INFORMS Journal on Computing current issue

Heuristic and Exact Algorithms for the Identical Parallel Machine Scheduling Problem

Dell'Amico, M., Iori, M., Martello, S., Monaci, M. — 2008-07-09

Given a set of jobs with associated processing times, and a set of identical machines, each of which can process at most one job at a time, the parallel machine scheduling problem is to assign each job to exactly one machine so as to minimize the maximum completion time of a job. The problem is strongly NP-hard and has been intensively studied since the 1960s. We present a metaheuristic and an exact algorithm and analyze their average behavior on a large set of test instances from the literature. The metaheuristic algorithm, which is based on a scatter search paradigm, computationally proves to be highly effective and capable of solving to optimality a very high percentage of the publicly available test instances. The exact algorithm, which is based on a specialized binary search and a branch-and-price scheme, was able to quickly solve to optimality all remaining instances.

Predicting Bidders' Willingness to Pay in Online Multiunit Ascending Auctions: Analytical and Empirical Insights

Bapna, R., Goes, P., Gupta, A., Karuga, G. — 2008-07-09

We develop a real-time estimation approach to predict bidders' maximum willingness to pay in a multiunit ascending uniform-price and discriminatory-price (Yankee) online auction. Our two-stage approach begins with a bidder classification step, which is followed by an analytical prediction model. The classification model identifies bidders as either adopting a myopic best-response (MBR) bidding strategy or a non-MBR strategy. We then use a generalized bid-inversion function to estimate the willingness to pay for MBR bidders. We empirically validate our two-stage approach using data from two popular online auction sites. Our joint classification-and-prediction approach outperforms two other naïve prediction strategies that draw random valuations between a bidder's current bid and the known market upper bound. Our prediction results indicate that, on average, our estimates are within 2% of bidders' revealed willingness to pay for Yankee and uniform-price multiunit auctions. We discuss how our results can facilitate mechanism-design changes such as dynamic-bid increments and dynamic buy-it-now prices.

Improving Intrusion Prevention Models: Dual-Threshold and Dual-Filter Approaches

Ryu, Y. U., Rhee, H.-S. — 2008-07-09

Intrusion detection, once considered as the last line of defense in the layered architecture for technical security, is observed not to deliver the promised protection. It suffers from high false-alarm rates and puts too much of a burden on the information security officers. Intrusion prevention has evolved from intrusion detection technologies to overcome difficulties faced in intrusion detection and more actively encounter ever-increasing attacks. While intrusion prevention provides immediate/real-time protection, it suffers from two deficiencies, which are the sensitivity and specificity trade-off and the accuracy and efficiency trade-off. To address these issues, we introduce two models of intrusion prevention. The first model is for a hybrid system playing both detection and protection roles. The second model suggests the use of dual filters in the evaluation of activities. Mathematical programming formulations for both models are developed and optional configuration solutions are proposed.

Extreme Point-Based Heuristics for Three-Dimensional Bin Packing

Crainic, T. G., Perboli, G., Tadei, R. — 2008-07-09

One of the main issues in addressing three-dimensional packing problems is finding an efficient and accurate definition of the points at which to place the items inside the bins, because the performance of exact and heuristic solution methods is actually strongly influenced by the choice of a placement rule. We introduce the extreme point concept and present a new extreme point-based rule for packing items inside a three-dimensional container. The extreme point rule is independent from the particular packing problem addressed and can handle additional constraints, such as fixing the position of the items. The new extreme point rule is also used to derive new constructive heuristics for the three-dimensional bin-packing problem. Extensive computational results show the effectiveness of the new heuristics compared to state-of-the-art results. Moreover, the same heuristics, when applied to the two-dimensional bin-packing problem, outperform those specifically designed for the problem.

