Showing papers on "Integer programming published in 1996"

Linear Programming: Foundations and Extensions

Abstract: Preface. Part 1: Basic Theory - The Simplex Method and Duality. 1. Introduction. 2. The Simplex Method. 3. Degeneracy. 4. Efficiency of the Simplex Method. 5. Duality Theory. 6. The Simplex Method in Matrix Notation. 7. Sensitivity and Parametric Analyses. 8. Implementation Issues. 9. Problems in General Form. 10. Convex Analysis. 11. Game Theory. 12. Regression. Part 2: Network-Type Problems. 13. Network Flow Problems. 14. Applications. 15. Structural Optimization. Part 3: Interior-Point Methods. 16. The Central Path. 17. A Path-Following Method. 18. The KKT System. 19. Implementation Issues. 20. The Affine-Scaling Method. 21. The Homogeneous Self-Dual Method. Part 4: Extensions. 22. Integer Programming. 23. Quadratic Programming. 24. Convex Programming. Appendix A: Source Listings. Answers to Selected Exercises. Bibliography. Index.

Computational study of a family of mixed-integer quadratic programming problems

Abstract: We present computational experience with a branch-and-cut algorithm to solve quadratic programming problems where there is an upper bound on the number of positive variables. Such problems arise in financial applications. The algorithm solves the largest real-life problems in a few minutes of run-time.

Hub Location and the p-Hub Median Problem

Abstract: Hub facilities serve as switching and transshipment points in transportation and communication networks. Hub networks concentrate flows on the hub-to-hub links and benefit from economies of scale in interhub transportation. Most hub location research has focused on problems where each origin/destination is allocated to a single hub. However, multiple allocation to more than one hub is necessary to minimize total transportation costs. This paper defines a p-hub median, analogous to a p-median, and presents integer programming formulations for the multiple and single allocation p-hub median problems. Two new heuristics for the single allocation p-hub median problem are evaluated. These heuristics derive a solution to the single allocation p-hub median problem from the solution to the multiple allocation p-hub median problem. Computational results are presented for problems with 10-40 origins/destinations and up to eight hubs. The new heuristics generally perform well in comparison with other heuristics.

Mixed-Integer Linear Programming Model for Refinery Short-Term Scheduling of Crude Oil Unloading with Inventory Management

Abstract: This paper addresses the problem of inventory management of a refinery that imports several types of crude oil which are delivered by different vessels. This problem involves optimal operation of crude oil unloading, its transfer from storage tanks to charging tanks, and the charging schedule for each crude oil distillation unit. A mixed-integer optimization model is developed which relies on time discretization. The problem involves bilinear equations due to mixing operations. However, the linearity in the form of a mixed-integer linear program (MILP) is maintained by replacing bilinear terms with individual component flows. The LP-based branch and bound method is applied to solve the model, and several techniques, such as priority branching and bounding, and special ordered sets are implemented to reduce the computation time. This formulation and solution method was applied to an industrial-size problem involving 3 vessels, 6 storage tanks, 4 charging tanks, and 3 crude oil distillation units over 15 time intervals. The MILP model contained 105 binary variables, 991 continuous variables, and 2154 constraints and was effectively solved with the proposed solution approach.

Mixed 0-1 Programming by Lift-and-Project in a Branch-and-Cut Framework

Abstract: We investigate the computational issues that need to be addressed when incorporating general cutting planes for mixed 0-1 programs into a branch-and-cut framework The cuts we use are of the lift-and-project variety Some of the issues addressed have a theoretical answer, but others are of an experimental nature and are settled by comparing alternatives on a set of test problems The resulting code is a robust solver for mixed 0-1 programs We compare it with several existing codes On a wide range of test problems it performs as well as, or better than, some of the best currently available mixed integer programming codes

Capacitated Network Design—Polyhedral Structure and Computation

Abstract: We study a capacity expansion problem that arises in telecommunication network design. Given a capacitated network and a traffic demand matrix, the objective is to add capacity to the edges, in multiples of various modularities, and route traffic, so that the overall cost is minimized. We study the polyhedral structure of a mixed-integer formulation of the problem and develop a cutting-plane algorithm using facet defining inequalities. The algorithm produces an extended formulation providing both a vary good lower bound and a starting point for branch and bound. The overall algorithm appears effective when applied to problem instances using real-life data.

Adaptive Penalty Methods for Genetic Optimization of Constrained Combinatorial Problems

Abstract: The application of genetic algorithms (GA) to constrained optimization problems has been hindered by the inefficiencies of reproduction and mutation when feasibility of generated solutions is impossible to guarantee and feasible solutions are very difficult to find. Although several authors have suggested the use of both static and dynamic penalty functions for genetic search, this paper presents a general adaptive penalty technique which makes use of feedback obtained during the search along with a dynamic distance metric. The effectiveness of this method is illustrated on two diverse combinatorial applications: (1) the unequal-area, shape-constrained facility layout problem and (2) the series-parallel redundancy allocation problem to maximize system reliability given cost and weight constraints. The adaptive penalty function is shown to be robust with regard to random number seed, parameter settings, number and degree of constraints, and problem instance.

