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Igor Ferst https://www.pyohio.org/2019/presentations/86 How do airlines choose which planes service which routes? How does a hospital optimize the shift schedule for hundreds of doctors and nurses? How do you choose the optimal location for a group of fulfillment centers, or oil derricks, or cell towers? These kinds of problems (and many others!) can be solved with integer linear programming (ILP), a powerful and decades-old framework for solving optimization problems. In this talk we will give a brief introduction to ILP and describe it's uses, strengths, and weaknesses. We will also show how to solve a real-world vehicle routing problem using Google's open-source python library for ILP. Trigger warning: this talk will contain high-school level math. Integer linear programming (ILP) is a powerful framework for solving optimization problems related to scheduling, resource allocation, vehicle routing, and many other areas. This talk will give a brief introduction to ILP and show how to solve a real-world vehicle routing problem using Google's open-source python library for ILP. === https://pyohio.org A FREE annual conference for anyone interested in Python in and around Ohio, the entire Midwest, maybe even the whole world. Produced by NDV: https://youtube.com/channel/UCQ7dFBzZGlBvtU2hCecsBBg?sub_confirmation=1 Sun Jul 28 14:30:00 2019 at Hays Cape

This volume was digitized and made accessible online due to deterioration of the original print copy.

We consider the problem of finding an n-agent joint-policy for the optimal finite-horizon control of a decentralized Pomdp (Dec-Pomdp). This is a problem of very high complexity (NEXP-hard in n >= 2). In this paper, we propose a new mathematical programming approach for the problem. Our approach is based on two ideas: First, we represent each agent's policy in the sequence-form and not in the tree-form, thereby obtaining a very compact representation of the set of joint-policies. Second, using this compact representation, we solve this problem as an instance of combinatorial optimization for which we formulate a mixed integer linear program (MILP). The optimal solution of the MILP directly yields an optimal joint-policy for the Dec-Pomdp. Computational experience shows that formulating and solving the MILP requires significantly less time to solve benchmark Dec-Pomdp problems than existing algorithms. For example, the multi-agent tiger problem for horizon 4 is solved in 72 secs with the MILP whereas existing algorithms require several hours to solve it.

In this paper we present methods for exemplar based clustering with outlier selection based on the facility location formulation. Given a distance function and the number of outliers to be found, the methods automatically determine the number of clusters and outliers. We formulate the problem as an integer program to which we present relaxations that allow for solutions that scale to large data sets. The advantages of combining clustering and outlier selection include: (i) the resulting clusters tend to be compact and semantically coherent (ii) the clusters are more robust against data perturbations and (iii) the outliers are contextualised by the clusters and more interpretable, i.e. it is easier to distinguish between outliers which are the result of data errors from those that may be indicative of a new pattern emergent in the data. We present and contrast three relaxations to the integer program formulation: (i) a linear programming formulation (LP) (ii) an extension of affinity propagation to outlier detection (APOC) and (iii) a Lagrangian duality based formulation (LD). Evaluation on synthetic as well as real data shows the quality and scalability of these different methods.

We propose a novel approach to automatically tracking cell populations in time-lapse images. To account for cell occlusions and overlaps, we introduce a robust method that generates an over-complete set of competing detection hypotheses. We then perform detection and tracking simultaneously on these hypotheses by solving to optimality an integer program with only one type of flow variables. This eliminates the need for heuristics to handle missed detections due to occlusions and complex morphology. We demonstrate the effectiveness of our approach on a range of challenging sequences consisting of clumped cells and show that it outperforms state-of-the-art techniques.

This report describes a heuristic algorithm for the pure, general integer linear programming problem (ILP). In attempting to quickly obtain a near-optimal solution (with-out concern for establishing optimality), the algorithm searches for a feasible 1-ceiling point. A feasible 1-ceiling point may be thought of as an integer solution lying on or near the boundary of the feasible region for the LP-relaxation associated with the ILP. Precise definitions of 1 -ceiling points and the role they play in an integer linear program are presented in a recent report by the authors. One key theorem therein demonstrates that all optimal solutions for an ILP whose feasible region is non- empty and bounded are feasible 1-ceiling points. Consequently, such a problem may be solved by enumerating just its feasible 1-ceiling points. Our heuristic approach is based upon the idea that a feasible 1-ceiling point found relatively near the optimal solution for the LP-relaxation is apt to have a high (possibly even optimal) objective function value. Having applied this Heuristic Ceiling Point Algorithm to 48 test problems taken from the literature, it appears that searching for such 1-ceiling points usually does provide a very good solution with a moderate amount of computational effort. Keywords: Subroutines, General integer variables.

