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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

Integer Programming, seminar 1970 - Control Data

Binary Knapsack Problem (BKP) is to select a subset of an element (item) set with the highest value while keeping the total weight within the capacity of the knapsack. This paper presents an integer programming model for a variation of BKP where the value of each element may depend on selecting or ignoring other elements. Strengths of such Value-Related Dependencies are assumed to be imprecise and hard to specify. To capture this imprecision, we have proposed modeling value-related dependencies using fuzzy graphs and their algebraic structure.

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

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

In this paper we consider the use of extended formulations in LP-based algorithms for mixed integer conic quadratic programming (MICQP). Extended formulations have been used by Vielma, Ahmed and Nemhauser (2008) and Hijazi, Bonami and Ouorou (2013) to construct algorithms for MICQP that can provide a significant computational advantage. The first approach is based on an extended or lifted polyhedral relaxation of the Lorentz cone by Ben-Tal and Nemirovski (2001) that is extremely economical, but whose approximation quality cannot be iteratively improved. The second is based on a lifted polyhedral relaxation of the euclidean ball that can be constructed using techniques introduced by Tawarmalani and Sahinidis (2005). This relaxation is less economical, but its approximation quality can be iteratively improved. Unfortunately, while the approach of Vielma, Ahmed and Nemhauser is applicable for general MICQP problems, the approach of Hijazi, Bonami and Ouorou can only be used for MICQP problems with convex quadratic constraints. In this paper we show how a homogenization procedure can be combined with the technique by Tawarmalani and Sahinidis to adapt the extended formulation used by Hijazi, Bonami and Ouorou to a class of conic mixed integer programming problems that include general MICQP problems. We then compare the effectiveness of this new extended formulation against traditional and extended formulation-based algorithms for MICQP. We find that this new formulation can be used to improve various LP-based algorithms. In particular, the formulation provides an easy-to-implement procedure that, in our benchmarks, significantly improved the performance of commercial MICQP solvers.

We present an integer programming model for the ferry scheduling problem, improving existing models in various ways. In particular, our model has reduced size in terms of the number of variables and constraints compared to existing models by a factor of approximately O(n), where n being the number of ports. The model also handles efficiently load/unload time constraints, crew scheduling and passenger transfers. Experiments using real world data produced high quality solutions in 12 hours using CPLEX 12.4 with a performance guarantee of within 15% of optimality, on average. This establishes that using a general purpose integer programming solver is a viable alternative in solving the ferry scheduling problem of moderate size.

To obtain a better understanding of the trade-offs between various objectives, Bi-Objective Integer Programming (BOIP) algorithms calculate the set of all non-dominated vectors and present these as the solution to a BOIP problem. Historically, these algorithms have been compared in terms of the number of single-objective IPs solved and total CPU time taken to produce the solution to a problem. This is equitable, as researchers can often have access to widely differing amounts of computing power. However, the real world has recently seen a large uptake of multi-core processors in computers, laptops, tablets and even mobile phones. With this in mind, we look at how to best utilise parallel processing to improve the elapsed time of optimisation algorithms. We present two methods of parallelising the recursive algorithm presented by Ozlen, Burton and MacRae. Both new methods utilise two threads and improve running times. One of the new methods, the Meeting algorithm, halves running time to achieve near-perfect parallelisation. The results are compared with the efficiency of parallelisation within the commercial IP solver IBM ILOG CPLEX, and the new methods are both shown to perform better.

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 function are considered on 32 AMC installations. An extensive empirical study demonstrates the applicability of the developed approach.

We study the combinatorial FIFO Stack-Up problem, where bins have to be stacked-up from conveyor belts onto pallets. Given k sequences of labeled bins and a positive integer p, the goal is to stack-up the bins by iteratively removing the first bin of one of the k sequences and put it onto a pallet located at one of p stack-up places. The FIFO Stack-Up problem asks whether there is some processing of the sequences of bins such that at most p stack-up places are used. In this paper we strengthen the hardness of the FIFO Stack-Up by considering practical cases and the distribution of the pallets onto the sequences. We introduce a digraph model for this problem, the so called decision graph, which allows us to give a breadth first search solution. Further we apply methods to solve hard problems to the FIFO Stack-Up problem. In order to evaluate our algorithms, we introduce a method to generate random, but realistic instances for the FIFO Stack-Up problem. Our experimental study of running times shows that the breadth first search solution on the decision graph combined with a cutting technique can be used to solve practical instances on several thousands of bins of the FIFO Stack-Up problem. Further we analyze two integer programming approaches implemented in CPLEX and GLPK. As expected CPLEX can solve the instances much faster than GLPK and our pallet solution approach is much better than the bin solution approach.