Integer Programming and Combinatorial Optimization

Abstract: 3 Non-linear Objective functions 4 3.1 Production problem with set-up costs . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3.2 Piecewise linear cost function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.3 Piecewise linear convex cost function . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.4 Disjunctive constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

A Dynamic Subgradient-Based Branch-and-Bound Procedure for Set Covering

Abstract: We discuss a branch and bound algorithm for set covering, whose centerpiece is a new integrated upper bounding/lower bounding procedure called dynamic subgradient optimization DYNSGRAD. This new procedure, applied to a Lagrangean dual at every node of the search tree, combines the standard subgradient method with primal and dual heuristics that interact to change the Lagrange multipliers and tighten the upper and lower bounds, fix variables, and periodically restate the Lagrangean itself. Extensive computational testing is reported. As a stand-alone heuristic, DYNSGRAD performs significantly better than other procedures in terms of the quality of solutions obtainable with a certain computational effort. When incorporated into a branch-and-bound algorithm, DYNSGRAD considerably advances the state of the art in solving set covering problems.

Heuristics for the integer one-dimensional cutting stock problem: A computational study

Abstract: In this paper the problem of generating integer solutions to the standard one-dimensional cutting stock problem is treated. In particular, we study a specific class of heuristic approaches that have been proposed in the literature, and some straightforward variants. These methods are compared with respect to solution quality and computing time. Our evaluation is based on having solved 4,000 randomly generated test problems. Not only will it be shown that two methods are clearly superior to the others but also that they solve almost any instance of the standard one-dimensional cutting stock problem to an optimum.

Progressive hedging and tabu search applied to mixed integer (0,1) multistage stochastic programming

Abstract: Many problems faced by decision makers are characterized by a multistage decision process with uncertainty about the future and some decisions constrained to take on values of either zero or one (for example, either open a facility at a location or do not open it). Although some mathematical theory exists concerning such problems, no general-purpose algorithms have been available to address them. In this article, we introduce the first implementation of general purpose methods for finding good solutions to multistage, stochastic mixed-integer (0, 1) programming problems. The solution method makes use of Rockafellar and Wets' progressive hedging algorithm that averages solutions rather than data. Solutions to the induced quadratic (0,1) mixed-integer subproblems are obtained using a tabu search algorithm. We introduce the notion of integer convergence for progressive hedging. Computational experiments verify that the method is effective. The software that we have developed reads standard (SMPS) data files.

Applying simulated annealing to location-planning models

Abstract: Simulated annealing is a computational approach that simulates an annealing schedule used in producing glass and metals. Originally developed by Metropolis et al. in 1953, it has since been applied to a number of integer programming problems, including the p-median location-allocation problem. However, previously reported results by Golden and Skiscim in 1986 were less than encouraging. This article addresses the design of a simulated-annealing approach for the p-median and maximal covering location problems. This design has produced very good solutions in modest amounts of computer time. Comparisons with an interchange heuristic demonstrate that simulated annealing has potential as a solution technique for solving location-planning problems and further research should be encouraged.

Analysis and design of metabolic reaction networks via mixed‐integer linear optimization

Abstract: Improvements in bioprocess performance can be achieved by genetic modifications of metabolic control structures. A novel optimization problem helps quantitative understanding and rational metabolic engineering of metabolic reaction pathways. Maximizing the performance of a metabolic reaction pathway is treated as a mixed-integer linear programming formulation to identify changes in regulatory structure and strength and in cellular content of pertinent enzymes which should be implemented to optimize a particular metabolic process. A regulatory superstructure proposed contains all alternative regulatory structures that can be considered for a given pathway. This approach is followed to find the optimal regulatory structure for maximization of phenylalanine selectivity in the microbial aromatic amino acid synthesis pathway. The solution suggests that from the eight feedback inhibitory loops in the original regulatory structure of this pathway, inactivation of at least three loops and overexpression of three enzymes will increase phenylalanine selectivity by 42%. Moreover, novel regulatory structures with only two loops, none of which exists in the original pathway, could result in a selectivity up to 95%.