Efficient Jump Ahead for F2-Linear Random Number Generators

Haramoto, H., Matsumoto, M., Nishimura, T., Panneton, F., L'Ecuyer, P. — 2008-07-09

The fastest long-period random number generators currently available are based on linear recurrences modulo 2. So far, software that provides multiple disjoint streams and substreams has not been available for these generators because of the lack of efficient jump-ahead facilities. In principle, it suffices to multiply the state (a k-bit vector) by an appropriate k x k binary matrix to find the new state far ahead in the sequence. However, when k is large (e.g., for a generator such as the popular Mersenne twister, for which k = 19,937), this matrix-vector multiplication is slow, and a large amount of memory is required to store the k x k matrix. In this paper, we provide a faster algorithm to jump ahead by a large number of steps in a linear recurrence modulo 2. The method uses much less than the k² bits of memory required by the matrix method. It is based on polynomial calculus modulo the characteristic polynomial of the recurrence, and uses a sliding window algorithm for the multiplication.

Optimal Broadcast Scheduling in Packet Radio Networks via Branch and Price

Menon, S., Gupta, R. — 2008-07-09

Packet radio networks use spatial time-division multiple-access to enable multiple network stations to communicate via the same frequency within the same time slot. Stations in close proximity are not allowed to use the same frequency, as their signals would interfere with each other. In this context, an important design problem is that of scheduling access to the high-speed communications channel in such a way as to maximize the utilization while avoiding interference and keeping the frame length to a minimum. This is frequently referred to as the broadcast scheduling problem and is known to be NP-hard. It is often formulated as a nonlinear discrete optimization problem for a given frame length and solved via heuristic approaches by parametrically varying the length of the frame. Despite this, the sizes of the problems solved have been small, with the solution times becoming prohibitive with increasing problem size. This paper introduces a set covering formulation for the problem and solves it optimally using branch and price. Columns are generated using a simple pricing heuristic whenever possible. A branching strategy adapted from [Vance, P. 1998. Branch-and-price algorithms for the one-dimensional cutting stock problem. Computational Optim. Appl. 9 211–228] is used, while branching first on the number of time slots used. Extensive computational results show that this approach is very effective, identifying optimal solutions quickly even on problems significantly larger than those solved previously.

The Bicriterion Multimodal Assignment Problem: Introduction, Analysis, and Experimental Results

Pedersen, C. R., Nielsen, L. R., Andersen, K. A. — 2008-07-09

We consider the bicriterion multimodal assignment problem, which is a new generalization of the classical linear assignment problem. A two-phase solution method using an effective ranking scheme is presented. The algorithm is valid for generating all nondominated criterion points or an approximation. Extensive computational results are conducted on a large library of test instances to test the performance of the algorithm and to identify hard test instances. Also, test results of the algorithm applied to the bicriterion assignment problem are provided.

A Maximal-Space Algorithm for the Container Loading Problem

Parreno, F., Alvarez-Valdes, R., Tamarit, J. M., Oliveira, J. F. — 2008-07-09

In this paper, a greedy randomized adaptive search procedure (GRASP) for the container loading problem is presented. This approach is based on a constructive block heuristic that builds upon the concept of maximal space, a nondisjoint representation of the free space in a container.

This new algorithm is extensively tested over the complete set of Bischoff and Ratcliff problems [Bischoff, E. E., M. S. W. Ratcliff. 1995. Issues in the development of approaches to container loading. Omega 23 377–390], ranging from weakly heterogeneous to strongly heterogeneous cargo, and outperforms all the known nonparallel approaches that, partially or completely, have used this set of test problems. When comparing against parallel algorithms, it is better on average but not for every class of problem. In terms of efficiency, this approach runs in much less computing time than that required by parallel methods. Thorough computational experiments concerning the evaluation of the impact of algorithm design choices and internal parameters on the overall efficiency of this new approach are also presented.

Tabu Search-Enhanced Graphical Models for Classification in High Dimensions

Bai, X., Padman, R., Ramsey, J., Spirtes, P. — 2008-07-09

Data sets with many discrete variables and relatively few cases arise in health care, e-commerce, information security, text mining, and many other domains. Learning effective and efficient prediction models from such data sets is a challenging task. In this paper, we propose a tabu search-enhanced Markov blanket (TS/MB) algorithm to learn a graphical Markov blanket model for classification of high-dimensional data sets. The TS/MB algorithm makes use of Markov blanket neighborhoods: restricted neighborhoods in a general Bayesian network based on the Markov condition. Computational results from real-world data sets drawn from several domains indicate that the TS/MB algorithm, when used as a feature selection method, is able to find a parsimonious model with substantially fewer predictor variables than is present in the full data set. The algorithm also provides good prediction performance when used as a graphical classifier compared with several machine-learning methods.