We study the combinatorial FIFO Stack-Up problem, where bins have to be stacked-up from conveyor belts onto pallets. Given k sequences of labeled bins and a positive integer p, the goal is to stack-up the bins by iteratively removing the first bin of one of the k sequences and put it onto a pallet located at one of p stack-up places. The FIFO Stack-Up problem asks whether there is some processing of the sequences of bins such that at most p stack-up places are used. In this paper we strengthen the hardness of the FIFO Stack-Up by considering practical cases and the distribution of the pallets onto the sequences. We introduce a digraph model for this problem, the so called decision graph, which allows us to give a breadth first search solution. Further we apply methods to solve hard problems to the FIFO Stack-Up problem. In order to evaluate our algorithms, we introduce a method to generate random, but realistic instances for the FIFO Stack-Up problem. Our experimental study of running times shows that the breadth first search solution on the decision graph combined with a cutting technique can be used to solve practical instances on several thousands of bins of the FIFO Stack-Up problem. Further we analyze two integer programming approaches implemented in CPLEX and GLPK. As expected CPLEX can solve the instances much faster than GLPK and our pallet solution approach is much better than the bin solution approach.

We study the combinatorial FIFO Stack-Up problem, where bins have to be stacked-up from conveyor belts onto pallets. Given k sequences of labeled bins and a positive integer p, the goal is to stack-up the bins by iteratively removing the first bin of one of the k sequences and put it onto a pallet located at one of p stack-up places. The FIFO Stack-Up problem asks whether there is some processing of the sequences of bins such that at most p stack-up places are used. In this paper we strengthen the hardness of the FIFO Stack-Up by considering practical cases and the distribution of the pallets onto the sequences. We introduce a digraph model for this problem, the so called decision graph, which allows us to give a breadth first search solution. Further we apply methods to solve hard problems to the FIFO Stack-Up problem. In order to evaluate our algorithms, we introduce a method to generate random, but realistic instances for the FIFO Stack-Up problem. Our experimental study of running times shows that the breadth first search solution on the decision graph combined with a cutting technique can be used to solve practical instances on several thousands of bins of the FIFO Stack-Up problem. Further we analyze two integer programming approaches implemented in CPLEX and GLPK. As expected CPLEX can solve the instances much faster than GLPK and our pallet solution approach is much better than the bin solution approach.

A model is developed for solving the optimization problem created when a manufacturer presents management with numerous proposed modifications which will improve the system effectiveness of an existing system. The optimization is constrained by the physical limitations of the system and by a limited budget. System effectiveness is defined and discussed in detail for an anti-submarine aircraft system with reliability considered the single most important factor. The model transforms the problem into an integer programming problem, and a numerical example is provided to demonstrate the versatility of this model.

The hybrid-dual algorithm is divided into two stages. In the first stage a linear program is solved to yield an optimal solution in fractional- valued variables. The final tableau given by the dual linear programming method is then transformed and expanded into a new tableau of a readily specifiable canonical form. In the second stage of the algorithm a variant of the bound escalation method is applied to the new tableau--and to the tableaus successively derived thereafter-until one or more of a distinguished set of columns (and a corresponding set of rows) attains a predetermined configuration. At this point the indicated rows and columns are dis carded, never to be recovered, and the method continues recursively with the bound escalation algorithm until the problem is solved.

The program solves integer linear programs of the form (P) Minimize cx subject to b + Ax = or 0, x sub j = 0 or 1 where c and x are n-vectors, b is an m-vector, and A is m by n. Any bounded integer linear program can be written in this form, using elementary manipulations if necessary. Familiarity with 2 previous papers in the series is assumed.

The program solves integer linear programs of the form (P) Minimize cx subject to b + Ax = or 0, x sub j = 0 or 1 where c and x are n-vectors, b is an m-vector, and A is m by n. Any bounded integer linear program can be written in this form, using elementary manipulations if necessary. Familiarity with 2 previous papers in the series is assumed.

The program solves integer linear programs of the form (P) Minimize cx subject to b + Ax = or 0, x sub j = 0 or 1 where c and x are n-vectors, b is an m-vector, and A is m by n. Any bounded integer linear program can be written in this form, using elementary manipulations if necessary. Familiarity with 2 previous papers in the series is assumed.

