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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

Since 1988, the United States Army has closed 112 and has completed or will soon complete realignment of another 27 of its domestic installations. The Army estimates the total cost (between 1988 and 2001) of these closures and realignments to be $5.3 billion, of which about $2.3 billion (43%) is associated with environmental cleanup. Beyond 2001, the Army expects to spend an additional $ 1.09 billion to complete cleanup and continue restoration. The Army Base Realignment and Closure Office (BRACO) is currently funding environmental cleanup at 649 sites on 39 current and former Army installations. BRACO' 5 environmental restoration budget from 2001 to 2007 to support cleanup at these installations (totaling over $620 million) is not sufficient to support each installation's requirement for those years. Considering environmental policies and yearly funding requests from 2001 to 2015 for each site, this thesis develops optimization models and a spreadsheet interface to help BRACO allocate its budget. Model results prescribe either funding each site as requested or delaying cleanup by one to five years. Extensive model use helped BRACO analyze alternate yearly budgets, suggest alternate site funding and determine site funding for 2001 to 2007

Bibliography: p. 91

A computer code, FEASBL, is developed to maximize a non-linear objective function over a convex feasible region. The feasible region is defined by a set of non-linear and linear constraints on the variables. FEASBL can solve problems involving up to fifty variables with a feasible region formed by up to fifty non-linear constraints, and fifty linear constraints. FEASBL uses a feasible direction method as its solution algorithm.

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.

We develop a framework for linear-programming (LP) decoding of non-binary linear codes over rings. We prove that the resulting LP decoder has the `maximum likelihood certificate' property, and we show that the decoder output is the lowest cost pseudocodeword. Equivalence between pseudocodewords of the linear program and pseudocodewords of graph covers is proved. LP decoding performance is illustrated for the (11,6,5) ternary Golay code with ternary PSK modulation over AWGN, and in this case it is shown that the LP decoder performance is comparable to codeword-error-rate-optimum hard-decision based decoding.

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In recent work, semantic games of independence-friendly logic were studied in strategic form in terms of (mixed strategy) Nash equilibria. The class of strategic games of independence-friendly logic is contained in the class of win-loss, zero-sum two-player games. In this note we draw on the theory of linear programming to develop tools to analyze the value of such games. We give two applications of these tools to independence-friendly logic under the so-called equilibrium semantics.

We prove an elementary yet useful inequality bounding the maximal value of certain linear programs. This leads directly to a bound on the martingale difference for arbitrarily dependent random variables, providing a generalization of some recent concentration of measure results. The linear programming inequality may be of independent interest.

We prove an elementary yet useful inequality bounding the maximal value of certain linear programs. This leads directly to a bound on the martingale difference for arbitrarily dependent random variables, providing a generalization of some recent concentration of measure results. The linear programming inequality may be of independent interest.

We prove an elementary yet useful inequality bounding the maximal value of certain linear programs. This leads directly to a bound on the martingale difference for arbitrarily dependent random variables, providing a generalization of some recent concentration of measure results. The linear programming inequality may be of independent interest.

F2 Decison Making 2- Limiting Factor And Linear Programming

Use of Chance-Constrained Programming to Account for Stochastic Variation in the A-Matrix of Large-Scale Linear Programs: A Forestry Application

Use of Chance-Constrained Programming to Account for Stochastic Variation in the A-Matrix of Large-Scale Linear Programs: A Forestry Application

Use of Chance-Constrained Programming to Account for Stochastic Variation in the A-Matrix of Large-Scale Linear Programs: A Forestry Application

Zlatar Ski Center has an extremely high potential as a ski resort that could be among the most visited ones in Serbia. What characterizes this center is the proximity of Kokin Brod Lake, the Tara River and the like. Therefore, Zlatar should be considered both as a ski center and in terms of other diversities. The aim of this paper is to analyze the possibility of expanding the capacity of ski resorts by increasing the possible flow of skiers on new ski lifts and ski slopes. The methods used in this paper belong to operational research, specifically, the geometric interpretation of linear programming. It is also shown how to optimize the extended capacities. If the capacities of ski slopes are to be increased, it would initiate greater investment in accommodation capacities in the area of the municipality of Nova Varoš, which would affect its improvement in terms of tourism.

