Showing papers in "Journal of Mathematical Modelling and Algorithms in 2011"
TL;DR: It is suggested that more needs to be done in resource-limited settings, such as sub-Saharan Africa, as far as the HIV/AIDS epidemic is concerned and a formalized information, education, and communication strategy should be given prominence in educational campaigns.
Abstract: We formulate a deterministic HIV/AIDS model to theoretically investigate how counselling and testing coupled with the resulting decrease in sexual activity could affect the HIV epidemic in resource-limited communities. The threshold quantities are determined and stabilities analyzed. Theoretical analysis and numerical simulations support the idea that increase in the number of sexually inactive HIV positive individuals who voluntarily abstain from sex has a positive impact on HIV/AIDS control. Results from this theoretical study suggest that effective counselling and testing have a great potential to partially control the epidemic (especially when HIV positive individuals either willingly withdraw from risky sexual activities or disclose their status beforehand) even in the absence of antiretroviral therapy (ART). Therefore, more needs to be done in resource-limited settings, such as sub-Saharan Africa, as far as the HIV/AIDS epidemic is concerned and a formalized information, education, and communication strategy should be given prominence in educational campaigns.
39 citations
TL;DR: This work considers a generalization of the Connected Facility Location Problem, suitable to model real world network extension scenarios such as fiber-to-the-curb, and presents two mixed integer programming based approaches which are solved using branch-and-cut and branch- and-cut-and price, respectively.
Abstract: We consider a generalization of the Connected Facility Location Problem (ConFL), suitable to model real world network extension scenarios such as fiber-to-the-curb. In addition to choosing a set of facilities and connecting them by a Steiner tree as in ConFL, we aim to maximize the resulting profit by potentially supplying only a subset of all customers. Furthermore, capacity constraints on potential facilities need to be considered. We present two mixed integer programming based approaches which are solved using branch-and-cut and branch-and-cut-and-price, respectively. By studying the corresponding polyhedra we analyze both approaches theoretically and show their advantages over previously presented models. Furthermore, using a computational study we are able to additionally show significant advantages of our models over previously presented ones from a practical point of view.
26 citations
TL;DR: The problem of optimum allocation in multivariate stratified random sampling in the presence of nonresponse has been formulated as a multiobjective integer nonlinear programming problem and a solution procedure is developed using goal programming technique.
Abstract: In a multivariate stratified sample survey with L strata and p > 1 characteristics, defined on each unit of the population, let the estimation of all the p-population means be of interest. As discussed by Cochran (1977), since the optimum allocation for one characteristic will not in general be optimum for other characteristics some compromise must be reached in a multiple characteristics stratified surveys. Various authors worked out allocations that are based on a compromise criterion. The resulting allocations are optimal for all characteristics in some sense, for example an allocation that minimizes the trace of the variance-covariance matrix of the estimators of the population means or an allocation that minimizes the weighted average of the variances or an allocation that maximizes the total relative efficiency of the estimators as compared to the corresponding individual optimum allocations. In the present paper the problem of optimum allocation in multivariate stratified random sampling in the presence of nonresponse has been formulated as a multiobjective integer nonlinear programming problem and a solution procedure is developed using goal programming technique. Three numerical examples are worked out to illustrate the computational details. A comparison of the proposed method with some well known methods is also carried out to show the practical utility of the proposed method.
18 citations
TL;DR: An improved and simplified approach is presented for design of nearly perfect reconstructed cosine-modulated (CM) filter banks with prescribed stopband attenuation and channel overlapping.
Abstract: An improved and simplified approach is presented for design of nearly perfect reconstructed cosine-modulated (CM) filter banks with prescribed stopband attenuation and channel overlapping. The method employs Kaiser window technique to design the prototype filter for filter banks with the novelty of exploiting spline functions in the transition band of the ideal filter instead of using the conventional brick-wall filter based on linear optimization of filter coefficients such that their value at frequency (??=??/2M) is 0.707. The simulation results illustrate the proposed method and its improvement over other existing methods in terms of amplitude distortion (e am ), number of iterations (NOI), aliasing distortion (e a ) and computation time (CPU time).