This is an introductory survey of integer programming, its theory, methodology and applications, for the Encyclopedia of Statistical Sciences. (Author)

A Multiple-Target Tracking Algorithm has been designed and tested for use with DIFAR (Directional Finding and Ranging) sonobuoys. The algorithm is implemented as a functionally modular computer program composed of five main subroutines. Operating in near real time and in less than 64K words of memory, the algorithm is capable of separating raw measurements into data sets corresponding to individual targets at at the sensor level (using cluster analysis), correlating target measurements across sensors (using physical constraint and statistical tests), and selecting the most likely track scenario among the various potential scenarios (using integer programming). The process requires no operator decision and no a priori information about the number or initial conditions of the targets. The algorithm is self initializing from the raw buoy data. Using synthetic data, the algorithm was tested on several multi-target scenarios with excellent results. (Author)

The motivation for this work has been the need for a practical procedure to solve the maximum-weight cut problem (MCP) in undirected graphs. Our primary focus has been on problems arising from considerations in statistical mechanics. These problems are typically posed on grid graphs and some natural variants. There has been significant progress in two areas: solution of the maximum-weight cut problem and development of simplex-based tools for integer programming. Codes developed have been widely used to improve solution time.

The limited success of exact algorithms for solving integer programming problems has encouraged the development of heuristic procedures for efficiently obtaining solutions that are at least close to optimal. This document presents three heuristic procedures for 0-1 integer programming problems having only inequality constraints. These procedures are based on Hillier's previous heuristic procedures for general integer linear programming. All three were successfully run on problems with up to 500 variables with only modest execution times. The quality of the solutions for these problems were, in general, very good and often were optimal. When the best of the solutions obtained by the three procedures was taken, the final solution was optimal for 24 of 45 randomly generated problems. These procedures can be used for problems that are too large to be computationally feasible for exact algorithms. In addition, they can be useful for smaller problems by quickly providing an advanced starting solution for an exact algorithm.

The report presents a synthesis of the Balasian implicit enumeration approach to integer linear programming with the approach typified by Land and Doig and by Roy, Bertier, and Nghiem. This synthesis results from the use of an imbedded linear program to compute surrogate constraints that are as 'strong' as possible in a sense slightly different from that originally used by Glover. A very simple implicit enumeration algorithm fitted with optional imbedded linear programming machinery was implemented and tested extensively on an IBM 7044 computer. Use of the imbedded linear program dramatically reduced solution time in virtually every case and sufficied to render the tested algorithm superior to the other five implicit enumeration algorithms for which comparable published experience was available. Existing evidence suggests that the present approach should permit the routine solution of practical integer problems involving hundreds of variables.

The paper presents a generalization, called polaroid, of the concept of polar sets. A list of properties satisfied by polaroids is established indicating that the new concept may be fruitfully used in an area of non-convex (called here polar) programming as well as in integer programming, by means of polaroid cuts; this class of new cuts contains the ones defined by Tuy for concave programming (a special case of polar programming) and by Balas for integer programming; it furthermore provides for new degrees of freedom in the construction of algorithms in the above-mentioned areas of mathematical programming.

Contents: Resource Decomposition: A Conceptual Outline; Branching in the Rudimentary Branch-and-Bound Algorithm; Computing Bounds: Single Linking Constraint Case; Computing Bounds: Multiple Linking Constraints Case; Computational Results; and Conclusions, Extensions, and Areas for Future Research.

Fundamental Disjunctive Conic Cut (DCC) methodology for Mixed-Integer Conic Linear Optimization (MICO) was developed. To describe the convex hull of the intersection of a convex set E and a linear disjunction is the fundamental problem, and that served as the core of solution techniques for MICO. It was proved that if there exists a cone K that has the same intersection with the boundary of the disjunction as the convex set E, then the convex hull of the disjunction is the intersection of E with K. While uniqueness of a DCC is proved for general MICO, the existence of such a cone is difficult to prove for the general case. Thorough analysis of a parametric family of quadrics allows to prove the existence and uniqueness of a second order cone, when E is the intersection of an affine space and a second order cone. An efficiently computable method was developed for finding that cone, which provided novel and powerful DCCs for Mixed Integer Second Order Cone Optimization (MISOCO), which can be used in branch-and-cut algorithms when solving MISOCO problems. All special and degenerate cases are carefully analyzed and easy to compute criteria are developed to compute a DCC for all cases. Limited, but rigorous computational experiments gave strong indication of the power of the DCCs.