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 authors discuss interior-point methods for linear programming derived by applying a logarithmic barrier transformation and performing projected Newton steps for a sequence of barrier parameters. Under certain conditions, one of these projected Newton barrier methods is shown to be equivalent to Karmarkar's (1984) projective method for linear programming. Details are given of a specific barrier algorithm and its practical implementation. Numerical results are given for several nontrivial test problems. Additional keywords: tables(data); numerical analysis; iterations; computations; least squares method. (Author)

This report forms the user's guide for Version 1.0 of LSSOL, a set of Fortran 77 subroutines for linearly constrained linear least-squares and convex quadratic programming. The method of LSSOL is of the two-phase, active-set type, and is related to the method used in the package SOL/QPSOL. Two main features of LSSOL are its exploitation of convexity and treatment of singularity. LSSOL may also be used for linear programming, and to find a feasible point with respect to a set of linear inequality constraints. LSSOL treats all matrices as dense, and hence is not intended for large sparse problems. Keywords: Algorithms; Parameters; Optimization; Linear programming; Mathematical software. (Author)

The L sub infinity norm has been widely studied as a criterion for curve fitting problems. This paper presents an algorithm to solve discrete approximation problems in the L sub infinity norm. The algorithm is a special- purpose linear programming dual method which employs a reduced basis and multiple pivots. Results of the computational experience with a computer code version of the algorithm are presented.

A special quadratic assignment problem is shown to be equivalent to a linear programming problem with n cubed constraints and n squared variables where n is the number of elements to be assigned. A labeling algorithm similar to that for the linear transportation problem is presented for solving the problem. An example is presented that deals with ' triangularizing' input-output matrices.

Presented is an optimization technique, using linear programming methods, which can effectively be used to design structural frames. Stress constraints as well as conditions of equilibrium and compatibility are considered. The approach is demonstrated to be more efficient than presently available nonlinear techniques on large problems. Although the method is iterative, a modification of the standard simplex method is used which considerably decreases computational time. A discussion is presented outlining how the technique can be extended to handle additional requirements such multiple loading conditions, non-nodal loads and displacement constraints. (Author)

Presented is an optimization technique, using linear programming methods, which can effectively be used to design structural frames. Stress constraints as well as conditions of equilibrium and compatibility are considered. The approach is demonstrated to be more efficient than presently available nonlinear techniques on large problems. Although the method is iterative, a modification of the standard simplex method is used which considerably decreases computational time. A discussion is presented outlining how the technique can be extended to handle additional requirements such multiple loading conditions, non-nodal loads and displacement constraints. (Author)

Presented is an optimization technique, using linear programming methods, which can effectively be used to design structural frames. Stress constraints as well as conditions of equilibrium and compatibility are considered. The approach is demonstrated to be more efficient than presently available nonlinear techniques on large problems. Although the method is iterative, a modification of the standard simplex method is used which considerably decreases computational time. A discussion is presented outlining how the technique can be extended to handle additional requirements such multiple loading conditions, non-nodal loads and displacement constraints. (Author)

This paper presents an algorithm for solving interval linear programming problems. The algorithm is a finite iterative method, which in each iteration solves a full row rank interval linear programming problem, with only one additional constraint. The solution and/or problem chosen appears to be computationally more efficient than that in the Ben-Israel and Robers algorithm.

This paper deals with a dynamic linear programming model on a pilot scale that attempts to describe in physical terms many of the technological interactions within and across the sections of the American Economy, including a detailed energy sector. The general aim of the model is to provide information on what the country would achieve over the long run in physical terms in the face of a changing energy picture. The model is expected to (1) incorporate most recent available data of sufficiently good quality (albeit in an aggregated form) that it can be used to generate some meaningful scenarios showing how the economy might be affected if the energy picture evolves in a specific way, and (2) provide us at the Systems Optimization Laboratory a prototype for research in solving large-scale linear programming models of energy systems.

As part of the management planning and control function, the U.S. Coast Guard's Pacific Area Commander schedules the operational missions for all High Endurance Cutters in the Pacific Area. To provide a powerful management tool to assist this scheduling process, an analytic model for this large scale problem has been developed and implemented. It contains mission requirements, restricted sequencing of missions, ships' physical limitations and crews' morale-related considerations. The modeling approach is based on the Geoffrion-Graves model for parallel production lines with significant changeover costs. The implementation solves a large (860 row) Koopmans-Beckmann fixed charge Quadratic Assignment model using a new method with an advanced, feasible starting solution provided by an imbedded network (with 1,720 nodes and 739,600 arcs). Many linear programming problems (200 row, 450 variable) are then solved with a linear programming subroutine of advanced design. The resulting model and these implementation techniques produce excellent quality working schedules with very reasonable execution time and memory requirements. Alternative solutions are easily generated.

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.

Given a collection of discrete random variables representing outcomes of learned local predictors in natural language. e.g.. named entities and relations. we seek an optimal global assignment to the variables in the presence of general (non-sequential) constraints. Examples of these constraints include the type of arguments a relation can take, and the mutual activity of different relations. etc. We develop a linear programing formulation for this problem and evaluate it in the context of simultaneously learning named entities and relations. Our approach allows us to efficiently incorporate domain and task specific constraints at decision time, resulting in significant improvements in the accuracy and the human-like quality of the inferences.