This is a final report on a contract whose objective was to provide research support to the Concepts Analysis Agency (CAA) in the solution of large- scale mixed-integer programming models. We assisted in the formulation of a base closing model and provided a solution procedure based on a branch-and-cut algorithm. As a result of this work, we are able to solve relatively small instances of the base closing problem. Further work is needed to provide a customized algorithm that is capable of solving the larger instances in a reasonable amount of time. Integer programming.

We develop Integer Programming (IP) solutions for some special college admission problems arising from the Hungarian higher education admission scheme. We focus on four special features, namely the solution concept of stable score-limits, the presence of lower and common quotas, and paired applications. We note that each of the latter three special feature makes the college admissions problem NP-hard to solve. Currently, a heuristic based on the Gale-Shapley algorithm is being used in the application. The IP methods that we propose are not only interesting theoretically, but may also serve as an alternative solution concept for this practical application, and also for other ones.

We develop Integer Programming (IP) solutions for some special college admission problems arising from the Hungarian higher education admission scheme. We focus on four special features, namely the solution concept of stable score-limits, the presence of lower and common quotas, and paired applications. We note that each of the latter three special feature makes the college admissions problem NP-hard to solve. Currently, a heuristic based on the Gale-Shapley algorithm is being used in the application. The IP methods that we propose are not only interesting theoretically, but may also serve as an alternative solution concept for this practical application, and also for other ones.

We develop Integer Programming (IP) solutions for some special college admission problems arising from the Hungarian higher education admission scheme. We focus on four special features, namely the solution concept of stable score-limits, the presence of lower and common quotas, and paired applications. We note that each of the latter three special feature makes the college admissions problem NP-hard to solve. Currently, a heuristic based on the Gale-Shapley algorithm is being used in the application. The IP methods that we propose are not only interesting theoretically, but may also serve as an alternative solution concept for this practical application, and also for other ones.

This report examines the role played by several kinds of ceiling points in solving the pure, general integer linear programming problem (ILP). While no assumptions are made concerning the structure or signs of the data of the problem, it is assumed that the feasible region for (ILP) is non-empty and bounded. A ceiling point with respect to a single constraint maybe thought of as an integer solution on or close to the boundary of the feasible region defined by the constraint. The definition of a ceiling point with respect to a single constraint is extended to take multiple constraints into consideration simultaneously, defining what is called a feasible ceiling point. It is shown that the set all feasible ceiling points contains at least one optimal solution for (ILP). A related class of solutions called feasible 1-ceiling points is also characterized and shown to contain all optimal solutions for (ILP). Moreover, 1- ceiling points are computationally easier to identify than ordinary ceiling points and may be sought with respect to one constant at a time. It is also demonstrated that solving (ILP) requires only enumerating feasible 1-ceiling points with respect to a subset of all functional constraints. Keywords: Integer variables; Enumeration algorithms.

The paper discusses duality for linear and nonlinear programs in which some of the variables are arbitrarily constrained. The most important class of such problems is that of mixed-integer (linear and nonlinear) programs. The paper introduces the duality constructions and discusses algorithms based on them.

We present a bounding technique for use in implicit enumeration algorithms for solving the integer linear programming problem with binary variables. The main assumptions used by this technique are the associated linear program, obtained by dropping the integrality constraints on the variables, possesses a unique optimal solution, this optimal solution is not binary, and a good feasible solution to the original problem is available. An alternative to the last assumption which is weaker is also presented. We show that joint bounds can be obtained on the values of a subset of the variables. In addition we given an efficient method to implement this bounding technique. Finally, a class of problems particularly well-suited to this bounding procedure is specified. (Author)

This report gives documentations for two computer coded, DSLC and DMLC for solving block angular integer programming problems. The first code, DSLC, is for the single linking constraint case and the second DMLC is for the multiple linking constraint case. (Author)