The Marine Corps has long been successful in assigning its available personnel to vacant billets. However, by our research, the Marine Corps has not been as successful in minimizing assignment costs when moving a Marine to another permanent duty station. With increased pressure on cost savings due to shrinking budgets, the importance of cost minimizing efforts is becoming more significant. This thesis examines the Marine Corps personnel assignment process and proposes a methodology for optimizing the allocation of Marine Corps personnel that minimizes assignment costs while taking into account constraints such as military occupational specialty, billet vacancies, duty station preference, and seniority. Optimization is achieved by incorporating an integer programming model into the personnel assignment process. The model is tested by contrasting the results of the actual assignments of a 15-Marine sample with the results of simulated optimization assignments of the same sample. The findings of this thesis show that the proposed methodology is both valid and feasible, and that it could yield significant monetary savings for the Marine Corps.

A primal feasible (all-integer) integer linear programming algorithm has been developed and programmed, together with a related procedure for obtaining a first feasible solution. Once a feasible solution is found, the algorithm maintains feasibility at each stage, in contrast to other algorithms that have been programmed and are currently available. These other algorithms do not achieve feasibility until the optimal solution is reached. The primal feasible algorithm is based on a particular way of applying the cutting planes previously developed by R. E. GOMORY, and on a specific interpretation of their role. The finiteness of convergence has been established for two-dimensional problems but not for the general case; however, there appears to be at least computational convergence in a considerable fraction of the cases. In addition, a Generalized Euclidean Algorithm for finding the greatest common divisor for more than two numbers is defined. The solution of systems of linear diophantine equations is presented in terms of integer linear programming. Some geometric considerations that help to illuminate the workings of the algorithm, are examined.

Detection of an Unmanned Air Vehicle by radar is dependent on many variables including range, altitude, and relative orientation. Given a radar location and appropriate model for the likelihood of detection, a path plan can be created for an Unmanned Air Vehicle which constrains the probability of detection. In this paper such an approach is taken using a linearized detection model. The detection model and the Unmanned Air Vehicle's dynamics are represented as a linear program subject to mixed integer constraints. This mixed integer linear program (MILP) is then solved with commercial software which has been traditionally used by the Operations Research community. This approach searches for all feasible solutions and produces the best path plan based on the user specified parameters.

The downsizing of military forces in the 1990's forces Navy Medicine to consider closure and realignment of its hospitals and clinics. Any major Department of Defense (DOD) closure or realignment must be decided according to Title XXIX of United States Public Law 101-510, the Defense Base Closure and Realignment Act of 1990 as amended. In 1991 and 1993, this act allowed the closure and realignment of numerous Naval installations. In 1995 (the last round of closures and realignments provided for by that law), Navy Medicine expects to undergo a significant restructuring of its hospitals. Through these hospitals and civilian providers the Navy cares for assigned active duty, active duty dependents and retiree beneficiaries from all services. This thesis develops an integer linear program, Hospital Efficient Location Program (HELP), which enables Navy Medicine to determine which of its hospitals to consider for closure. Using resource and demand data available from standard DOD medical information systems, HELP has identified $0.52 billion annually in potential savings from the closure of 7 hospitals by 1999. At this savings, demand for all assigned beneficiaries is satisfied with Naval hospitals providing care for over 95% of active duty inpatient and outpatient demand. Facility location, Hospital location, Base realignment and closure.

Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject to integrality requirements for the variables. This chapter is dedicated to this topic. The primary goal is a study of a simple version of general nonlinear integer problems, where all constraints are still linear. Our focus is on the computational complexity of the problem, which varies significantly with the type of nonlinear objective function in combination with the underlying combinatorial structure. Numerous boundary cases of complexity emerge, which sometimes surprisingly lead even to polynomial time algorithms. We also cover recent successful approaches for more general classes of problems. Though no positive theoretical efficiency results are available, nor are they likely to ever be available, these seem to be the currently most successful and interesting approaches for solving practical problems. It is our belief that the study of algorithms motivated by theoretical considerations and those motivated by our desire to solve practical instances should and do inform one another. So it is with this viewpoint that we present the subject, and it is in this direction that we hope to spark further research.

