Showing papers in "Informs Journal on Computing in 1989"
[...]
TL;DR: The elements of staged search and structured move sets are characterized, which bear on the issue of finiteness, and new dynamic strategies for managing tabu lists are introduced, allowing fuller exploitation of underlying evaluation functions.
Abstract: This is the second half of a two part series devoted to the tabu search metastrategy for optimization problems. Part I introduced the fundamental ideas of tabu search as an approach for guiding other heuristics to overcome the limitations of local optimality, both in a deterministic and a probabilistic framework. Part I also reported successful applications from a wide range of settings, in which tabu search frequently made it possible to obtain higher quality solutions than previously obtained with competing strategies, generally with less computational effort. Part II, in this issue, examines refinements and more advanced aspects of tabu search. Following a brief review of notation, Part II introduces new dynamic strategies for managing tabu lists, allowing fuller exploitation of underlying evaluation functions. In turn, the elements of staged search and structured move sets are characterized, which bear on the issue of finiteness. Three ways of applying tabu search to the solution of integer programmin...
5,883 citations
TL;DR: Preliminary computational results indicate that this implementation compares favorably with a comparable implementation of a dual affine interior point method, and with MINOS 5.0, a state-of-the-art implementation of the simplex method.
Abstract: The purpose of this paper is to describe in detail an implementation of a primal-dual interior point method for solving linear programming problems. Preliminary computational results indicate that this implementation compares favorably with a comparable implementation of a dual affine interior point method, and with MINOS 5.0, a state-of-the-art implementation of the simplex method. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.
191 citations
TL;DR: This paper describes data structures and programming techniques used in an implementation of Karmarkar's algorithm for linear programming, which relies on a direct factorization scheme, with an extensive symbolic factorization step performed in a preparatory stage of the linear programming algorithm.
Abstract: This paper describes data structures and programming techniques used in an implementation of Karmarkar's algorithm for linear programming. Most of our discussion focuses on applying Gaussian elimination toward the solution of a sequence of sparse symmetric positive definite systems of linear equations, the main requirement in Karmarkar's algorithm. Our approach relies on a direct factorization scheme, with an extensive symbolic factorization step performed in a preparatory stage of the linear programming algorithm. An interpretative version of Gaussian elimination makes use of the symbolic information to perform the actual numerical computations at each iteration of algorithm. We also discuss ordering algorithms that attempt to reduce the amount of fill-in in the LU factors, a procedure to build the linear system solved at each iteration, the use of a dense window data structure in the Gaussian elimination method, a preprocessing procedure designed to increase the sparsity of the linear programming coeffi...
121 citations
TL;DR: A neural network-based algorithm was developed for the static weapon-target assignment problem in ballistic missile defense and has proven to be stable and to converge to solutions very close to global optima.
Abstract: A neural network-based algorithm was developed for the static weapon-target assignment problem in ballistic missile defense. An optimal assignment policy is one which allocates targets to weapon platforms such that the total expected leakage value of targets surviving the defense is minimized. This involves the minimization of a nonlinear objective function subject to inequality constraints specifying the maximum number of interceptors available to each platform and the maximum number of interceptors allowed to be fired at each target as imposed by the battle management/command control and communications system. The algorithm consists of solving a system of ordinary differential equations whose trajectories are the assignment variables of the problem. Simulations of the algorithm on PC and VAX computers were carried out using a simple numerical scheme. In all the battle instances tested, the algorithm has proven to be stable and to converge to solutions very close to global optima. The time to achieve con...
99 citations
TL;DR: A formal framework for event-oriented simulation is introduced and event graphs are examined using this framework and comprehensive rules are presented for identifying situations where event execution order priorities may be necessary.
Abstract: Schruben introduced event graphs as a graphical technique for visualizing event-oriented system structures. In this paper, a formal framework for event-oriented simulation is introduced and event graphs are examined using this framework. Comprehensive rules are presented for identifying situations where event execution order priorities may be necessary. The concept of expanded event graphs and super events are introduced. A procedure for generating expanded event graphs which show hierarchy and possible grouping of events as one single unit without violating predefined execution order priorities is described. Expanded event graphs generated by this procedure can be used as bases for structured and efficient simulation programs. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.