Asymptotic experimental analysis for the Held-Karp traveling salesman bound

Abstract: The Held-Karp (HK) lower bound is the solution to the linear programming relaxation of the standard integer programming formulation of the traveling salesman problem (TSP). For numbers of cities N up to 30,000 or more it can be computed exactly using the Simplex method and appropriate separation algorithms, and for N up to a million good approximations can be obtained via iterative Lagrangean relaxation techniques first suggested by Held and Karp. In this paper, we consider three applications of our ability to compute/approximate this bound. First, we provide empirical evidence in support of using the HK bound as a stand-in for the optimal tour length when evaluating the quality of near-optimal tours. We show that for a wide variety of randomly generated instance types the optimal tour length averages less than 0.8% over the HK bound, and even for the real-world instances in TSPLIB the gap is almost always less than 2%. Moreover, our data indicates that the HK bound can provide substantial ‘‘variance reduction’’ in experimental studies involving randomly generated instances. Second, we estimate the expected HK bound as a function of N for a variety of random instance types, based on extensive computations. For example, for random Euclidean instances it is known that the ratio of the HeldKarp bound to √+ + N approaches a constant C HK, and we estimate both that constant and the rate of convergence to it. Finally, we combine this information with our earlier results on expected HK gaps to obtain estimates for expected optimal tour lengths. For random Euclidean instances, we conclude that C OPT, the limiting ratio of the optimal tour length to √+ + N , is .7124 ± .0002, thus invalidating the commonly cited estimates of .749 and .765 and undermining many claims of good heuristic performance based on those estimates. For random distance matrices, the expected optimal tour length appears to be about 2.042, adding support to a conjec

Selection of vendors—a mixed-integer programming approach

Abstract: In this paper, we propose a mixed-integer programming model to select vendors and determine the order quantities. The model considers the stochastic nature of demand, the quality of supplied parts, the cost of purchasing and transportation, the fixed cost for establishing vendors, and the cost of receiving poor quality parts. The model also considers the lead time requirements for the parts.

Swing module scheduling: a lifetime-sensitive approach

Abstract: This paper presents a novel software pipelining approach, which is called Swing Modulo Scheduling (SMS). It generates schedules that are near optimal in terms of initiation interval, register requirements and stage count. Swing Modulo Scheduling is an heuristic approach that has a low computational cost. The paper describes the technique and evaluates it for the Perfect Club benchmark suite. SMS is compared with other heuristic methods showing that it outperforms them in terms of the quality of the obtained schedules and compilation time. SMS is also compared with an integer linear programming approach that generates optimum schedules but with a huge computational cost, which makes it feasible only for very small loops. For a set of small loops, SMS obtained the optimum initiation interval in all the cases and its schedules required only 5% more registers and a 1% higher stage count than the optimum.

Power distribution system planning with reliability modeling and optimization

Abstract: A new approach for the systemized optimization of power distribution systems is presented in this paper. Distribution system reliability is modelled in the optimization objective function via outage costs and costs of switching devices, along with the nonlinear costs of investment, maintenance and energy losses of both the substations and the feeders. The optimization model established is multi-stage, mixed-integer and nonlinear, which is solved by a network-flow programming algorithm. A multi-stage interlacing strategy and a nonlinearity iteration method are also designed. Supported by an extensive database, the planning software tool has been applied to optimize the power distribution system of a developing city.

Hardware/software partitioning using integer programming

Abstract: One of the key problems in hardware/software codesign is hardware/software partitioning. This paper describes a new approach to hardware/software partitioning using integer programming (IP). The advantage of using IP is that optimal results are calculated respective to the chosen objective function. The partitioning approach works fully automatic and supports multi-processor systems, interfacing and hardware sharing. In contrast to other approaches where special estimators are used, we use compilation and synthesis tools for cost estimation. The increased time for calculating the cost metrics is compensated by an improved quality of the estimations compared to the results of estimators. Therefore, fewer iteration steps of partitioning will be needed. The paper will show that using integer programming to solve the hardware/software partitioning problem is feasible and leads to promising results.

Two-stage stochastic integer programming : a survey

Abstract: Stochastic integer programming is more complicated than stochastic linear programming, as will be explained for the case of the two-stage stochastic programming model. A survey of the results accomplished in this recent field of research is given.

Optimal liner fleet routeing strategies.

Abstract: The objective of this paper is to suggest practical optimization models for routing strategies for liner fleets. Many useful routing and scheduling problems have been studied in the transportation literature. As for ship scheduling or routing problems, relatively less effort has been devoted, in spite of the fact that sea transportation involves large capital and operating costs. This paper suggests two optimization models that can be useful to liner shipping companies. One is a linear programming model of profit maximization, which provides an optimal routing mix for each ship available and optimal service frequencies for each candidate route. The other model is a mixed integer programming model with binary variables which not only provides optimal routing mixes and service frequencies but also best capital investment alternatives to expand fleet capacity. This model is a cost minimization model.

Discrete linear bilevel programming problem

Abstract: In this paper, we analyze some properties of the discrete linear bilevel program for different discretizations of the set of variables We study the geometry of the feasible set and discuss the existence of an optimal solution We also establish equivalences between different classes of discrete linear bilevel programs and particular linear multilevel programming problems These equivalences are based on concave penalty functions and can be used to design penalty function methods for the solution of discrete linear bilevel programs