Load disaggregation based on aided linear integer programming (ALIP) is proposed. We start with a conventional linear integer programming (IP) based disaggregation and enhance it in several ways. The enhancements include additional constraints, correction based on a state diagram, median filtering, and linear programming-based refinement. With the aid of these enhancements, the performance of IP-based disaggregation is significantly improved. The proposed ALIP system relies only on the instantaneous load samples instead of waveform signatures, and hence does not crucially depend on high sampling frequency. Experimental results show that the proposed ALIP system performs better than the conventional IP-based load disaggregation system.

In the Integer Quadratic Programming problem input is an n*n integer matrix Q, an m*n integer matrix A and an m-dimensional integer vector b. The task is to find a vector x in Z^n, minimizing x^TQx, subject to Ax

This paper introduces an improved recursive algorithm to generate the set of all nondominated objective vectors for the Multi-Objective Integer Programming (MOIP) problem. We significantly improve the earlier recursive algorithm of \"Ozlen and Azizo\u{g}lu by using the set of already solved subproblems and their solutions to avoid solving a large number of IPs. A numerical example is presented to explain the workings of the algorithm, and we conduct a series of computational experiments to show the savings that can be obtained. As our experiments show, the improvement becomes more significant as the problems grow larger in terms of the number of objectives.

We transform join ordering into a mixed integer linear program (MILP). This allows to address query optimization by mature MILP solver implementations that have evolved over decades and steadily improved their performance. They offer features such as anytime optimization and parallel search that are highly relevant for query optimization. We present a MILP formulation for searching left-deep query plans. We use sets of binary variables to represent join operands and intermediate results, operator implementation choices or the presence of interesting orders. Linear constraints restrict value assignments to the ones representing valid query plans. We approximate the cost of scan and join operations via linear functions, allowing to increase approximation precision up to arbitrary degrees. Our experimental results are encouraging: we are able to find optimal plans for joins between 60 tables; a query size that is beyond the capabilities of prior exhaustive query optimization methods.

In this paper, an integer programming approach is introduced to construct Unequal Error Protection (UEP) codes for multiuser broadcast channels. We show that the optimal codes can be constructed that satisfy the integer programming bound. Based on the bound, we compute asymptotic code rate and perform throughput analysis for the degraded broadcast channel.

Answering science questions posed in natural language is an important AI challenge. Answering such questions often requires non-trivial inference and knowledge that goes beyond factoid retrieval. Yet, most systems for this task are based on relatively shallow Information Retrieval (IR) and statistical correlation techniques operating on large unstructured corpora. We propose a structured inference system for this task, formulated as an Integer Linear Program (ILP), that answers natural language questions using a semi-structured knowledge base derived from text, including questions requiring multi-step inference and a combination of multiple facts. On a dataset of real, unseen science questions, our system significantly outperforms (+14%) the best previous attempt at structured reasoning for this task, which used Markov Logic Networks (MLNs). It also improves upon a previous ILP formulation by 17.7%. When combined with unstructured inference methods, the ILP system significantly boosts overall performance (+10%). Finally, we show our approach is substantially more robust to a simple answer perturbation compared to statistical correlation methods.

Answering science questions posed in natural language is an important AI challenge. Answering such questions often requires non-trivial inference and knowledge that goes beyond factoid retrieval. Yet, most systems for this task are based on relatively shallow Information Retrieval (IR) and statistical correlation techniques operating on large unstructured corpora. We propose a structured inference system for this task, formulated as an Integer Linear Program (ILP), that answers natural language questions using a semi-structured knowledge base derived from text, including questions requiring multi-step inference and a combination of multiple facts. On a dataset of real, unseen science questions, our system significantly outperforms (+14%) the best previous attempt at structured reasoning for this task, which used Markov Logic Networks (MLNs). It also improves upon a previous ILP formulation by 17.7%. When combined with unstructured inference methods, the ILP system significantly boosts overall performance (+10%). Finally, we show our approach is substantially more robust to a simple answer perturbation compared to statistical correlation methods.

Considering the intermittency of renewable energy systems, a sizing and scheduling model is proposed for a finite number of static electric loads. The model objective is to maximize solar energy utilization with and without storage. For the application of optimal load size selection, the energy production of a solar photovoltaic is assumed to be consumed by a finite number of discrete loads in an off-grid system using mixed-integer linear programming. Additional constraints are battery charge and discharge limitations and minimum uptime and downtime for each unit. For a certain solar power profile the model outputs optimal unit size as well as the optimal scheduling for both units and battery charge and discharge (if applicable). The impact of different solar power profiles and minimum up and down time constraints on the optimal unit and battery sizes are studied. The battery size required to achieve full solar energy utilization decreases with the number of units and with increased flexibility of the units (shorter on and off-time). A novel formulation is introduced to model quasi-dynamic units that gradually start and stop and the quasi-dynamic units increase solar energy utilization. The model can also be applied to search for the optimal number of units for a given cost function.

