Showing papers on "Integer programming published in 1991"

Operations Research: Applications and Algorithms

Abstract: 1. INTRODUCTION TO MODEL BUILDING. An Introduction to Modeling. The Seven-Step Model-Building Process. Examples. 2. BASIC LINEAR ALGEBRA. Matrices and Vectors. Matrices and Systems of Linear Equations. The Gauss-Jordan Method for Solving Systems of Linear Equations. Linear Independence and Linear Dependence. The Inverse of a Matrix. Determinants. 3. INTRODUCTION TO LINEAR PROGRAMMING. What is a Linear Programming Problem? The Graphical Solution of Two-Variable Linear Programming Problems. Special Cases. A Diet Problem. A Work-Scheduling Problem. A Capital Budgeting Problem. Short-term Financial Planning. Blending Problems. Production Process Models. Using Linear Programming to Solve Multiperiod Decision Problems: An Inventory Model. Multiperiod Financial Models. Multiperiod Work Scheduling. 4. THE SIMPLEX ALGORITHM AND GOAL PROGRAMMING. How to Convert an LP to Standard Form. Preview of the Simplex Algorithm. The Simplex Algorithm. Using the Simplex Algorithm to Solve Minimization Problems. Alternative Optimal Solutions. Unbounded LPs. The LINDO Computer Package. Matrix Generators, LINGO, and Scaling of LPs. Degeneracy and the Convergence of the Simplex Algorithm. The Big M Method. The Two-Phase Simplex Method. Unrestricted-in-Sign Variables. Karmarkar"s Method for Solving LPs. Multiattribute Decision-Making in the Absence of Uncertainty: Goal Programming. Solving LPs with Spreadsheets. 5. SENSITIVITY ANALYSIS: AN APPLIED APPROACH. A Graphical Introduction to Sensitivity Analysis. The Computer and Sensitivity Analysis. Managerial Use of Shadow Prices. What Happens to the Optimal z-value if the Current Basis is No Longer Optimal? 6. SENSITIVITY ANALYSIS AND DUALITY. A Graphical Introduction to Sensitivity Analysis. Some Important Formulas. Sensitivity Analysis. Sensitivity Analysis When More Than One Parameter is Changed: The 100% Rule. Finding the Dual of an LP. Economic Interpretation of the Dual Problem. The Dual Theorem and Its Consequences. Shadow Prices. Duality and Sensitivity Analysis. 7. TRANSPORTATION, ASSIGNMENT, AND TRANSSHIPMENT PROBLEMS. Formulating Transportation Problems. Finding Basic Feasible Solutions for Transportation Problems. The Transportation Simplex Method. Sensitivity Analysis for Transportation Problems. Assignment Problems. Transshipment Problems. 8. NETWORK MODELS. Basic Definitions. Shortest Path Problems. Maximum Flow Problems. CPM and PERT. Minimum Cost Network Flow Problems. Minimum Spanning Tree Problems. The Network Simplex Method. 9. INTEGER PROGRAMMING. Introduction to Integer Programming. Formulation Integer Programming Problems. The Branch-and-Bound Method for Solving Pure Integer Programming Problems. The Branch-and-Bound Method for Solving Mixed Integer Programming Problems. Solving Knapsack Problems by the Branch-and-Bound Method. Solving Combinatorial Optimization Problems by the Branch-and-Bound Method. Implicit Enumeration. The Cutting Plane Algorithm. 10. ADVANCED TOPICS IN LINEAR PROGRAMMING. The Revised Simplex Algorithm. The Product Form of the Inverse. Using Column Generation to Solve Large-Scale LPs. The Dantzig-Wolfe Decomposition Algorithm. The Simplex Methods for Upper-Bounded Variables. Karmarkar"s Method for Solving LPs. 11. NONLINEAR PROGRAMMING. Review of Differential Calculus. Introductory Concepts. Convex and Concave Functions. Solving NLPs with One Variable. Golden Section Search. Unconstrained Maximization and Minimization with Several Variables. The Method of Steepest Ascent. Lagrange Multiples. The Kuhn-Tucker Conditions. Quadratic Programming. Separable Programming. The Method of Feasible Directions. Pareto Optimality and Tradeoff Curves. 12. REVIEW OF CALCULUS AND PROBABILITY. Review of Integral Calculus. Differentiation of Integrals. Basic Rules of Probability. Bayes" Rule. Random Variables. Mean Variance and Covariance. The Normal Distribution. Z-Transforms. Review Problems. 13. DECISION MAKING UNDER UNCERTAINTY. Decision Criteria. Utility Theory. Flaws in Expected Utility Maximization: Prospect Theory and Framing Effects. Decision Trees. Bayes" Rule and Decision Trees. Decision Making with Multiple Objectives. The Analytic Hierarchy Process. Review Problems. 