduce these micro-servers? We propose a cost model and an integer linear programming (ILP) problem formulation for minimizing energy usage in a hybrid sensor network. Then, we prove that the integer linear optimization problem is NP-hard and introduce an efficient approximation algorithm using tabu-search technique. Our studies show that network lifetime can be increased dramatically with the addition of extra micro-servers; and the placement of micro-servers can affect the lifetime of network significantly. Moreover, we propose a network performance-cost ratio model to analyze the cost-effectiveness of the network and show that a hybrid sensor network is financially cost-efficient for a large case. Our optimization algorithm, together with the performance-cost ratio model, can be used to estimate the lifetime and financial cost of a hybrid sensor network before actual deployment. 4 This paper is a comprehensive extension of our earlier work in [W. Hu, C.T. Chou, S. Jha, N. Bulusu, Deploying long-lived and cost-effective hybrid sensor networks, in: Proceedings of the First Workshop on Broadband Advanced Sensor Networks (BaseNets 2004), San Jose, CA, October 25, 2004]. 4

NETWORK DESIGN OF INTEGRATED E-SUPPLY CHAIN FOR AGILE MANUFACTURING

Supply chains are distributed manufacturing systems composed of various resources belonging to different companies. The configuration of the supply chain network, integrated with Internet and web-based electronic market places, is essential for business to pursue a competitive advantage. This paper develops a model describing the integrated e-supply chain network and formulates a multi-criteria integer linear optimization problem to select the candidates and the links connecting the stages of the e-supply chain. Hence, some multi-criteria objective functions are defined and suited constraints are introduced on the basis of the digraph modelling the supply chain network. The proposed methodology is illustrated by way of a case study describing a network for desktop computer production.

Traffic engineering approach to path selection in optical burst switching networks

It is usually assumed that optical burst switching (OBS) networks use the shortest path routing along with next-hop burst forwarding. The shortest path routing minimizes delay and optimizes utilization of resources, however, it often causes certain links to become congested while others remain underutilized. In a bufferless OBS network in which burst drop probability is the primary metric of interest, the existence of a few highly congested links could lead to unacceptable performance for the entire network. We take a traffic engineering approach to path selection in OBS networks with the objective of balancing the traffic across the network links to reduce congestion and to improve overall performance. We present an approximate integer linear optimization problem as well as a simple integer relaxation heuristic to solve the problem efficiently for large networks. Numerical results demonstrate that our approach is effective in reducing the network-wide burst drop probability, in many cases significantly, over the shortest path routing.

Time-optimal scheduling for high throughput screening processes using cyclic discrete event models

A method for solving the scheduling problem for a class of cyclic systems with respect to throughput maximization is presented. A strictly cyclic mode of operation is considered, where the time offset between the start of consecutive jobs is always constant. All jobs have to follow an identical time scheme. The time scheme may be restricted by due dates or time window constraints. There are no buffers between the resources of the system. Based on discrete events systems (DES) modeling, this job shop scheduling problem can be formulated as a mixed integer linear optimization problem. Throughput is maximized by minimization of the cycle time. The method is applied to high throughput screening (HTS) problems and illustrated by means of a small example.

Modeling and Optimization for High-Throughput-Screening Systems

The problem of cyclic scheduling under the requirement of throughput maximization is considered for a special class of cyclically repeated batch processes. All batches have to follow an identical time scheme. The same resource may be visited more than ouce by the same batch and time window constraints may be stated by the user. It is shown that the cyclic scheduling problem can be transformed into a mixed integer linear optimization problem. The method'sapplication to High-Throughput-Screening processes is demonstrated.

Optimal energy management in pulp and paper mills

In this paper, we examine the utilization of mathematical programming tools for optimum energy management of the power plant in pulp and paper mills. The objective is the fulfillment of the total plant requirements in energy and steam with the minimum possible cost. The proposed methodology is based on the development of a detailed model of the power plant using mass and energy balances and a mathematical formulation of the electrical purchase contract, which can be translated into a rigorous mixed integer linear programming optimization problem. The results show that the method can be a very useful tool for the reduction of production cost due to minimization of the fuel and electricity costs.