Considering the intermittency of renewable energy systems, a sizing and scheduling model is proposed for a finite number of static electric loads. The model objective is to maximize solar energy utilization with and without storage. For the application of optimal load size selection, the energy production of a solar photovoltaic is assumed to be consumed by a finite number of discrete loads in an off-grid system using mixed-integer linear programming. Additional constraints are battery charge and discharge limitations and minimum uptime and downtime for each unit. For a certain solar power profile the model outputs optimal unit size as well as the optimal scheduling for both units and battery charge and discharge (if applicable). The impact of different solar power profiles and minimum up and down time constraints on the optimal unit and battery sizes are studied. The battery size required to achieve full solar energy utilization decreases with the number of units and with increased flexibility of the units (shorter on and off-time). A novel formulation is introduced to model quasi-dynamic units that gradually start and stop and the quasi-dynamic units increase solar energy utilization. The model can also be applied to search for the optimal number of units for a given cost function.

Considering the intermittency of renewable energy systems, a sizing and scheduling model is proposed for a finite number of static electric loads. The model objective is to maximize solar energy utilization with and without storage. For the application of optimal load size selection, the energy production of a solar photovoltaic is assumed to be consumed by a finite number of discrete loads in an off-grid system using mixed-integer linear programming. Additional constraints are battery charge and discharge limitations and minimum uptime and downtime for each unit. For a certain solar power profile the model outputs optimal unit size as well as the optimal scheduling for both units and battery charge and discharge (if applicable). The impact of different solar power profiles and minimum up and down time constraints on the optimal unit and battery sizes are studied. The battery size required to achieve full solar energy utilization decreases with the number of units and with increased flexibility of the units (shorter on and off-time). A novel formulation is introduced to model quasi-dynamic units that gradually start and stop and the quasi-dynamic units increase solar energy utilization. The model can also be applied to search for the optimal number of units for a given cost function.

Considering the intermittency of renewable energy systems, a sizing and scheduling model is proposed for a finite number of static electric loads. The model objective is to maximize solar energy utilization with and without storage. For the application of optimal load size selection, the energy production of a solar photovoltaic is assumed to be consumed by a finite number of discrete loads in an off-grid system using mixed-integer linear programming. Additional constraints are battery charge and discharge limitations and minimum uptime and downtime for each unit. For a certain solar power profile the model outputs optimal unit size as well as the optimal scheduling for both units and battery charge and discharge (if applicable). The impact of different solar power profiles and minimum up and down time constraints on the optimal unit and battery sizes are studied. The battery size required to achieve full solar energy utilization decreases with the number of units and with increased flexibility of the units (shorter on and off-time). A novel formulation is introduced to model quasi-dynamic units that gradually start and stop and the quasi-dynamic units increase solar energy utilization. The model can also be applied to search for the optimal number of units for a given cost function.

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.

Thesis advisor(s): Dell, Robert F

Thesis advisor(s): Dell, Robert F

Thesis advisor(s): Dell, Robert F

Bibliography: p. 41-42

This paper presents Multi-Objective Integer Non-Linear Programming (MOINLP) involving Negative Total Float (NTF) for improving the basic model of Multi-Objective Programming (MOP) in case the optimization of the additional cost for Project Scheduling Compression (PSC). Using the basic MOP to solve the more complex problems is a challenging task. We suspect that Negative Total Float (NTF) having an indication to make the basic MOP to solve the more general case, both simple and complex of PSC. The purpose of this research is identifying the conflicting objectives in PSC problem using NTF and improving MOINLP by involving the NTF parameter to solve the PSC problem. The Solver Application, which is an add-in of MS Excel, is used to perform optimization process to the model developed. The results show that NTF has an important role to identify the conflicting objectives in PSC. We define NTF is an automatic maximum value of the activity duration reduction to achieve due date of PSC. Furthermore, the use of NTF as a constraint in MOINLP can solve the more general case for both simple and complex PSC problem. Base on the condition, we state that the basic MOP is still significant to solve the PSC complex problems using MOINLP as a sophisticated MOP technique. 

"NPS-55-82-009"--Cover

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.