14. GAME THEORY. Two-Person Zero-Sum and Constant-Sum Games: Saddle Points. Two-Person Zero-Sum Games: Randomized Strategies, Domination, and Graphical Solution. Linear Programming and Zero-Sum Games. Two-Person Nonconstant-Sum Games. Introduction to n-Person Game Theory. The Core of an n-Person Game. The Shapley Value. 15. DETERMINISTIC EOQ INVENTORY MODELS. Introduction to Basic Inventory Models. The Basic Economic Order Quantity Model. Computing the Optimal Order Quantity When Quantity Discounts Are Allowed. The Continuous Rate EOQ Model. The EOQ Model with Back Orders Allowed. Multiple Product Economic Order Quantity Models. Review Problems. 16. PROBABILISTIC INVENTORY MODELS. Single Period Decision Models. The Concept of Marginal Analysis. The News Vendor Problem: Discrete Demand. The News Vendor Problem: Continuous Demand. Other One-Period Models. The EOQ with Uncertain Demand: the (r, q) and (s,S models). The EOQ with Uncertain Demand: the Service Level Approach to Determining Safety Stock Level. Periodic Review Policy. The ABC Inventory Classification System. Exchange Curves. Review Problems. 17. MARKOV CHAINS. What is a Stochastic Process. What is a Markov Chain? N-Step Transition Probabilities. Classification of States in a Markov Chain. Steady-State Probabilities and Mean First Passage Times. Absorbing Chains. Work-Force Planning Models. 18.DETERMINISTIC DYNAMIC PROGRAMMING. Two Puzzles. A Network Problem. An Inventory Problem. Resource Allocation Problems. Equipment Replacement Problems. Formulating Dynamic Programming Recursions. The Wagner-Whitin Algorithm and the Silver-Meal Heuristic. Forward Recursions. Using Spreadsheets to Solve Dynamic Programming Problems. Review Problems. 19. PROBABILISTIC DYNAMIC PROGRAMMING. When Current Stage Costs are Uncertain but the Next Period"s State is Certain. A Probabilistic Inventory Model. How to Maximize the Probability of a Favorable Event Occurring. Further Examples of Probabilistic Dynamic Programming Formulations. Markov Decision Processes. Review Problems. 20. QUEUING THEORY. Some Queuing Terminology. Modeling Arrival and Service Processes. Birth-Death Processes. M/M/1/GD/o/o Queuing System and the Queuing Formula L=o W, The M/M/1/GD/o Queuing System. The M/M/S/ GD/o/o Queuing System. The M/G/ o/GD/oo and GI/G/o/GD/o/oModels. The M/ G/1/GD/o/o Queuing System. Finite Source Models: The Machine Repair Model. Exponential Queues in Series and Opening Queuing Networks. How to Tell whether Inter-arrival Times and Service Times Are Exponential. The M/G/S/GD/S/o System (Blocked Customers Cleared). Closed Queuing Networks. An Approximation for the G/G/M Queuing System. Priority Queuing Models. Transient Behavior of Queuing Systems. Review Problems. 21.SIMULATION. Basic Terminology. An Example of a Discrete Event Simulation. Random Numbers and Monte Carlo Simulation. An Example of Monte Carlo Simulation. Simulations with Continuous Random Variables. An Example of a Stochastic Simulation. Statistical Analysis in Simulations. Simulation Languages. The Simulation Process. 22.SIMULATION WITH PROCESS MODEL. Simulating an M/M/1 Queuing System. Simulating an M/M/2 System. A Series System. Simulating Open Queuing Networks. Simulating Erlang Service Times. What Else Can Process Models Do? 23. SPREADSHEET SIMULATION WITH @RISK. Introduction to @RISK: The Newsperson Problem. Modeling Cash Flows From A New Product. Bidding Models. Reliability and Warranty Modeling. Risk General Function. Risk Cumulative Function. Risktrigen Function. Creating a Distribution Based on a Point Forecast. Forecasting Income of a Major Corporation. Using Data to Obtain Inputs For New Product Simulations. Playing Craps with @RISK. Project Management. Simulating the NBA Finals. 24. FORECASTING. Moving Average Forecasting Methods. Simple Exponential Smoothing. Holt"s Method: Exponential Smoothing with Trend. Winter"s Method: Exponential Smoothing with Seasonality. Ad Hoc Forecasting, Simple Linear Regression. Fitting Non-Linear Relationships. Multiple Regression. Answers to Selected Problems. Index.