Relation betwen integer linear vector optimization and multicriteria problems on groups and graphs

We relax an integer linear vector optimization problem [[Pbar]]. whose vector of variables ia additionally bounded from above. neglecting the upper and lowcr bounds of the basic variables. The relaxation is transformed into an equivalent muliizriteria prcup knapsack problem and this into a shortest path problem on a vectorially valued graph. The efficient points of the relaxation can be calculated from the solutions ol the corresponding group knapsack or shortesr path problem respectively. We derive a sufficient condition for the fact that the efficiency set of the relaxation contains elements feasible and thus efficient for problem [[Pbar]] Besides. criteria for finding the complete solution of the integer linear vector optimization problem by solving the relaxation are developed.

Distribution of gas cylinders

A software package was developed in Microsoft Windows 3.1 environment to solve the problem of gas cylinder delivery for the international company Prímagáz-Hungária. This task consists of a linear integer optimization problem which can be transformed into a linear optimization one with an approximately 1700 × 12 000 matrix and an n-travelling salesman problem under limited capacities ( n ≈ 10–20). A GIS module developed by us serves for presenting the results on maps. Computational experience is reported.

A decomposition approach for balancing large-scale acyclic data flow graphs

An efficient decomposition technique that provides a more systematic approach in solving the optimal buffer assignment problem of an acyclic data-flow graph (ADFG) with a large number of computational nodes is presented. The buffer assignment problem is formulated as an integer linear optimization problem that can be solved in pseudopolynomial time. However, if the size of an ADFG increases, then integer linear constraint equations may grow exponentially, making the optimization problem more intractable. The decomposition approach utilizes the critical path concept to decompose a directed ADFG into a set of connected subgraphs, and the integer linear optimization technique can be used to solve the buffer assignment problem in each subgraph. Thus, a large-scale integer linear optimization problem is divided into a number of smaller-scale subproblems, each of which can be easily solved in pseudopolynomial time. Examples are given to illustrate the proposed decomposition technique.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A maximum pipelined CORDIC architecture for inverse kinematic position computation

A cost-effective coordinate rotation digital computer (CORDIC) architecture is described for the computation of inverse kinematic position solution based on a functional decomposition of the closed-form joint equations. The functional decomposition shows a limited amount of parallelism with a large amount of sequentialism in the flow of computation and data dependencies and reveals the requirement for computing a large set of elementary operations: multiplications, additions, divisions, square roots, trigonometric functions and their inverse. However, these elementary operations, in general, cannot be efficiently computed in general-purpose uniprocessor computers. The CORDIC algorithms are the natural candidates for efficiently computing these elementary operations and the interconnection of these CORDIC processors to exploit the great potential of pipelining provides a better solution for computing the inverse kinematic position solution. The functional decomposition of the inverse kinematic position solution into a set of computational tasks can be represented as a directed task graph. The inclusion of input data modifies the task graph to an acyclic data dependency graph (ADDG). The nodes of the ADDG correspond to the computational modules, each of which can be realized by a CORDIC processor. The operands or data move along the edges, each of which connects a pair of nodes. Due to different paths and computation time for each CORDIC processor, operands may arrive at multi-input modules at different arrival time, causing a longer pipelined time. Delay buffers may be inserted at various paths to achieve a balanced ADDG. The optimal buffer assignment problem is reduced to an integer linear optimization problem which can be solved easily by computers. The realization of the balanced ADDG results in a maximum pipelined CORDIC architecture with a minimum number of delay buffer stages for the computation of inverse kinematic position solution.

An MILP formulation for heat‐integrated distillation sequence synthesis

AbstractIn this paper the problem of distillation sequence synthesis with heat integration is formulated and solved as a mixed integer linear superstructure optimization problem. Allowing both conventional and multieffect distillation, two alternatives for generating a superstructure are shown, then a formulation is presented which approximates the synthesis problem as a mixed integer linear programming (MILP) problem. Examples illustrate the method. Reported computer times suggest that earlier algorithmic methods for discovering the better sequences among those allowed by the problem formulation, and without the option of multieffecting, are an order of magnitude slower than this approach.

Verfahren zur lösung ganzzahliger linearer optimierungsprobleiue

In the paper [2] a calculus for solving integer optimization problems which can arithmetico proposition logical was developed. In the present paper these studies are used to obtain procedures for solving integer linear optimization problems based on switching algebra algorithms. These procedures differ both from cutting methods and also the known combinational methods. Three procedures, which may allow further modifications, are considered.