Abstract: Given an infeasible set of linear constraints, finding the maximum cardinality feasible subsystem is known as themaximum feasible subsystem problem. This problem is known to be NP-hard, but has many practical applications. This paper presents improved heuristics for solving the maximum feasible subsystem problem that are significantly faster than the original, but still highly accurate.

Abstract: We examine key convergence properties of the steady-state simulation analysis method of nonoverlapping batch means (NOBM) when it is applied to a stationary, phi-mixing process. For an increasing batch size and a fixed batch count, we show that the standardized vector of batch means converges in distribution to a vector of independent standard normal variates--a well-known result underlying the NOBM method for which there appears to be no direct, readily accessible justification. To characterize the asymptotic behavior of the classical NOBM confidence interval for the mean response, we formulate certain moment conditions on the components (numerator and denominator) of the associated Student'st-ratio that are necessary to ensure the validity of the confidence interval. For six selected stochastic systems, we summarize an extensive numerical analysis of the convergence to steady-state limits of these moment conditions; and for two systems we present a simulation-based analysis exemplifying the corresponding convergence in distribution of the components of the NOBMt-ratio. These results suggest that in many simulation output processes, approximate joint normality of the batch means is achieved at a substantially smaller batch size than is required to achieve approximate independence; and an improved batch means method should exploit this property whenever possible.

Abstract: In the online traveling salesman problem, requests for visits to cities (points in a metric space) arrive online while the salesman is traveling. The salesman moves at no more than unit speed and starts and ends his work at a designated origin. The objective is to find a routing for the salesman that finishes as early as possible.Performance of algorithms is measured through their competitive ratio, comparing the outcome of the algorithms with that of an adversary who provides the problem instance and therefore is able to achieve the optimal offline solution. Objections against such omnipotent adversaries have lead us to devise an adversary that is in a natural way, in the context of routing problems, more restricted in power.For the exposition we consider the online traveling salesman problem on the metric space given by , the non-negative part of the real line. We show that a very natural strategy is 3/2-competitive against the conventional adversary, which matches the lower-bound on competitive ratios achievable for algorithms for this problem.Against the more"fair adversary", that we propose, we show that there exists an algorithm with competitive ratioand provide a matching lower bound.We also show competitiveness results for a special class of algorithms (calledzealous algorithms) that do not allow waiting time for the server as long as there are requests unserved.

Abstract: Complementarity solvers are continually being challenged by modelers demanding improved reliability and scalability. Building upon a strong theoretical background, the semismooth algorithm has the potential to meet both of these requirements. We discuss relevant theory associated with the algorithm and then describe a sophisticated implementation in detail. Particular emphasis is given to the use of preconditioned iterative methods to solve the (nonsymmetric) systems of linear equations generated at each iteration and robust methods for dealing with singularity. Results on the MCPLIB test suite indicate that the code is reliable and efficient and scales well to very large problems.

Abstract: The use of predicates to state constraints in Constraint Satisfaction is explained. If, as an alternative, the traditional approach of Integer Programming (IP) is used, it is desirable to model these constraints so as to give as tight a linear programming relaxation as possible. One of the most commonly used predicates is the"all_different" predicate. Different applications of this are described together with different IP formulations. The facet defining constraints for the convex hull are then described and proved to be facet defining.

Abstract: We consider the bounded cycle-cover problem, which is to find a minimum cost cycle cover of a two-connected graph such that no cycle in the cover contains more than a prescribed numbered of edges. This problem arises in the design of fiber-optic telecommunications networks that employ multiple self-healing rings to provide routing for communication traffic, even in the event of a fiber cut or other type of link failure. We present this problem, along with several related problems, and develop heuristic algorithms that find near optimal solutions for the bounded cycle-cover problem based on solution techniques for these related problems. Empirical results of these algorithms, applied to randomly generated problem instances, are presented and discussed.

Abstract: Multiserver queues are often encountered in telecommunication systems and have special importance in the design of ATM networks. This paper analyzes a discrete-time multiserver queueing system with batch arrivals in which the interbatch and service times are, respectively, arbitrarily and geometrically distributed. Using supplementary-variable and embedded-Markov-chain techniques, the queue is analyzed only for the early arrival system. Since the late arrival system can be discussed similarly, it is not considered here. In addition to developing relations among state probabilities at prearrival, arbitrary, and outside observer's observation epochs, the numerical evaluation of state probabilities is also discussed. It is also shown that, in the limiting case, the relations developed here tend to continuous-time counterparts. Further, the waiting-time distribution of a random customer of a batch is obtained. Finally, in some cases simulation experiments have been performed to validate our results.