The Omega test: a fast and practical integer programming algorithm for dependence analysis

Abstract: The Omega test is an integer programming algorithm that can determine whether a dependence exists between two array references, and if so, under what conditions. Conventional wisdom holds that integer programming techniques are far too expensive to be used for dependence analysis, except as a method of last resort for situations that cannot be decided by simpler methods. We present evidence that suggests this wisdom is wrong, and that the Omega test is competitive with approximate algorithms used in practice and suitable for use in production compilers. The Omega test is based on an extension of FourierMotzkin variable elimination to integer programming, and has worst-case exponential time complexity. However, we show that for many situations in which other (polynomial) methods are accurate, the Omega test has low order polynomial time complexity. The Omega test can be used to simplify integer programming problems, rather than just deciding them. This has many applications, including accurately and efficiently computing dependence direction and distance vectors.

A formal approach to the scheduling problem in high level synthesis

Abstract: An integer linear programming (ILP) model for the scheduling problem in high-level synthesis is presented. In addition to time-constrained scheduling and resource-constrained scheduling, a scheduling problem called feasible scheduling, which provides a paradigm for exploring the solution space, is constructed. Extensive consideration is given to the following applications: scheduling with chaining, multicycle operations by nonpipelined function units, and multicycle operations by pipelined function units; functional pipelining; loop folding; mutually exclusive operations; scheduling under bus constraint; and minimizing lifetimes of variables. The complexity of the number of variables in the formulation is O(s*n) where s and n are the number of control steps and operations, respectively. Since the as soon as possible (ASAP), as late as possible (ALAP), and list scheduling techniques are used to reduce the solution space, the formulation becomes very efficient. A solution to a practical problem, such as the fifth-order filter, can be found optimally in a few seconds. >