18 citations
TL;DR: A new method is proposed to find the fuzzy optimal solution of fuzzy transportation problems with the following transshipment: From a source to any another source, from a Destination to another destination, and from a destination to any source.
Abstract: To find the fuzzy optimal solution of fuzzy transportation problems it is assumed that the direct route between a source and a destination is a minimum-cost route. However, in actual application, the minimum-cost route is not known a priori. In fact, the minimum-cost route from one source to another destination may well pass through another source first. In this paper, a new method is proposed to find the fuzzy optimal solution of fuzzy transportation problems with the following transshipment: (1) From a source to any another source, (2) from a destination to another destination, and (3) from a destination to any source. In the proposed method all the parameters are represented by trapezoidal fuzzy numbers. To illustrate the proposed method a fuzzy transportation problem with transshipment is solved. The proposed method is easy to understand and to apply for finding the fuzzy optimal solution of fuzzy transportation problems with transshipment occurring in real life situations.
18 citations
TL;DR: The results reported in this paper indicate that decoy generation can be heavily constrained using top-ranked β-topologies as they are very likely to contain native or native-consistent β- topologies.
Abstract: One reason why ab initio protein structure predictors do not perform very well is their inability to reliably identify long-range interactions between amino acids. To achieve reliable long-range interactions, all potential pairings of β-strands (β-topologies) of a given protein are enumerated, including the native β-topology. Two very different β-topology scoring methods from the literature are then used to rank all potential β-topologies. This has not previously been attempted for any scoring method. The main result of this paper is a justification that one of the scoring methods, in particular, consistently top-ranks native β-topologies. Since the number of potential β-topologies grows exponentially with the number of β-strands, it is unrealistic to expect that all potential β-topologies can be enumerated for large proteins. The second result of this paper is an enumeration scheme of a subset of β-topologies. It is shown that native-consistent β-topologies often are among the top-ranked β-topologies of this subset. The presence of the native or native-consistent β-topologies in the subset of enumerated potential β-topologies relies heavily on the correct identification of β-strands. The third contribution of this paper is a method to deal with the inaccuracies of secondary structure predictors when enumerating potential β-topologies. The results reported in this paper are highly relevant for ab initio protein structure prediction methods based on decoy generation. They indicate that decoy generation can be heavily constrained using top-ranked β-topologies as they are very likely to contain native or native-consistent β-topologies.
11 citations
TL;DR: A matheuristic approach, where concepts from linear programming are integrated into an evolutionary algorithm, is proposed and tested on a problem arising in wireless sensor networks: a topology with minimum total power expenditure, that connects a source node to all the other nodes of the network.
Abstract: A matheuristic approach, where concepts from linear programming are integrated into an evolutionary algorithm, is proposed. It is tested on a problem arising in wireless sensor networks: a topology with minimum total power expenditure, that connects a source node to all the other nodes of the network, has to be identified. Experimental results are presented.
9 citations
TL;DR: It is shown that one of them is an NP-hard problem but the other is in P, presenting a novel methodology that links linear algebra theory to the graph problems as a part of proving the facts.
Abstract: We analyze two essential problems arising from edge-based graph partitioning. We show that one of them is an NP-hard problem but the other is in P, presenting a novel methodology that links linear algebra theory to the graph problems as a part of proving the facts. This is a significant trial in that linear algebra, which has been mostly adopted as a theoretical analysis tool, is practically applied to solving actual graph problems. As a result of the linear algebraic manipulation, we could devise a linear-time algorithm for the problem in P.
7 citations
TL;DR: An Economic Production Quantity model is developed with flexibility and reliability consideration of production process in an imprecise and uncertain mixed environment and is optimized using a multi-objective genetic algorithm (MOGA).