Abstract: This investigation presents a strategy to construct a compact mathematical model of the path-restoration version of the spare capacity allocation problem. The strategy uses a node-arc formulation and combines constraints whenever multiple working paths affected by an edge failure have identical origins or destinations. Another unique feature of this model is the inclusion of modularity restrictions corresponding to the discrete capacities of the equipment used in telecommunication networks.The new model can be solved using a classical branch-and-bound algorithm with a linear-programming relaxation. A preprocessing module is developed, which generates a set of cuts that strengthens this linear programming relaxation. The overhead associated with the cuts is offset by the improved bounds produced. A new branch-and-bound algorithm is developed that exploits the modularity restrictions. In an extensive empirical analysis, a software implementation of this algorithm was found to be substantially faster than CPLEX 6.5.3. For a test suite of 50 problems, each having 50 nodes and 200 demands from a uniform distribution with a small variance, our new software obtained solutions guaranteed to be within 4% of optimality in five minutes of CPU time on a DEC AlphaStation.

Abstract: We describe an exact algorithm for the problem of sorting a permutation by the minimum number of reversals, originating from evolutionary studies in molecular biology. Our approach is based on an integer linear programming formulation of a graph-theoretic relaxation of the problem, calling for a decomposition of the edge set of a bicolored graph into the maximum number of alternating cycles. The formulation has one variable for each alternating cycle, and the associated linear programming relaxation is solved by column generation.A major advantage with respect to previous approaches is that the subproblem to face in the column-generation phase no longer requires the solution of min-cost general matching problems, but of min-cost bipartite matching problems. Experiments show that there is a tremendous speed-up in going from general matching to bipartite matching, although the best-known algorithms for the two problems have the same theoretical worst-case complexity. We also show the worst-case ratio between the lower bound value obtained by our new method and previous ones.We illustrate the effectiveness of our approach through extensive computational experiments. In particular, we can solve to proven optimality the largest real-world instances from the literature in a few seconds, and the other (smaller) real-world instances within a few milliseconds on a workstation. Moreover, we can solve to optimality random instances with n = 100 within 3 seconds, and with n = 200 within 15 minutes, where n is the size of the permutation, whereas the size of the instances solvable by previous approaches was at most 100. We also describe a polynomial-time heuristic algorithm that consistently finds solutions within 2% of the optimum for random instances with n up to 1000.

Abstract: In this article we propose a model for the topological design problem of multitechnology networks that includes the location of switches and their port configuration, the design of an access network (with single and double access links) and a backbone network. The model specifically takes into account different types of modular switches where each type is characterized by its cost, its capacity in terms of the number of slots, and by its switch fabric capacity. The mutitechnology qualifier stems from the fact that several technologies and rates can be used in the access network. The proposed model is of the integer-programming variety, and in order to find a good solution, we propose a starting heuristic that provides an initial solution and the tabu-search algorithm to improve the solution. Lower bounds are proposed and used to assess the performance of the tabu-based approach. Numerical results for randomly generated problems with up to 500 clients and 50 potential switch sites are presented. The tabu-search algorithm produced solutions that were, on average, within 2.11% of the best lower bound.

Abstract: We examine the practice of batching of certain quadratic-form estimators for the variance parameter of a stochastic process. The class of batched quadratic-form estimators includes, among others, the standardized time series (STS) weighted area and weighted Cram�©r-von Mises estimators. We give results on the expected value and variance of such estimators as the batch size and/or the number of batches increase. In particular, we show that the above STS estimators are consistent for the variance parameter in terms of mean squared error. An analytical example involving a first-order autoregressive process illustrates our findings.

Abstract: In this note we point out that the assumptions of Propositions 1 and 2 in Gondzio (1997) are not sufficiently restrictive. We give an example that demonstrates the lack of precision in these propositions and discuss the necessary modifications of the propositions.

Abstract: This paper presents a new gradient estimator for the steady-state expected sojourn (system) time in a nonpreemptive priority queueing system. The estimator uses the concept of a phantom system, together with the basic ideas in harmonic gradient estimation, to develop a single simulation run estimator, termed thephantom harmonic gradient (PHG) estimator. The estimator is shown to be strongly consistent and strongly consistent in the average sense as the sample size grows. An upper bound for the variance of the PHG estimator is presented. This bound is used to show that under mild conditions, the variance of the PHG estimator tends to zero as both the number of phantom systems and the sample size approach infinity. A variance-reduction technique that simultaneously uses both common and antithetic random numbers is presented. Computational results on several nonpreemptive queueing systems illustrate the effectiveness of the method and show that common and antithetic random numbers can be used simultaneously to reduce the variance of the phantom harmonic gradient estimator.