Introduction to mathematical programming

Abstract: 1. INTRODUCTION TO MODEL BUILDING. An Introduction to Modeling. The Seven-Step Model-Building Process. Examples. 2. BASIC LINEAR ALGEBRA. Matrices and Vectors. Matrices and Systems of Linear Equations. The Gauss-Jordan Method for Solving Systems of Linear Equations. Linear Independence and Linear Dependence. The Inverse of a Matrix. Determinants. 3. INTRODUCTION TO LINEAR PROGRAMING. What is a Linear Programming Problem? The Graphical Solution of Two-Variable Linear Programming Problems. Special Cases. A Diet Problem. A Work-Scheduling Problem. A Capital Budgeting Problem. Short-term Financial Planning. Blending Problems. Production Process Models. Using Linear Programming to Solve Multiperiod Decision Problems: An Inventory Model. Multiperiod Financial Models. Multiperiod Work Scheduling. 4. THE SIMPLEX ALGORITM AND GOAL PROGRAMING. How to Convert an LP to Standard Form. Preview of the Simplex Algorithm. The Simplex Algorithm. Using the Simplex Algorithm to Solve Minimization Problems. Alternative Optimal Solutions. Unbounded LPs. The LINDO Computer Package. Matrix Generators, LINGO, and Scaling of LPs. Degeneracy and the Convergence of the Simplex Algorithm. The Big M Method. The Two-Phase Simplex Method. Unrestricted-in-Sign Variables. Karmarkar?s Method for Solving LPs. Multiattribute Decision-Making in the Absence of Uncertainty: Goal Programming. Solving LPs with Spreadsheets. 5. SENSITIVITY ANALYSIS: AN APPLIED APPROACH. A Graphical Introduction to Sensitivity Analysis. The Computer and Sensitivity Analysis. Managerial Use of Shadow Prices. What Happens to the Optimal z-value if the Current Basis is no Longer Optimal? 6. SENSITIVITY ANALYSIS AND DUALITY. A Graphical Introduction to Sensitivity Analysis. Some Important Formulas. Sensitivity Analysis. Sensitivity Analysis When More Than One Parameter is Changed: The 100% Rule. Finding the Dual of an LP. Economic Interpretation of the Dual Problem. The Dual Theorem and Its Consequences. Shadow Prices. Duality and Sensitivity Analysis. 7. TRANSPORTATION, ASSIGNMENT, AND TRANSSHIPMENT PROBLEMS. Formulating Transportation Problems. Finding Basic Feasible Solutions for Transportation Problems. The Transportation Simplex Method. Sensitivity Analysis for Transportation Problems. Assignment Problems. Transshipment Problems. 8. NETWORK MODELS. Basic Definitions. Shortest Path Problems. Maximum Flow Problems. CPM and PERT. Minimum Cost Network Flow Problems. Minimum Spanning Tree Problems. The Network Simplex Method. 9. INTEGER PROGRAMMING. Introduction to Integer Programming. Formulation Integer Programming Problems. The Branch-and-Bound Method for Solving Pure Integer Programming Problems. The Branch-and-Bound Method for Solving Mixed Integer Programming Problems. Solving Knapsack Problems by the Branch-and-Bound Method. Solving Combinatorial Optimization Problems by the Branch-and-Bound Method. Implicit Enumeration. The Cutting Plane Algorithm. 10. ADVANCED TOPICS IN LINEAR PROGRAMMING. The Revised Simplex Algorithm. The Product Form of the Inverse. Using Column Generation to Solve Large-Scale LPs. The Dantzig-Wolfe Decomposition Algorithm. The Simplex Method for Upper-Bounded Variables. Karmarkar?s Method for Solving LPs. 11. GAME THEORY. Two-Person Zero-Sum and Constant-Sum Games: Saddle Points. Two-Person Zero-Sum Games: Randomized Str4ategies, Domination, and Graphical Solution. Linear Programming and Zero-Sum Games. Two-Person Nonconstant-Sum Games. Introduction to n-Person Game Theory. The Core o f an n-Person Game. The Shapely Value. 12. NONLINEAR PROGRAMMING. Review of Differential Calculus. Introductory Concepts. Convex and Concave Functions. Solving NLPs with One Variable. Golden Section Search. Unconstrained Maximization and Minimization with Several Variables. The Method of Steepest Ascent. Lagrange Multiples. The Kuhn-Tucker Conditions. Quadratic Programming. Separable Programming. The Method of Feasible Directions. Pareto Optimality and Tradeoff Curves. 13. DETERMINISTIC DYNAMIC PROGRAMMING. Two Puzzles. A Network Problem. An Inventory Problem. Resource Allocation Problems. Equipment Replacement Problems. Formulation Dynamic Programming Recursions. Using Spreadsheets to Solve Dynamic Programming Problems. 14. HEURISTIC METHODS. 15. NEURAL NETWORKS. Answers To Selected Problems. Index.