Presented is an integer-programming approach to item pool design that can be used to calculate an optimal blueprint for an item pool to support an existing testing program. The results are optimal in the sense that they minimize the efforts involved in actually producing the items as revealed by current item writing patterns. Also presented is an adaptation of the models for use as a set of monitoring tools in item pool management. The approach is demonstrated empirically for an item pool designed for the Law School Admission Test. (Contains 2 tables and 30 references.) (Author/SLD)

There were several accomplishments of this research, both theoretical and computational. In joint work with Todd, we presented a cutting plane primal projective interior point method which we applied to matching problems, with encouraging computational results. Primal projective methods require a method to update the dual; we showed how various dual updates are related to each other and we also derived a dual projective algorithm. We derived a polynomial-time shifted barrier warm start algorithm which can be used in a cutting plane method; we showed that the directions obtained are strongly related to the directions derived in the work with Todd; computational results showed that the algorithm can be useful in some situations. The grant partially supported a Ph. D. student, Brian Borchers, who received his degree in August, 1992. His thesis concerned the use of branch-and-bound methods and contained good computational results as well as interesting theoretical observations. One paper from this thesis describes how the primal-dual interior point method can be used efficiently in a branch-and-bound method for solving mixed integer linear programming problem. Another paper describes how branch and bound algorithms for nonlinear integer programming problems can be improved. Borchers and I also developed a primal-dual interior point cutting plane method for solving linear ordering problems; the computational results for this algorithm were very encouraging, with run times comparable to those required by a simplex based cutting plane algorithm.

The Army is reducing and reshaping its force structure to adapt to the nation's changing defense needs and budget constraints. In response to these changes, Army Materiel Command (AMC) will submit facility realignment and closure recommendations in FY93 and FY95. This thesis develops a bi-criteria mixed integer programming model with the objectives of minimizing operating costs and maximizing a measure of military value to assist AMC in the generation of alternative realignments. Realignment of depot maintenance, research and development, test and evaluation, and administrative functions are considered on 32 AMC installations. An extensive empirical study demonstrates the applicability of the developed approach.

The development is documented of a heuristic method for the solution of pure integer linear programming problems. The procedure draws its methodology from the ideas of Hooke and Jeeves type 1 and 2 exploratory searches, greedy procedures, and neighborhood searches. It uses an efficient rounding method to obtain its first feasible integer point from the optimal continuous solution obtained via the simplex method. Since this method is based entirely on simple addition or subtraction of one to each variable of a point in n-space and the subsequent comparison of candidate solutions to a given set of constraints, it facilitates significant complexity improvements over existing techniques. It also obtains the same optimal solution found by the branch-and-bound technique in 44 of 45 small to moderate size test problems. Two example problems are worked in detail to show the inner workings of the method. Furthermore, using an established weighted scheme for comparing computational effort involved in an algorithm, a comparison of this algorithm is made to the more established and rigorous branch-and-bound method. A computer implementation of the procedure, in PC compatible Pascal, is also presented and discussed.

The focus of this project is new computational tools for mixed-integer programming (MIP). During the course of this project we have studied and obtained results on the following topics. 1. Dual heuristics for integer programs in order to rapidly improve dual bounds. 2. Choosing good branching variables in branch-and-bound algorithms for MIP. 3. Machine Learning in solving MIPs.4. Parallel Processing in Solving MIPS. The new algorithms are computational tested and, in many cases, outperform existing algorithms. This research has been presented at several conferences and has and will appear in archival journals.

A parametric integer linear program (PILP) may be defined as a family of closely related integer linear programs (ILP). Within this definition the author incorporates not only continuous scalar parameterizations but also finite parameterizations. These may include an ILP with a finite number of objective functions or right hand sides or constraint matrices or any combination of these. A general framework for PILP is presented. It begins by outlining the need for PILP algorithms. Basic solution methodologies are explained and two rudimentary approaches for the PILP are stated. Theoretical properties for special parameterizations are proved, and techniques for improving algorithmic efficiency are discussed. The framework concludes with an examination of underlying factors which intimately relate to the scheduling of solution priorities in a PILP algorithm.