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.

A modified simplex method has been developed for attacking large linear programs with inexact data in the right hand sides. Results from performing a limited series of computational experiments are reported. These results indicate reductions in computer time of 30 to 70 per cent over the ordinary simplex method.

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.

Several algorithms in linear and nonlinear programming have been developed and analyzed. A worst-case analysis of the steepest edge simplex method showed it to have exponential time-complexity. This algorithm was specialized for solving minimum cost network flow problems and a partial pricing variant was developed. After extensive testing on randomly generated large problems the method was found to be inferior to efficiently coded partial pricing variants of the 'standard' simplex method except for the max flow problem and the problem of finding a feasible flow. On the max flow problem the algorithm was compared with the Edmonds-Karp and Dinic algorithms and found to be superior. In quadratic programming, the use of the steepest edge (face) criterion for dropping constraints was found to be helpful. Dual methods were found to be even more efficient and their use in recursive quadratic programming algorithms for nonlinear programming problems is recommended. A numerically stable ellipsoid algorithm for linear programming was developed and analyzed. At present the main promise that this method holds is as a powerful theoretical tool. Several minimization algorithms for taking advantage of negative curvature were developed as was a curvilinear steplength algorithm which ensures convergence to a positive semidefinite point. (Author)

This Workshop on Large-scale Mathematical Programs reflects the active research taking place in many parts of the world along a very broad front--namely: on the theory of solution; on software development; on experiments on representative problems; on application to real problems; on matrix input generators; on matrix analyzers; on output report generators; and on alternative methods of formulation. This paper is a historical review of the author's interest in one important facet of this field - namely the solution of time-staged programs. Indeed it was dynamic L.P. that initiated the linear programming field back in 1947. Over the years, many good ideas have been proposed, some that still merit serious consideration. This Workshop may provide the answer to the question whether or not we have begun at last to achieve the efficiency of solution necessary for successful application. (Author)

The purpose of this study is to formulate and code a mathematical model of the coal blending and preparation process at the Martiki Coal mine in Lovely, Kentucky, which will reduce wash loss by improving the daily tonnage and specific gravity decision. A model of the Martiki Coal Corporation blending and preparation process is developed with minimization of wash loss as the objective. Solution is by iterative linear programming using the Tucker Tableau algorithm on an Apple II microcomputer. Output serves as an aid to preparation plant personnel in making the daily specific gravity and tonnage decision. Each percentage reduction in Martiki's 1984 wash loss would have decreased disposal costs and increased revenues by approximately $550,700.

This thesis effort produced a linear programming package, called LPAFIT. Two Fortran programs were written. The first, LPSOLVE, solves linear programming problems using the simplex method. It allows a user to do interactive sensitivity analyses. The second program, LPFRONT, is a preprocessor for LPSOLVE. LPFRONT assists the user in creating the input for LPSOLVE. A procedure controls all file manipulations. The only thing the user must be able to do is to express a problem in terms of a constrained objective function. Both programs are currently formatted to process up to 99 decision variables and 99 constraints. The routines will not solve integer or mixed integer problems. The package runs on a CDC 6600. (Author)

In this note we consider a large step modification of the Mizuno-Todd-Ye O(square root of nL) predictor-corrector interior-point algorithm for linear programming. We demonstrate that the modified algorithm maintains its O(square root of nL)-iteration complexity, while exhibiting superlinear convergence for general problems and quadratic convergence for nondegenerate problems. To our knowledge, this is the first construction of a superlinearly convergent algorithm with O(square root of nL)-iteration complexity.

STEP FSC 2ND YEAR PART II XII MATHEMATICS LECTURES, DO NOT SELL!!, FREE FOR STUDIOUS STUDENTS. ALL COPYRIGHTS BELONGS TO STEP BY PGC

A backpacker approaches a road with a marker on it desirous of finding the marker but having only a rough idea of where it is located. It is well known among backpackers that it is best to aim either right or left of the marker since otherwise it will not be clear which way to turn upon reaching the road. The problem of deciding exactly where to aim can be formalized as a modification of the Linear Search Problem. This paper does so, and also discusses dynamic programming as a solution method.