Abstract: In this paper, an Economic Production Quantity (EPQ) model is developed with flexibility and reliability consideration of production process in an imprecise and uncertain mixed environment. The model has incorporated fuzzy random demand, an imprecise production preparation time and shortage. Here, the setup cost and the reliability of the production process along with the backorder replenishment time and production run period are the decision variables. Due to fuzzy-randomness of the demand, expected average demand is a fuzzy quantity and also imprecise preparation time is represented by fuzzy number. Therefore, both are first transformed to a corresponding interval number and then using the interval arithmetic, the single objective function for expected profit over the time cycle is changed to respective multi-objective functions. Due to highly nonlinearity of the expected profit functions it is optimized using a multi-objective genetic algorithm (MOGA). The associated profit maximization problem is illustrated by numerical examples and also its sensitivity analysis is carried out.
7 citations
TL;DR: A deterministic HIV/AIDS model with delay is presented and extended by adjoining terms capturing stochastic effects, which shows no significant differences in the behavior of the two models.
Abstract: We present a deterministic HIV/AIDS model with delay. We then extend the model by adjoining terms capturing stochastic effects. The intensity of the fluctuations in the stochastic system is analytically evaluated using Fourier transform methods. We carry out simulations to assess differences in the dynamical behavior of the deterministic and stochastic models. Simulation results show that they are no significant differences in the behavior of the two models.
7 citations
TL;DR: A new algorithm, CLAM, is proposed, using a hybrid metaheuristic between VNS and Tabu Search to solve the problem of k-medoid clustering, and is compared to the well-known CLARANS.
Abstract: Clustering remains one of the most difficult challenges in data mining. This paper proposes a new algorithm, CLAM, using a hybrid metaheuristic between VNS and Tabu Search to solve the problem of k-medoid clustering. The new technique is compared to the well-known CLARANS. Experimental results show that, given the same computation times, CLAM is more effective.
TL;DR: A polynomial graph extension procedure that provides a graph coloring capable of rapidly guiding a simple-but-effective heuristic toward the solution of graph isomorphism (GI) properties is introduced.
Abstract: This paper deals with algorithms for detecting graph isomorphism (GI) properties. The GI literature consists of numerous research directions, from highly theoretical studies (e.g. defining the GI complexity class) to very practical applications (pattern recognition, image processing). We first present the context of our work and provide a brief overview of various algorithms developed in such disparate contexts. Compared to well-known NP-complete problems, GI is only rarely tackled with general-purpose combinatorial optimization techniques; however, classical search algorithms are commonly applied to graph matching (GM). We show that, by specifically focusing on exploiting isomorphism properties, classical GM heuristics can become very useful for GI. We introduce a polynomial graph extension procedure that provides a graph coloring (labeling) capable of rapidly guiding a simple-but-effective heuristic toward the solution. The resulting algorithm (GI-Ext) is quite simple, very fast and practical: it solves GI within a time in the region of O(|V|3) for numerous graph classes, including difficult (dense and regular) graphs with up to 20.000 vertices and 200.000.000 edges. GI-Ext can compete with recent state-of-the-art GI algorithms based on well-established GI techniques (e.g. canonical labeling) refined over the last three decades. In addition, GI-Ext also solves certain GM problems, e.g. it detects important isomorphic structures induced in non-isomorphic graphs.
TL;DR: The concept of snapshot dynamic indices as centrality measures to analyse how the importance of nodes changes over time in dynamic networks is introduced and some algorithms for computing these indices in the discrete-time case are introduced.
Abstract: The article introduces the concept of snapshot dynamic indices as centrality measures to analyse how the importance of nodes changes over time in dynamic networks. In particular, the dynamic stress-snapshot and dynamic betweenness snapshot are investigated. We present theoretical results on dynamic shortest paths in first-in first-out dynamic networks, and then introduce some algorithms for computing these indices in the discrete-time case. Finally, we present some experimental results exploring the algorithms' efficiency and illustrating the variation of the dynamic betweenness snapshot index for some sample dynamic networks.