Throughout history, successful military leaders have recognized that weather conditions on the battlefield can play a significant role in determining the victor. For this reason, the United States maintains and equips several different types of military units that are tasked to provide dedicated weather support to operational commanders. These units use a variety of types of sensors with differing capabilities to collect current weather conditions on the battlefield. In support of the commander's Concept of Operations (CONOP), United States military doctrine dictates that, as a part of general military campaign planning, a Meteorological and Oceanographic (METOC) collection plan be developed. This collection plan should specify the allocation of all weather sensing sources within the operational theater and throughout all phases of the military operation. This paper describes a methodology for creating a robust METOC collection plan in support of any given military campaign plan that deploys air, land, maritime, and special operations component weather sensing equipment in a way that maximizes expected detection of operationally significant weather conditions over the largest area possible for a given set of available weather sensors.

An integer linear programming model which determines the optimal allocation of files in a multiple computer network has been analyzed to determine under what circumstances the model can be used. The feasibility of using the model on the CDC 6000 series computers was also studied. The use of the model requires and integer linear programming system and a computerized means of generating and formatting the large amount of input data required by the model. Two integer linear programming systems, ARRIBA and APEX III, were analyzed for use with the model. Either system could be used. The use of ARRIBA was limited to relatively small problems (problems in which the sum of the number of files and computers is ten or less). APEX III could be used to solve both small and large problems, but its use with large problems required costly computer run times. Both systems required essentially the same input data but in different formats. A FORTRAN computer program, DATASUP, was developed to generate the data input for either system (ARRIBA or APEX III) at the user's option. (Author)

A multiple objective fuzzy liner programming approach to the capital budgeting problem is developed. Since much of the available data in any capital budgeting decision situation is either of an imprecise or ill-defined nature, a mathematical optimization technique is required that is capable of incorporating this inherent uncertainty. Fuzzy linear programming provides an effective methodology for this analysis. Specifically, a mathematical model is developed which utilizes fuzzy linear programming as a solution technique for the research and development program or project selection problem. In addition an exchange heuristic, a modified form of C. C. Peterson's exchange algorithm, is presented. A limited bibliography of works in multiple objective optimization is presented. Two computer codes are included. The first utilizes the IBM MPSX/Mixed Integer Programming procedures to solve the (0-1) linear integer programming problem. The second is a FORTRAN program to solve the exchange heuristic algorithm discussed previously. (Author)

A multiple objective fuzzy liner programming approach to the capital budgeting problem is developed. Since much of the available data in any capital budgeting decision situation is either of an imprecise or ill-defined nature, a mathematical optimization technique is required that is capable of incorporating this inherent uncertainty. Fuzzy linear programming provides an effective methodology for this analysis. Specifically, a mathematical model is developed which utilizes fuzzy linear programming as a solution technique for the research and development program or project selection problem. In addition an exchange heuristic, a modified form of C. C. Peterson's exchange algorithm, is presented. A limited bibliography of works in multiple objective optimization is presented. Two computer codes are included. The first utilizes the IBM MPSX/Mixed Integer Programming procedures to solve the (0-1) linear integer programming problem. The second is a FORTRAN program to solve the exchange heuristic algorithm discussed previously. (Author)

Split-plot designs are commonly used in industrial experiments when there are hard-to-change and easy-to-change factors. Due to the number of factors and resource limitations, it is more practical to run a fractional factorial split-plot (FFSP) design. These designs are variations of the fractional factorial (FF) design, with the restricted randomization structure to account for the whole plots and subplots. We begin by discussing the formulation of FFSP designs using integer programming (IP) to achieve various design criteria. We specifically look at the maximum number of clear two-factor interactions and variations on this criterion. By making restrictions on some of the general linear constraints, we are able to customize the alias structure of these FFSP designs. Additional constraints allow for the generation of blocked FFSP designs that are shown to meet performance standards shown in today's literature. By generalizing the model formulation, we show how designs for numerous stages can be generated. In addition, we explore using a genetic algorithm heuristic to search for split-plot designs from a candidate matrix of factor effects generated using the Kronecker product.