A Jinear formulation of the machine-part cell formation problem

Abstract: The machine-part group formation is an important issue in the design of cellular manufacturing systems. The present paper first discusses some of the alternative formulations of this problem, their advantages and disadvantages, and then suggests a new linear zero-one formulation which seems to have removed most of the disadvantages observed in other models. It will be shown that most of the integrality conditions of the proposed formulation can be relaxed. This considerably improves its computational feasibility and efficiency. Finally, a simulated annealing approach to deal with large-scale problems is also presented.

A multi-band approach to arterial traffic signal optimization

Abstract: Progression schemes are widely used for traffic signal control in arterial streets. Under such a scheme a continuous green band of uniform width is provided in each direction along the artery at the desired speed of travel. A basic limitation of existing bandwidth-based programs is that they do not consider the actual traffic volumes and flow capacities on each link in their optimization criterion. Consequently they cannot guarantee the most suitable progression scheme for different traffic flow patterns. In this paper we present a new optimization approach for arterial progression that incorporates a systematic traffic-dependent criterion. The method generates a variable bandwidth progression in which each directional road section can obtain an individually weighted bandwidth (hence, the term multi-band). Mixed-integer linear programming is used for the optimization. Simulation results indicate that this method can produce considerable gains in performance when compared with traditional progression methods. It also lends itself to a natural extension for the optimization of grid networks.

Efficient and exact data dependence analysis

Abstract: Data dependence testing is the basic step in detecting loop level parallelism in numerieal programs. The problem is equivalent to integer linear programming and thus in general cannot be solved efficiently. Current methods in use employ inexact methods that sacrifice potential parallelism in order to improve compiler efficiency. This paper shows that in practice, data dependence can be computed exactly and efficiently. There are three major ideas that lead to this result. First, we have developed and assembled a small set of efficient algorithms, each one exact for special case inputs. Combined with a moderately expensive backup test, they are exact for all the cases we have seen in practice. Second, we introduce a memorization technique to save results of previous tests, thus avoiding calling the data dependence routines multiple times on the same input. Third, we show that this approach can both be extended to compute distance and direction vectors and to use unknowns ymbolic terms without any loss of accuracy or efficiency, We have implemented our algorithm in the SUIF system, a general purpose compiler system developwl at Stanford. We ran the algorithm on the PERFECT Club Benchmarks and our data dependence analyzer gave an exact solution in all cases efficiently,

An efficient algorithm to solve integer-programming problems arising in system-reliability design

Abstract: A simple and efficient technique for solving integer-programming problems that normally arise in system-reliability design is introduced. It quickly solves even a very large system problem. It consists of a systematic search near the boundary of constraints and involves functional evaluations only. It can handle system-reliability design problems of any type in which the decision variables are restricted to integer values. Several illustrative examples are given to substantiate these assertions. >

Maintenance scheduling by using simulated annealing method (for power plants)

Abstract: The thermal power plant generator maintenance scheduling problem is addressed. The problem is formulated as a mixed-integer programming problem, and it is solved by using an optimization method known as simulated annealing. Since the simulated annealing method assumes an analogy between a physical multiparticle system and a combinatorial optimization problem, a global minimum can be found with high probability through a careful annealing process. Numerical results on a real-scale test system are given, and the effectiveness of the proposed method is demonstrated. >

Stacking-Sequence Optimization for Buckling of Laminated Plates by Integer Programming

Abstract: 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.

An algorithm for the three-index assignment problem

Abstract: We describe a branch-and-bound algorithm for solving the axial three-index assignment problem. The main features of the algorithm include a Lagrangian relaxation that incorporates a class of facet inequalities and is solved by a modified subgradient procedure to find good lower bounds, a primal heuristic based on the principle of minimizing maximum regret plus a variable depth interchange phase for finding good upper bounds, and a novel branching strategy that exploits problem structure to fix several variables at each node and reduce the size of the total enumeration tree. Computational experience is reported on problems with up to 78 equations and 17,576 variables. The primal heuristics were tested on problems with up to 210 equations and 343,000 variables.