TL;DR: The sensitivity analysis carried out suggests that the unit inspection cost, deterioration rate of units in inventory and stock-dependent parameter are the critical factors.
Abstract: In this paper, an integrated inventory model for a supply chain comprising of single buyer and single supplier is studied when demand is stock-dependent and units in inventory deteriorate at a constant rate. The total cost of the integrated system consists of the transportation cost, inspection cost and the cost of less flexibility under the assumption of JIT deliveries. The total integrated cost of single-supplier and single-buyer is minimized with respect to number of inspections and deliveries, the cycle time of deliveries and the delivery size for the replenishment time. A numerical example is given to validate the model. The sensitivity analysis carried out suggests that the unit inspection cost, deterioration rate of units in inventory and stock-dependent parameter are the critical factors.
TL;DR: This paper investigates a production lot-size inventory model for perishable items under two levels of trade credit for a retailer to reflect the supply chain management situation and proves that the annual total variable cost for the retailer is convex, that is, unique and global-optimal solution exists.
Abstract: This paper investigates a production lot-size inventory model for perishable items under two levels of trade credit for a retailer to reflect the supply chain management situation. We assume that the retailer maintains a powerful position and can obtain full trade credit offered by supplier yet retailer just offers the partial trade credit to customers. Under these conditions, retailer can obtain the most benefits. Then, we investigate the retailer's inventory policy as a cost minimization problem to determine the retailer's inventory policy. A rigorous mathematical analysis is used to prove that the annual total variable cost for the retailer is convex, that is, unique and global-optimal solution exists. Mathematical theorems are developed to efficiently determine the optimal ordering policies for the retailer. The results in this paper generalize some already published results. Finally, numerical examples are given to illustrate the theorems and obtain a lot of managerial phenomena.
TL;DR: This work proposes data structures for reporting violations of the minimum extension rule in a query window of interest with respect to VLSI design rule checking.
Abstract: Design Rule Checking (DRC) in VLSI design involves checking if a given VLSI layout satisfies a given set of rules and reporting the violations if any. We propose data structures for reporting violations of the minimum extension rule in a query window of interest.
TL;DR: This work formulate the dual power management problem in wireless sensor networks by a binary integer programming model to minimize the total power consumption and provides an iterative approximation based on iterative methods in combinatorial optimization.
Abstract: We study the dual power management problem in wireless sensor networks. Given a wireless sensor network with two possible power levels (heigh and low) for each sensor, the problem consists in minimizing the number of sensors assigned heigh power while ensuring the connectivity of the network. We formulate the problem by a binary integer programming model to minimize the total power consumption. Since the problem is NP-complete, we provide an iterative approximation based on iterative methods in combinatorial optimization. We solve the separation subproblem as a minimum spanning tree.
TL;DR: A method is described that uses unlabeled data to estimate the weight parameters needed to build an ensemble predictor integrating multiple trained component predictors, readily derived from a mathematical model of ensemble learning based on a generalized mixture of probability density functions and corresponding information divergence measures.
Abstract: When there are multiple trained predictors, one may want to integrate them into one predictor. However, this is challenging if the performances of the trained predictors are unknown and labeled data for evaluating their performances are not given. In this paper, a method is described that uses unlabeled data to estimate the weight parameters needed to build an ensemble predictor integrating multiple trained component predictors. It is readily derived from a mathematical model of ensemble learning based on a generalized mixture of probability density functions and corresponding information divergence measures. Numerical experiments demonstrated that the performance of our method is much better than that of simple average-based ensemble learning, even when the assumption placed on the performances of the component predictors does not hold exactly.