Special Operations Forces (SOF) are frequently employed to conduct missions not within the limited boundaries of unilateral special operations. These operations often involve cooperation with general purpose forces (GPF) and are often under their command. This thesis argues that these cooperative efforts are better examined as integrated operations rather than special or conventional operations. These operations require SOF to conduct specialized tasks facilitating the introduction of follow-on GPF to complete the mission. This thesis develops a theory of integrated operations by examining six operations, previously considered under conventional wisdom as either special or conventional. It rejects much of the myth which surrounds these operations and offers a revisionist interpretation of the necessary and sufficient conditions for success in these endeavors. The thesis then goes on to compare cases of these special units using organizational theory to determine the sources of integration. The cases examined indicate a causal relationship between organizational factors related to command and training and a special units ability to integrate with GPF. The thesis concludes by recommending the realignment of select SOF in the current force structure to better meet the challenges of future integrated operations.

Special Operations Forces (SOF) are frequently employed to conduct missions not within the limited boundaries of unilateral special operations. These operations often involve cooperation with general purpose forces (GPF) and are often under their command. This thesis argues that these cooperative efforts are better examined as integrated operations rather than special or conventional operations. These operations require SOF to conduct specialized tasks facilitating the introduction of follow-on GPF to complete the mission. This thesis develops a theory of integrated operations by examining six operations, previously considered under conventional wisdom as either special or conventional. It rejects much of the myth which surrounds these operations and offers a revisionist interpretation of the necessary and sufficient conditions for success in these endeavors. The thesis then goes on to compare cases of these special units using organizational theory to determine the sources of integration. The cases examined indicate a causal relationship between organizational factors related to command and training and a special units ability to integrate with GPF. The thesis concludes by recommending the realignment of select SOF in the current force structure to better meet the challenges of future integrated operations.

Special Operations Forces (SOF) are frequently employed to conduct missions not within the limited boundaries of unilateral special operations. These operations often involve cooperation with general purpose forces (GPF) and are often under their command. This thesis argues that these cooperative efforts are better examined as integrated operations rather than special or conventional operations. These operations require SOF to conduct specialized tasks facilitating the introduction of follow-on GPF to complete the mission. This thesis develops a theory of integrated operations by examining six operations, previously considered under conventional wisdom as either special or conventional. It rejects much of the myth which surrounds these operations and offers a revisionist interpretation of the necessary and sufficient conditions for success in these endeavors. The thesis then goes on to compare cases of these special units using organizational theory to determine the sources of integration. The cases examined indicate a causal relationship between organizational factors related to command and training and a special units ability to integrate with GPF. The thesis concludes by recommending the realignment of select SOF in the current force structure to better meet the challenges of future integrated operations.

Special Operations Forces (SOF) are frequently employed to conduct missions not within the limited boundaries of unilateral special operations. These operations often involve cooperation with general purpose forces (GPF) and are often under their command. This thesis argues that these cooperative efforts are better examined as integrated operations rather than special or conventional operations. These operations require SOF to conduct specialized tasks facilitating the introduction of follow-on GPF to complete the mission. This thesis develops a theory of integrated operations by examining six operations, previously considered under conventional wisdom as either special or conventional. It rejects much of the myth which surrounds these operations and offers a revisionist interpretation of the necessary and sufficient conditions for success in these endeavors. The thesis then goes on to compare cases of these special units using organizational theory to determine the sources of integration. The cases examined indicate a causal relationship between organizational factors related to command and training and a special units ability to integrate with GPF. The thesis concludes by recommending the realignment of select SOF in the current force structure to better meet the challenges of future integrated operations.

Mixed-Integer Programming has traditionally been restricted to deterministic models. Recent research has opened the door to stochastic optimization models, which are typically dynamic in nature. This project lays the foundation for stochastic dynamic mixed-integer and linear programming (SD-MIP). This project has produced several new ideas in connection with a) convexification of two-stage mixed-integer sets and b) multi-stage (including two-stage) stochastic linear programming. Together a) and b) provide the foundations for SD-MIP problems. From new concepts and algorithms to applications and software, this project has made significant breakthroughs in all aspects. This report provides a synopsis of both theoretical and computational results. As a preview, we mention that currently available deterministic MIP solvers, as powerful as they are known to be, are unable to solve SD-MIP models of modest size within an hour of computing. In contrast, our decomposition approach provides provably optimal solutions within the hour time-limit.