Solving Multi-Item Lot-Sizing Problems Using Strong Cutting Planes

Abstract: We consider two classes of multi-item lot-sizing problems. The first is a class of single stage problems involving joint machine capacity constraints and/or start up costs, and the second is a class of multistage problems with general product structure. The problems are solved as mixed integer programs based on i an appropriate choice of the initial problem formulation and ii the addition of cuts which are generated automatically by a mathematical programming system MPSARX. Our results extend and complement those of Karmarkar and Schrage 1985, Afentakis and Gavish 1986, Eppen and Martin 1987 and Van Roy and Wolsey 1987. A major advantage of this approach is its robustness or flexibility. By using just a matrix generator and a mathematical programming system with automatic cut generation routines we can formulate and solve model variants without incurring the costs of adapting an algorithm.

A mixed integer-discrete-continuous programming method and its application to engineering design optimization

Abstract: An algorithm for solving non-linear programming problems containing integer, discrete and continuous variables is presented. Based on a commonly employed optimization algorithm, penalties on integer and/or discrete violations are imposed on the objective function to force the search to converge upon standard values. Examples are included to illustrate the practical use of this algorithm in the area of engineering design.

A note on “level schedules for mixed-model assembly lines in just-in-time production systems”

Abstract: This note formulates an assignment problem for obtaining optimal level schedules for mixed-model assembly lines in JIT production systems. The problem was formulated as a quadratic integer programming problem in a recent paper by Miltenburg 1989 where, however, only enumerative algorithms and heuristics were proposed for its solution. Our assignment formulation can also be extended to more general objective functions than the one used by Miltenburg.

Power plant maintenance scheduling: optimizing economics and reliability

Abstract: The objective of this study is to show the effects that costs, reliability, and constraints have on each other in power plant outage scheduling. A unique and powerful optimizing method is used to study data from a medium-sized utility. Four optimization studies were made. It was found that different optimization criteria give different best maintenance schedules. The optimal reliability and production cost values are coupled to operating constraints and may be improved by relaxing some constraints. The potential savings must be evaluated against the inconvenience and costs of relaxing these operating constraints. Use of an optimum maintenance schedule and judicious relaxation of constraints can lead to production cost reduction on the order of 0.3%. Integer programming can solve real-life maintenance-scheduling problems in reasonable computer time. >

Multi-year expansion planning for distribution systems

Abstract: A multi-term distribution system expansion planning method is proposed. Many mathematical programming approaches have been proposed in this area. However, because of the complexity of the problem or the limitations of a computational time and memory size, these methods can only be applied to a small-scale system. To solve large-scale problems, the authors propose a new decomposition algorithm based on the branch exchange method. A n-years planning problem is decomposed into n one-year planning problems, and one-year results are coordinated through what can be called the forward/backward path. The validity and effectiveness of the algorithm are ascertained by applying it to real-scale numerical examples. >

A multiphase approach to the period routing problem

Abstract: In this article, we present a multiphase approach to the period routing problem. The period routing problem involves the design of effective vehicle routes that satisfy customer service frequencies over a specified planning horizon. The first phase of analysis consists of a generalized network approximation to achieve an efficient initial solution. The second phase involves an interchange heuristic that reduces distribution costs by solving a surrogate traveling salesman problem. The third phase consists of an interchange heuristic that further reduces the distribution costs by addressing the actual vehicle routes of the period routing problem. A fourth phase utilizes a 0–1 integer model to attempt further improvements. Computational results on test problems indicate that the multiphase approach yields improvements over previous best solutions.

A neural network approach to job-shop scheduling

Abstract: A novel analog computational network is presented for solving NP-complete constraint satisfaction problems, i.e. job-shop scheduling. In contrast to most neural approaches to combinatorial optimization based on quadratic energy cost function, the authors propose to use linear cost functions. As a result, the network complexity (number of neurons and the number of resistive interconnections) grows only linearly with problem size, and large-scale implementations become possible. The proposed approach is related to the linear programming network described by D.W. Tank and J.J. Hopfield (1985), which also uses a linear cost function for a simple optimization problem. It is shown how to map a difficult constraint-satisfaction problem onto a simple neural net in which the number of neural processors equals the number of subjobs (operations) and the number of interconnections grows linearly with the total number of operations. Simulations show that the authors' approach produces better solutions than existing neural approaches to job-shop scheduling, i.e. the traveling salesman problem-type Hopfield approach and integer linear programming approach of J.P.S. Foo and Y. Takefuji (1988), in terms of the quality of the solution and the network complexity. >