52 citations
TL;DR: The dual affine interior point method is extended to handle variables with simple upper bounds as well as free variables and a variant of the big- M artificial variable method to attain feasibility is derived.
Abstract: The dual affine interior point method is extended to handle variables with simple upper bounds as well as free variables. During execution, variables which appear to be going to zero are fixed at zero, and rows with slack variables bounded away from zero are removed. A variant of the big-M artificial variable method to attain feasibility is derived. The simplex method is used to recover an optimal basis upon completion of the algorithm, and the effects of scaling are discussed. Computational experience on a variety of problems is presented. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.
52 citations
TL;DR: This work classifies and comment on the literature in parallel optimization with particular emphasis on the numerical and computational aspects of the field and work on the related areas of performance evaluation models, parallel linear algebra and ben...
Abstract: Parallel computing is becoming a basic tool for research in several areas of computational mathematical programming Algorithms and models that were intractable by the performance standards of von Neumann computers are becoming increasingly attractive New algorithms are designed specifically for parallel architectures; the insight obtained from the design and implementation of such algorithms leads occasionally to improved sequential algorithms Researchers report computational experiments with linear programming problems approaching a million variables and nonlinear problems with thousands of variables are solved routinely on state-of-the-art supercomputers We classify and comment on the literature in parallel optimization with particular emphasis on the numerical and computational aspects of the field Discussion of the parallel optimization literature is preceded by a tutorial on parallel computing in general Work on the related areas of performance evaluation models, parallel linear algebra and ben
43 citations
TL;DR: A branch-and-bound algorithm for mixed-integer programming (MIP) is presented in which a different integer variable is designated for branching at each depth in the search tree in order to achieve economies of scale in solving the linear programming relaxations to obtain bounds for the MIP algorithm.
Abstract: A branch-and-bound algorithm for mixed-integer programming (MIP) is presented in which a different integer variable is designated for branching at each depth in the search tree. This is done in order to achieve economies of scale in solving the linear programming relaxations to obtain bounds for the (MIP) algorithm. This algorithm is the foundation for the zoom software system, which is briefly described. Illustrative computational experience is included. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.
41 citations
TL;DR: Input resolution and “unit support” resolution (a generalization of unit resolution) are complete inference methods for Horn clauses in propositional logic and it is shown that they have a close analog in cutting plane theory.
Abstract: Input resolution and “unit support” resolution (a generalization of unit resolution) are complete inference methods for Horn clauses in propositional logic. We show that they have a close analog in cutting plane theory. Namely, a logical clause can be deduced using input or unit support resolution if and only if it belongs to the elementary closure of the premises and is therefore a rank one cut in Chvatal's sense. This connection leads to a cutting plane algorithm for solving non-Horn inference problems. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.
35 citations
TL;DR: This paper examines several methods for numerically solving linear equations that arise in the study of Markov chains and concludes that state-reduction is the most accurate and the matrix solutions have the least computation time.
Abstract: We examine several methods for numerically solving linear equations that arise in the study of Markov chains. These methods are Gaussian elimination, state-reduction, closed-form matrix solutions, and some hybrid methods. The emphasis is on moments of first-passage times and times to absorption. We compare the methods on the basis of accuracy and computation. We conclude that state-reduction is the most accurate and that the matrix solutions have the least computation time. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.
30 citations
TL;DR: The possibilistic linear program in this paper is an unconstrained linear program with several objective functions whose coefficients are represented by possibility distributions whose coefficient distributions are derived from a possibility distribution.
Abstract: In this paper, a possibilistic linear program is formulated when a measurable multiattribute value function is given. The possibilistic linear program in this paper is an unconstrained linear program with several objective functions whose coefficients are represented by possibility distributions. A possibility measure and a necessity measure are derived from a possibility distribution. Using fuzzy integrals of the measurable multiattribute value function with respect to the possibility measure and the necessity measure, the possible value and the necessary value are defined respectively. In an analogy of the expected utility, the principles of maximizing the possible value and the necessary value are considered as decision procedures under a possibility distribution. The possibilistic linear program is formulated based on these decision procedures and reduced to a nonlinear program. A solution method using linear programming technique is proposed. INFORMS Journal on Computing, ISSN 1091-9856, was publishe...