We study the generalization of split and intersection cuts from Mixed Integer Linear Programming to the realm of Mixed Integer Nonlinear Programming. Constructing such cuts requires calculating the convex hull of the difference of two convex sets with specific geometric structures. We introduce two techniques to give precise characterizations of such convex hulls and use them to construct split and intersection cuts for several classes of sets. In particular, we give simple formulas for split cuts for essentially all convex sets described by a single quadratic inequality and for more general intersection cuts for a wide variety of convex quadratic sets.

This study develops a prototype model which can be used to allocate strategic sealift resources in crisis deployments. The first part of the model is a GAMS-Based Integer Program that extends a classic network flow optimization model developed by Dantzig and Fulkerson. The second part uses a Fortran program to convert the GAMS output into ship schedules. Using intelligent reduction methods, the formulation reduces the number of constraints by 60-70% and the number of variables and nonzero elements in the matrix by 90-99%. Results of this study indicate integer programming with these reduction methods is a viable alternative to modelling sealift as continuous flow variables.

Bibliography: pt. 1, p. 46-47; pt. 2, p. 48

Bibliography: p. 58-59

This research develops a mixed integer linear programming (MILP) model that considers simultaneously both the traditional reservoir rule curves and the hedging rules to manage and operate a multipurpose, multireservoir system. During normal periods of operation, when inflows are plentiful, this optimization model efficiently distributes the available stored water from different reservoirs to meet the planned demands imposed by competing users. However, during periods of drought, or when anticipating a drought, the planned demands cannot be fully met, and a water shortage occurs. By considering the hedging rules along with the rule curves, guidelines are provided for reservoir releases. To minimize the impact of drought, the hedging rules effectively reduce the ongoing water supply to balance with the target storage requirement. The MILP model is applied to a multireservoir system in the southern region of Taiwan, where the results obtained demonstrate the applicability and utility of the model. Read More: http://ascelibrary.org/action/showAbstract?page=86&volume=129&issue=2&journalCode=jwrmd5

ADA743746

Journal of Research of the National Bureau of Standards

Integer-programming formulations for the design of symmetric and balanced laminated plates under biaxial compression are presented. Both maximization of buckling load for a given total thickness and the minimization of total thickness subject to a buckling constraint are formulated. The design variables that define the stacking sequence of the laminate are zero-one integers. It is shown that the formulation results in a linear optimization problem that can be solved on readily available software. This is in contrast to the continuous case, where the design variables are the thicknesses of layers with specified ply orientations, and the optimization problem is nonlinear. Constraints on the stacking sequence such as a limit on the number of contiguous plies of the same orientation and limits on in-plane stiffnesses are easily accommodated. Examples are presented for graphite-epoxy plates under uniaxial and biaxial compression using a commercial software package based on the branch-and-bound algorithm.

Bibliography: pt. 1, p. 46-47; pt. 2, p. 48

The Integer Programming Problem (IP) for a polytope P \subseteq R^n is to find an integer point in P or decide that P is integer free. We give an algorithm for an approximate version of this problem, which correctly decides whether P contains an integer point or whether a (1+\eps) scaling of P around its barycenter is integer free in time O(1/\eps^2)^n. We reduce this approximate IP question to an approximate Closest Vector Problem (CVP) in a "near-symmetric" semi-norm, which we solve via a sieving technique first developed by Ajtai, Kumar, and Sivakumar (STOC 2001). Our main technical contribution is an extension of the AKS sieving technique which works for any near-symmetric semi-norm. Our results also extend to general convex bodies and lattices.

In many common scenarios, programmers need to implement functionality that is already provided by some third party library. This paper presents a tool called Hunter that facilitates code reuse by finding relevant methods in large code bases and automatically synthesizing any necessary wrapper code. The key technical idea underlying our approach is to use types to both improve search results and guide synthesis. Specifically, our method computes similarity metrics between types and uses this information to solve an integer linear programming (ILP) problem in which the objective is to minimize the cost of synthesis. We have implemented Hunter as an Eclipse plug-in and evaluate it by (a) comparing it against S6, a state-of-the-art code reuse tool, and (b) performing a user study. Our evaluation shows that Hunter compares favorably with S6 and significantly increases programmer productivity.