History of mathematical programming : a collection of personal reminiscences

Abstract: The Origins of the Impossibility Theorem (K.J. Arrow). Mathematical Programming: Journals, Society, Recollections (M.L. Balinski). Linear Programming (G.B. Dantzig). A Glimpse of Heaven (J. Edmonds). Early Integer Programming (R.E. Gomory). Linear Programming at the National Bureau of Standards (A.J. Hoffman). Growth of Mathematical Programming in Japan (M. Iri). On the Origin of the Hungarian Method (H.W. Kuhn). Nonlinear Programming: A Historical Note (H.W. Kuhn). Old Stories (E.L. Lawler). Mathematical Programming Musings (O.L. Mangasarian). Mathematical Programming at Cornell and CORE: The Super Seventies (G.L. Nemhauser). A View of Nonlinear Optimization (M.J.D. Powell). The Origins of Fixed Point Methods (H.E. Scarf). The Development of Numerical Methods for Nonsmooth Optimization in the USSR (N.Z. Shor). Addresses.

On the multiway cut polyhedron

Abstract: Given a graph G = (V,E) and a set N ⊆ V, we consider the problem of finding a minimum-weight multiway cut that separates each pair of nodes in N. In this paper we give an integer programming formulation of this problem and study the associated polyhedron. We give some computational results to support the strength of our facets. We also give some efficiently solvable instances.

Simultaneous scheduling and allocation for cost constrained optimal architectural synthesis

Abstract: An integer programming (IP) model, which simultaneously schedules and allocates functional units, registers, and busses, is presented for synthesizing cost-constrained globally optimal architectures. This research is important for industry by providing optimal schedules which minimize interconnect costs and interface to analog and asynchronous processes, since these are seen as key to synthesizing high performance architectures. A partially structured tight IP formulation of the architectural synthesis problem provides globally optimal schedules for peicewise linear cost functions, using branch and bound, in execution times faster than previous research. This research breaks new ground by 1. simultaneously scheduling and allocating hardware resources including interconnect, 2. support for asynchronous and analog interfaces, and 3. guaranteeing globally optimal solutions in practical execution times.

An analytical approach to floorplan design and optimization

Abstract: An analytical method for general floorplan design and optimization is proposed. This method is based on a mixed integer programming model and application of a standard mathematical software. The method allows arbitrary combinations of rigid and flexible modules. Various objective functions such as chip area, interconnection length, timing delays or any combination of them are permitted. Routing space is estimated by the global router. Experimental data are provided. >

Computational experience with an interior point algorithm on the satisfiability problem

Abstract: We apply the zero-one integer programming algorithm described in Karmarkar [12] and Karmarkar, Resende and Ramakrishnan [13] to solve randomly generated instances of the satisfiability problem (SAT). The interior point algorithm is briefly reviewed and shown to be easily adapted to solve large instances of SAT. Hundreds of instances of SAT (having from 100 to 1000 variables and 100 to 32,000 clauses) are randomly generated and solved. For comparison, we attempt to solve the problems via linear programming relaxation with MINOS.

An interior point algorithm to solve computationally difficult set covering problems

Abstract: We present an interior point approach to the zero–one integer programming feasibility problem based on the minimization of a nonconvex potential function. Given a polytope defined by a set of linear inequalities, this procedure generates a sequence of strict interior points of this polytope, such that each consecutive point reduces the value of the potential function. An integer solution (not necessarily feasible) is generated at each iteration by a rounding scheme. The direction used to determine the new iterate is computed by solving a nonconvex quadratic program on an ellipsoid. We illustrate the approach by considering a class of difficult set covering problems that arise from computing the 1-width of the incidence matrix of Steiner triple systems.