TL;DR: It is concluded, for the assumed message-length distribution, that the convex delay function predicts the simulated delayed messages of the network, even for networks with hundreds or thousands of nodes.
Abstract: We formulate nonlinear programming models for design of large-scale packet-switched telecommunication networks. In these models, the network’s link capacities and source-destination message routes are chosen simultaneously. Although leased communication lines are available only in discrete units of capacity, public telephone lines with high-speed modems can be used to augment them, thus effectively obtaining fractional equivalents of leased-line capacity. Therefore, our network-design models contain continuous link-capacity variables. These continuous models can be solved for ϵ-optimal solutions, even for networks with hundreds or thousands of nodes. We examine conventional link delay functions used by previous researchers and suggest an alternative class of convex delay functions. Using computer simulation to analyze link delays, we compare the convex delay function to the conventional one. We conclude, for our assumed message-length distribution, that the convex delay function predicts the simulated del...
TL;DR: It is shown how the structure of proofs in a Horn clause knowledge base is completely described by certain of the extreme solutions to a suitable “dual” linear constraint set.
Abstract: We show how the structure of proofs in a Horn clause knowledge base is completely described by certain of the extreme solutions to a suitable “dual” linear constraint set. The extreme points of this linear system are integer vectors, and give the count of the number of times that a given proposition is used in a proof of a “target” proposition. The “primal” to this dual provides the pointwise maximum vector which solves a set of dynamic programming recursions, and the latter recursions are derived from the Horn clause knowledge base. Variation in the facts or in the rules of the knowledge base corresponds to changes in only the criterion vector of the dual linear program. This linear programming approach to inference in expert systems also allows for the detection of “near proofs.” The latter are, by definition, proof structures which would become valid, if only exactly one more fact were known to be true. The first author, Robert G. Jeroslow, deceased August 31, 1988. INFORMS Journal on Computing, ISSN 1...
TL;DR: A new technique for improving two-terminal reliability problem for communication networks with unreliable links via approximation by series-parallel graphs is presented.
Abstract: The two-terminal reliability problem for communication networks with unreliable links is a computationally difficult problem. Upper and lower bounds can be efficiently computed using graph-theoretical techniques based on edge-packing. We present a new technique for improving these bounds via approximation by series-parallel graphs. We also present some computational results for comparison with the known edge-packing bounds. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.
TL;DR: A number of procedures to reduce the size of the recourse problem are described, including a procedure for generating efficiently the feasibility cuts, and it is shown that further reductions are possible if more information about the node-types is taken into account.
Abstract: Preprocessing can speed up the solution procedures for two-stage stochastic programming. We consider the case when the second-stage problem is a pure, uncapacitated network. We describe a number of procedures to reduce the size of the recourse problem. We describe a procedure for generating efficiently the (induced) feasibility cuts, and show that further reductions are possible if more information about the node-types is taken into account. We also investigate network collapsing techniques that would simplify the work required to find both optimality cuts and feasibility cuts, if we had not yet reduced the problem to one with relatively complete recourse. Computational results confirm that substantial savings are possible. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.
TL;DR: This paper describes a software package for the specification and solution of stiff CTMC and uses a language for the description of Markov chains for exact and approximate solution techniques.
Abstract: Continuous-time Markov chains (CTMC) are widely used mathematical models. Reliability models, queueing networks, and inventory models all require transient solutions of CTMC. The cost of CTMC transient solution increases with size, stiffness, and mission time. To eliminate stiffness and reduce the cost of solution, approximation techniques have been proposed. In this paper, we describe a software package for the specification and solution of stiff CTMC. As an interface, we use a language for the description of Markov chains. The language also provides facilities for controlling the solution procedure. Both exact and approximate solution techniques are provided. To conclude the paper, we use several examples to show the use of our specification language and the utility of our approximation technique. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.
TL;DR: Several new algorithms that use the dual affine direction and a recentering direction in a multidirection approach are derived and the most promising of these algorithms is based on minimizing the cost function on a sequence of two-dimensional cross sections of the feasible region.