The Lovasz Local Lemma due to Erdos and Lovasz is a powerful tool in proving the existence of rare events. We present an extension of this lemma, which works well when the event to be shown to exist is a conjunction of individual events, each of which asserts that a random variable does not deviate much from its mean. As applications, we consider two classes of NP-hard integer programs: minimax and covering integer programs. A key technique, randomized rounding of linear relaxations, was developed by Raghavan and Thompson to derive good approximation algorithms for such problems. We use our extension of the Local Lemma to prove that randomized rounding produces, with non-zero probability, much better feasible solutions than known before, if the constraint matrices of these integer programs are column-sparse (e.g., routing using short paths, problems on hypergraphs with small dimension/degree). This complements certain well-known results from discrepancy theory. We also generalize the method of pessimistic estimators due to Raghavan, to obtain constructive (algorithmic) versions of our results for covering integer programs.

We consider the feasibility problem of integer linear programming (ILP). We show that solutions of any ILP instance can be naturally represented by an FO-definable class of graphs. For each solution there may be many graphs representing it. However, one of these graphs is of path-width at most 2n, where n is the number of variables in the instance. Since FO is decidable on graphs of bounded path- width, we obtain an alternative decidability result for ILP. The technique we use underlines a common principle to prove decidability which has previously been employed for automata with auxiliary storage. We also show how this new result links to automata theory and program verification.

Voting problems are central in the area of social choice. In this article, we investigate various voting systems and types of control of elections. We present integer linear programming (ILP) formulations for a wide range of NP-hard control problems. Our ILP formulations are flexible in the sense that they can work with an arbitrary number of candidates and voters. Using the off-the-shelf solver Cplex, we show that our approaches can manipulate elections with a large number of voters and candidates efficiently.

We give a survey of work on the number of vertices of the convex hull of integer points defined by the system of linear inequalities. Also, we present our improvement of some of these.

This thesis presents an integer programming model to help the Navy develop long-range shipbuilding plans. The model is of a general nature, but is proposed specifically as a decision aid for the developers of the Navy's Extended Planning Annex (EPA). The EPA sets forth planned ship purchase five to 20 years in the future. It is currently produced with a mainly manual process that takes weeks at a time, hence it is extremely difficult for the EPA planners to respond quickly to changes in the given data and assumptions. The optimization model suggests delivery dates for new ships, based on given budgets and requirements, and accounts for such complexities as the extra costs of building a leadship or of resuming construction after a production break. The model has been formulated with the General Algebraic Modeling System (GAMS) and effectively solved with two commercial optimization packages. It performs fast enough to allow the planner to make several 'what if' runs in the course of developing the EPA. Keywords: Optimization; Integer programming; Military applications; Shipbuilding.

This thesis presents an integer programming model to help the Navy develop long-range shipbuilding plans. The model is of a general nature, but is proposed specifically as a decision aid for the developers of the Navy's Extended Planning Annex (EPA). The EPA sets forth planned ship purchase five to 20 years in the future. It is currently produced with a mainly manual process that takes weeks at a time, hence it is extremely difficult for the EPA planners to respond quickly to changes in the given data and assumptions. The optimization model suggests delivery dates for new ships, based on given budgets and requirements, and accounts for such complexities as the extra costs of building a leadship or of resuming construction after a production break. The model has been formulated with the General Algebraic Modeling System (GAMS) and effectively solved with two commercial optimization packages. It performs fast enough to allow the planner to make several 'what if' runs in the course of developing the EPA. Keywords: Optimization; Integer programming; Military applications; Shipbuilding.

This thesis presents an integer programming model to help the Navy develop long-range shipbuilding plans. The model is of a general nature, but is proposed specifically as a decision aid for the developers of the Navy's Extended Planning Annex (EPA). The EPA sets forth planned ship purchase five to 20 years in the future. It is currently produced with a mainly manual process that takes weeks at a time, hence it is extremely difficult for the EPA planners to respond quickly to changes in the given data and assumptions. The optimization model suggests delivery dates for new ships, based on given budgets and requirements, and accounts for such complexities as the extra costs of building a leadship or of resuming construction after a production break. The model has been formulated with the General Algebraic Modeling System (GAMS) and effectively solved with two commercial optimization packages. It performs fast enough to allow the planner to make several 'what if' runs in the course of developing the EPA. Keywords: Optimization; Integer programming; Military applications; Shipbuilding.

Slides used for group presentation.

Slides used for group presentation.