Abstract: Degraeve and Schrage (1999) claim that “to the best of our knowledge, we are the first to find guaranteed integer optima to cutting stock problems having the typical real world complications of: 1) upper bounds on the amount by which a demand may be oversatisfied, 2) a limit on maximum waste allowed in each pattern and 3) a limit on the maximum slits in a cutting pattern.” Contrary to this claim, such integer optimal answers have been reported previously by Goulimis (1990b), with additional details by Goulimis (1990a). More recent work by Vanderbeck (1996, 1999) and also de Carvalho (1998) would seem to also bear many resemblances to the work presented in this paper, by combining dynamic column generation in a branchand-bound algorithm. References

Abstract: We describe a parallel, linear programming and implication-based heuristic for solving set partitioning problems on distributed memory computer architectures. Our implementation is carefully designed to exploit parallelism to greatest advantage in advanced techniques like preprocessing and probing, primal heuristics, and cut generation. A primaldual subproblem simplex method is used for solving the linear programming relaxation, which breaks the linear programming solution process into natural phases from which we can exploit information to find good solutions on the various processors. Implications from the probing operation are shared among the processors. Combining these techniques allows us to obtain solutions to large and difficult problems in a reasonable amount of computing time.

Abstract: We propose a specific method for generatingn-dimensional random vectors with given marginal distributions and correlation matrix. The method uses the NORTA (NORmal To Anything) approach, which generates a standard normal random vector and then transforms it into a random vector with specified marginal distributions. During initialization,n( n-1)/2 nonlinear equations need to be solved to ensure that the generated random vector has the specified correlation structure. To solve these equations, we apply retrospective approximation, a generic stochastic root-finding algorithm, with slight changes. Internal control variates are used to estimate function values. Empirical comparisons show that the control-variate variance-reduction technique improves the algorithm's convergence speed as well as its robustness. Simulation results for a variety of marginal distributions and correlation matrices are also presented.

Abstract: In this paper, we study a problem of scheduling and batching on two machines in a flow-shop and open-shop environment. Each machine processes operations in batches, and the processing time of a batch is the sum of the processing times of the operations in that batch. A setup time, which depends only on the machine, is required before a batch is processed on a machine, and all jobs in a batch remain at the machine until the entire batch is processed. The aim is to make batching and sequencing decisions, which specify a partition of the jobs into batches on each machine, and a processing order of the batches on each machine, respectively, so that the makespan is minimized. The flow-shop problem is shown to be strongly NP-hard. We demonstrate that there is an optimal solution with the same batches on the two machines; we refer to these asconsistent batches. A heuristic is developed that selects the best schedule among several with one, two, or three consistent batches, and is shown to have a worst-case performance ratio of 4/3. For the open-shop, we show that the problem is NP-hard in the ordinary sense. By proving the existence of an optimal solution with one, two or three consistent batches, a close relationship is established with the problem of scheduling two or three identical parallel machines to minimize the makespan. This allows a pseudo-polynomial algorithm to be derived, and various heuristic methods to be suggested.

Abstract: This paper concerns a decision-tree pruning method, a key issue in the development of decision trees. We propose a new method that applies the classical optimization technique, dynamic programming, to a decision-tree pruning procedure. We show that the proposed method generates a sequence of pruned trees that are optimal with respect to tree size. The dynamic-programming-based pruning (DPP) algorithm is then compared with cost-complexity pruning (CCP) in an experimental study. The results of our study indicate that DPP performs better than CCP in terms of classification accuracy.

Abstract: We provide several non-approximability results for deterministic scheduling problems whose objective is to minimize the total job completion time. Unless , none of the problems under consideration can be approximated in polynomial time within arbitrarily good precision. Most of our results are derived by APX-hardness proofs.We show that, whereas scheduling on unrelated machines with unit weights is polynomially solvable, the problem becomes APX-hard if release dates or weights are added. We further show APX-hardness for scheduling in flow shops, job shops, and open shops. We also investigate the problems of scheduling on parallel machines with precedence constraints and unit processing times, and two variants of the latter problem with unit communication delays; for these problems we provide lower bounds on the worst-case behavior of any polynomial-time approximation algorithm through the gap-reduction technique.