Abstract: Interior point algorithms for solving linear programming problems are considered. The techniques are derived from a continuous version of Huard's method of centers that yields a family of trajectories in the feasible region that all converge to an optimal solution. The tangential direction of these trajectories is the dual affine direction. Deficiencies in some of these trajectories are discussed, and the need to recenter is argued. Several new algorithms that use the dual affine direction and a recentering direction in a multidirection approach are then derived. The most promising of these algorithms is based on minimizing the cost function on a sequence of two-dimensional cross sections of the feasible region. Numerical results are presented. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.
TL;DR: The analysis suggests a method for analytically bounding the derivatives, and yields a proof that a large class of queueing functions are infinitel...
Abstract: Consider an open queueing system that is stable for arrival rates, 0 ≤ λ 0 is by observing the effect of additional customers on the sample path of a simulation. We make this technique rigorous by showing that a certain function of the sample paths is “admissible.” The analysis suggests a method for analytically bounding the derivatives, and yields a proof that a large class of queueing functions are infinitel...
TL;DR: This paper studies a class of problems for which this type of a greedy algorithm does not optimize the given cost function, but for which there exists a second objective function, called a greedy rule, such that applying the greedy algorithm to the secondary objective function yields a solution which is optimal with respect to the original cost function.
Abstract: The greedy method is a well-known approach for problem solving directed mainly at the solution of optimization problems. Leading theoretical frameworks dealing with the optimality of greedy solutions (e.g., the matroid and greedoid theories) tacitly assume that the greedy algorithm is always guided by the cost function to be optimized, namely, it builds a solution by adding, in each step, an element that contributes the most to the value of the cost function. This paper studies a class of problems for which this type of a greedy algorithm does not optimize the given cost function, but for which there exists a secondary objective function, called a greedy rule, such that applying the greedy algorithm to the secondary objective function yields a solution which is optimal with respect to the original cost function. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.
TL;DR: This paper develops a jackknife estimator for α that is appropriate to computational settings in which the total computer budget to be used is constrained, and shows that the estimator reduces bias without increasing asymptotic variance.
Abstract: In this paper, we consider the problem of estimating a parameter α that can be expressed as a nonlinear function of sample means. We develop a jackknife estimator for α that is appropriate to computational settings in which the total computer budget to be used is constrained. Despite the fact that the jackknifed observations are not i.i.d., we are able to show that our jackknife estimator reduces bias without increasing asymptotic variance. This makes the estimator particularly suitable for small sample applications. Because a special case of this estimator problem is that of estimating a ratio of two means, the results in this paper are partinent to regenerative steady-state simulations. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.
TL;DR: An ϵ-approximate algorithm is presented for the maximum concurrent flow problem (MCFP) with uniform demand and the results indicate that the algorithm is efficient and an efficient combinatorial algorithm for the MCFP in planar graphs is presented.
Abstract: The maximum concurrent flow problem (MCFP) is the optimization version of the feasibility problem in multicommodity flows. The objective is to maximize the percentage of the demands which is realizable for all commodities, subject to the capacity constraints. A fully polynomial ϵ-approximate algorithm was developed by Shahrokhi and Matula to solve the MCFP when the edge capacities are the same (the MCFP with uniform capacity). In this paper, we present an ϵ-approximate algorithm for the MCFP with uniform demand (when all demands are equal). Our ϵ-approximate algorithm employs a linear size reduction from the MCFP with uniform demand to the MCFP with uniform capacity and the fully polynomial ϵ-approximate algorithm for the MCFP with uniform capacity. The computational results indicate that the algorithm is efficient. We also present an efficient combinatorial algorithm for the MCFP in planar graphs. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 u...
TL;DR: A relatively simple example of a multiple-cost-row linear program is presented in which the parallel algorithm gives a speedup, over its sequential version, greater than the number of processors.
Abstract: Earlier parallel computational results on constrained global optimization problems have shown that speedups greater than the number of processors can occur in practice. To show how this is possible, a relatively simple example of a multiple-cost-row linear program is presented in which the parallel algorithm gives a speedup, over its sequential version, greater than the number of processors. In addition, it is shown that for a particular problem instance (taken from another special class of multiple-cost-row linear programming problems), the average parallel speedup, taken over all orderings of the cost rows, can also be greater than the number of processors. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.