A Lifted Linear Programming Branch-and-Bound Algorithm for Mixed-Integer Conic Quadratic Programs

Vielma, J. P., Ahmed, S., Nemhauser, G. L. — 2008-07-09

This paper develops a linear-programming-based branch-and-bound algorithm for mixed-integer conic quadratic programs. The algorithm is based on a known higher-dimensional or lifted polyhedral relaxation of conic quadratic constraints. The algorithm is different from other linear-programming-based branch-and-bound algorithms for mixed-integer nonlinear programs in that it is not based on cuts from gradient inequalities and it sometimes branches on integer feasible solutions. The algorithm is tested on a series of portfolio optimization problems. It is shown that it significantly outperforms commercial and open-source solvers based on both linear and nonlinear relaxations.

A Review and Evaluation of Multiobjective Algorithms for the Flowshop Scheduling Problem

Minella, G., Ruiz, R., Ciavotta, M. — 2008-07-09

This paper contains a complete and updated review of the literature for multiobjective flowshop problems, which are among the most studied environments in the scheduling research area. No previous comprehensive reviews exist in the literature. Papers about lexicographical, goal programming, objective weighting, and Pareto approaches have been reviewed. Exact, heuristic, and metaheuristic methods have been surveyed. Furthermore, a complete computational evaluation is also carried out. A total of 23 different algorithms including both flowshop-specific methods as well as general multiobjective optimization approaches have been tested under three different two-criteria combinations with a comprehensive benchmark. All methods have been studied under recent state-of-the-art quality measures. Parametric and nonparametric statistical testing is profusely employed to support the observed performance of the compared methods. As a result, we have identified the best-performing methods from the literature, which along with the review, constitutes a reference work for further research.

A Multiobjective Branch-and-Bound Framework: Application to the Biobjective Spanning Tree Problem

Sourd, F., Spanjaard, O. — 2008-07-09

This paper focuses on a multiobjective derivation of branch-and-bound procedures. Such a procedure aims to provide the set of Pareto-optimal solutions of a multiobjective combinatorial optimization problem. Unlike previous works on this issue, the bounding is performed here via a set of points rather than a single ideal point. The main idea is that a node in the search tree can be discarded if one can define a separating hypersurface in the objective space between the set of feasible solutions in the subtree and the set of points corresponding to potential Pareto-optimal solutions. Numerical experiments on the biobjective spanning tree problem are provided that show the efficiency of the approach in a biobjective setting.

Evaluation of the ARTAFIT Method for Fitting Time-Series Input Processes for Simulation

Biller, B., Nelson, B. L. — 2008-07-09

Time-series input processes occur naturally in the stochastic simulation of many service, communications, and manufacturing systems, and there are a variety of time-series input models available to match a given collection of properties, typically a marginal distribution and an autocorrelation structure specified via the use of one or more time lags. The focus of this paper is the situation in which the collection of properties are not "given," but data are available from which a time-series input model is to be estimated. The input model we consider is the very flexible autoregressive-to-anything (ARTA) model of Cario and Nelson [Cario, M. C., B. L. Nelson. 1996. Autoregressive to anything: Time-series input processes for simulation. Oper. Res. Lett. 19 51–58]. Recently, we developed a statistically valid algorithm (ARTAFIT) for fitting this model to stationary univariate time-series data using marginal distributions from the Johnson translation system. In this paper, we perform a comprehensive numerical study to assess the performance of our algorithm relative to the two most commonly used approaches: (a) fitting the marginal distribution but ignoring the autocorrelation structure, and (b) fitting separately the marginal distribution as in (a) and the autocorrelation structure using the sample autocorrelation function. We find that ARTAFIT, which fits the marginal distribution and the autocorrelation structure jointly, outperforms both (a) and (b), and we demonstrate the importance of taking dependencies into account while developing input models for stochastic simulation.