Learning and retention may be influenced by subtle instructional stimulus characteristics and certain visual memory aptitudes. Ten stimulus characteristics were chosen for study; 50 sequences of programed instructional material were specially written to conform to sampled values of each stimulus characteristic. Seventy-three freshman subjects received the 50 sequences and then took an immediate and a delayed (one-week) posttest to assess learning. Measures on four visual memory and cognition aptitude factors were available for 43 of the subjects. By means of tear-down regression algorithms, the 10 stimulus characteristics were used to predict to the learning criteria. The ratio of examples within a sequence to the number of frames in the sequence had a correlation of about -.70 with both the immediate and delayed posttest. The inclusion of other variables did not increase the prediction significantly. Together, total frames and number of responses per frame predicted item difficulty on the posttest (multiple R to the second power=.90). Of the aptitude variables, Vocabulary aptitude and Short Term Object Memory tended to increase prediction to the delayed posttest criterion, while Serial Integration aptitude and short Term Color Memory did not. (LS)

Learning and retention may be influenced by subtle instructional stimulus characteristics and certain visual memory aptitudes. Ten stimulus characteristics were chosen for study; 50 sequences of programed instructional material were specially written to conform to sampled values of each stimulus characteristic. Seventy-three freshman subjects received the 50 sequences and then took an immediate and a delayed (one-week) posttest to assess learning. Measures on four visual memory and cognition aptitude factors were available for 43 of the subjects. By means of tear-down regression algorithms, the 10 stimulus characteristics were used to predict to the learning criteria. The ratio of examples within a sequence to the number of frames in the sequence had a correlation of about -.70 with both the immediate and delayed posttest. The inclusion of other variables did not increase the prediction significantly. Together, total frames and number of responses per frame predicted item difficulty on the posttest (multiple R to the second power=.90). Of the aptitude variables, Vocabulary aptitude and Short Term Object Memory tended to increase prediction to the delayed posttest criterion, while Serial Integration aptitude and short Term Color Memory did not. (LS)

Learning and retention may be influenced by subtle instructional stimulus characteristics and certain visual memory aptitudes. Ten stimulus characteristics were chosen for study; 50 sequences of programed instructional material were specially written to conform to sampled values of each stimulus characteristic. Seventy-three freshman subjects received the 50 sequences and then took an immediate and a delayed (one-week) posttest to assess learning. Measures on four visual memory and cognition aptitude factors were available for 43 of the subjects. By means of tear-down regression algorithms, the 10 stimulus characteristics were used to predict to the learning criteria. The ratio of examples within a sequence to the number of frames in the sequence had a correlation of about -.70 with both the immediate and delayed posttest. The inclusion of other variables did not increase the prediction significantly. Together, total frames and number of responses per frame predicted item difficulty on the posttest (multiple R to the second power=.90). Of the aptitude variables, Vocabulary aptitude and Short Term Object Memory tended to increase prediction to the delayed posttest criterion, while Serial Integration aptitude and short Term Color Memory did not. (LS)

The idea of a fundamental solution to a problem in linear programming is introduced. A method of determining the fundamental solution and of applying this method to the solution of a problem in linear programming is proposed. Numerical examples are cited.

The idea of a fundamental solution to a problem in linear programming is introduced. A method of determining the fundamental solution and of applying this method to the solution of a problem in linear programming is proposed. Numerical examples are cited.

This project has two objectives. The first is to determine whether linear programming techniques can improve performance when handling design optimization problems with a large number of design variables and constraints relative to the feasible directions algorithm. The second purpose is to determine whether using the Kreisselmeier-Steinhauser (KS) function to replace the constraints with one constraint will reduce the cost of total optimization. Comparisons are made using solutions obtained with linear and non-linear methods. The results indicate that there is no cost saving using the linear method or in using the KS function to replace constraints.

This project has two objectives. The first is to determine whether linear programming techniques can improve performance when handling design optimization problems with a large number of design variables and constraints relative to the feasible directions algorithm. The second purpose is to determine whether using the Kreisselmeier-Steinhauser (KS) function to replace the constraints with one constraint will reduce the cost of total optimization. Comparisons are made using solutions obtained with linear and non-linear methods. The results indicate that there is no cost saving using the linear method or in using the KS function to replace constraints.

This project has two objectives. The first is to determine whether linear programming techniques can improve performance when handling design optimization problems with a large number of design variables and constraints relative to the feasible directions algorithm. The second purpose is to determine whether using the Kreisselmeier-Steinhauser (KS) function to replace the constraints with one constraint will reduce the cost of total optimization. Comparisons are made using solutions obtained with linear and non-linear methods. The results indicate that there is no cost saving using the linear method or in using the KS function to replace constraints.

This project has two objectives. The first is to determine whether linear programming techniques can improve performance when handling design optimization problems with a large number of design variables and constraints relative to the feasible directions algorithm. The second purpose is to determine whether using the Kreisselmeier-Steinhauser (KS) function to replace the constraints with one constraint will reduce the cost of total optimization. Comparisons are made using solutions obtained with linear and non-linear methods. The results indicate that there is no cost saving using the linear method or in using the KS function to replace constraints.

Thesis--Purdue University, 1956

Thesis--Purdue University, 1956