TL;DR: To find a control function which puts the heat equation in an unknown minimum time into a stationary regime, using an embedding method the problem of finding the time optimal control is reduced to one consisting of minimizing a linear form over a set of positive measures.
Abstract: To find a control function which puts the heat equation in an unknown minimum time into a stationary regime is considered. Using an embedding method, the problem of finding the time optimal control is reduced to one consisting of minimizing a linear form over a set of positive measures. The resulting problem can be approximated by a finite dimensional linear programming (LP) problem. The nearly optimal control is constructed from the solution of the final LP problem. To find the lower bound of the optimal time a search algorithm is proposed. Some examples demonstrate the effectiveness of the method.
TL;DR: The algorithm introduced here is especially efficient in the case of large problems, where cardinality and/or dimensions are large.
Abstract: The positive hull of a finite set of vectors, ${\cal V}$ , in d-dimensional space may or may not contain a lineality space ${\cal L}$ . This article presents an algorithm that identifies the vectors of ${\cal V}$ that belong to ${\cal L}$ . This is done by means of a sequence of supporting hyperplanes because every supporting hyperplane of the positive hull of ${\cal V}$ contains ${\cal L}$ . Computational results show the effectiveness of the algorithm, which is compared to the best procedure currently available (to the best knowledge of the author) that solves the same problem. The algorithm introduced here is especially efficient in the case of large problems, where cardinality and/or dimensions are large.
TL;DR: The result applies to any point-symmetric set in any dimension for all Lp metrics, 1 p < ∞ and provides asymptotic estimates as m and n grow large for the actual maximum value achieved by the above sum.
Abstract: Consider the set S of points in the plane consisting of the ordered pairs (i, j ), where $1 \leqslant i \leqslant m$ and $1 \leqslant j \leqslant n$ . A problem related to the study of segmentation evaluation of visual images concerns finding a permutation ? of the points of S for which the sum $$ \sum\limits_{s \in S}d(s, \sigma(s)) $$ is maximal among all possible permutations of S, where d denotes the Euclidean metric. In this note, we show that this maximum is achieved by exactly those permutations of S for which the line joining the points s and ?(s) passes through the point $(\frac{m+1}{2},\frac{n+1}{2})$ for all s???S. In fact, the result applies to any point-symmetric set in any dimension for all L p metrics, 1?
TL;DR: It is shown that, the erasure(t erasures mean that t components of a code vector are erased) decoding Gabidulin code can be seen as a computation of three matrice and an affine permutation, instead of computing an inverse from the generator or parity check matrix.
Abstract: We present a new approach of the decoding algorithm for Gabidulin Codes. In the same way as efficient erasure decoding for Generalized Reed Solomon codes by using the structure of the inverse of the VanderMonde matrices, we show that, the erasure(t erasures mean that t components of a code vector are erased) decoding Gabidulin code can be seen as a computation of three matrice and an affine permutation, instead of computing an inverse from the generator or parity check matrix. This significantly reduces the decoding complexity compared to others algorithms. For t erasures with t ? r, where r?=?n???k, the erasure algorithm decoding for Gab n, k (g) Gabidulin code compute the t symbols by simple multiplication of three matrices. That requires rt?+?r(k???1) Galois field multiplications, t(r???1)?+?(t + r)k field additions, r 2?+?r(k?+?1) field negations and t(k?+?1) field inversions.
TL;DR: This paper considers a trust region algorithm for unconstrained optimization problems that includes memory of the past iteration, which makes the algorithm less myopic in the sense that its behavior is not completely dominated by the local nature of the objective function, but rather by a more global view.
Abstract: In this paper, we consider a trust region algorithm for unconstrained optimization problems. Unlike the traditional memoryless trust region methods, our trust region model includes memory of the past iteration, which makes the algorithm less myopic in the sense that its behavior is not completely dominated by the local nature of the objective function, but rather by a more global view. The global convergence is established by using a nonmonotone technique. The numerical tests are also given to show the efficiency of our proposed method.