Showing papers on "Integer programming published in 2003"
TL;DR: This work proposes a robust integer programming problem of moderately larger size that allows controlling the degree of conservatism of the solution in terms of probabilistic bounds on constraint violation, and proposes an algorithm for robust network flows that solves the robust counterpart by solving a polynomial number of nominal minimum cost flow problems in a modified network.
Abstract: We propose an approach to address data uncertainty for discrete optimization and network flow problems that allows controlling the degree of conservatism of the solution, and is computationally tractable both practically and theoretically. In particular, when both the cost coefficients and the data in the constraints of an integer programming problem are subject to uncertainty, we propose a robust integer programming problem of moderately larger size that allows controlling the degree of conservatism of the solution in terms of probabilistic bounds on constraint violation. When only the cost coefficients are subject to uncertainty and the problem is a 0−1 discrete optimization problem on n variables, then we solve the robust counterpart by solving at most n+1 instances of the original problem. Thus, the robust counterpart of a polynomially solvable 0−1 discrete optimization problem remains polynomially solvable. In particular, robust matching, spanning tree, shortest path, matroid intersection, etc. are polynomially solvable. We also show that the robust counterpart of an NP-hard α-approximable 0−1 discrete optimization problem, remains α-approximable. Finally, we propose an algorithm for robust network flows that solves the robust counterpart by solving a polynomial number of nominal minimum cost flow problems in a modified network.
1,747 citations
TL;DR: This work investigates the general problem of phase unwrapping for arbitrary N‐dimensional phase maps and a cost function‐based approach is outlined that leads to an integer programming problem, and a best‐pair‐first region merging approach is adopted as the optimization method.
Abstract: This work investigates the general problem of phase unwrapping for arbitrary N-dimensional phase maps. A cost function-based approach is outlined that leads to an integer programming problem. To solve this problem, a best-pair-first region merging approach is adopted as the optimization method. The algorithm was implemented and tested with 3D MRI medical data for venogram studies, as well as for fMRI applications in EPI unwarping and rapid, automated shimming.
709 citations
TL;DR: In this article, the authors consider single-level lot sizing problems, their variants and solution approaches, together with exact and heuristic approaches for their solution, and conclude with some suggestions for future research.
Abstract: Lot sizing is one of the most important and also one of the most difficult problems in production planning. This subject has been studied extensively in the literature. In this article, we consider single-level lot sizing problems, their variants and solution approaches. After introducing factors affecting formulation and the complexity of production planning problems, and introducing different variants of lot sizing and scheduling problems, we discuss single-level lot sizing problems, together with exact and heuristic approaches for their solution. We conclude with some suggestions for future research.
670 citations
TL;DR: A network flow model for identifying optimal lane-based evacuation routing plans in a complex road network is presented, an integer extension of the minimum-cost flow problem that can be used to generate routing plans that trade total vehicle travel-distance against merging, while preventing traffic crossing-conflicts at intersections.
Abstract: Most traffic delays in regional evacuations occur at intersections. Lane-based routing is one strategy for reducing these delays. This paper presents a network flow model for identifying optimal lane-based evacuation routing plans in a complex road network. The model is an integer extension of the minimum-cost flow problem. It can be used to generate routing plans that trade total vehicle travel-distance against merging, while preventing traffic crossing-conflicts at intersections. A mixed-integer programming solver is used to derive optimal routing plans for a sample network. Manual capacity analysis and microscopic traffic simulation are used to compare the relative efficiency of the plans. An application is presented for Salt Lake City, Utah.
483 citations
TL;DR: In this article, a mixed-integer LP approach to the solution of the long-term transmission expansion planning problem is presented. But this approach is not suitable for large-scale systems, as the problem is large scale, mixed integer, nonlinear, and nonconvex.
Abstract: This paper presents a mixed-integer LP approach to the solution of the long-term transmission expansion planning problem. In general, this problem is large-scale, mixed-integer, nonlinear, and nonconvex. We derive a mixed-integer linear formulation that considers losses and guarantees convergence to optimality using existing optimization software. The proposed model is applied to Garver's 6-bus system, the IEEE Reliability Test System, and a realistic Brazilian system. Simulation results show the accuracy as well as the efficiency of the proposed solution technique.
454 citations
TL;DR: This work describes a decomposition-based separation methodology for the capacity constraints that takes advantage of the ability to solve small instances of the TSP efficiently and presents some extensions of this basic concept and a general framework within which it can be applied to other combinatorial models.
Abstract: We consider the Vehicle Routing Problem, in which a fixed fleet of delivery vehicles of uniform capacity must service known customer demands for a single commodity from a common depot at minimum transit cost. This difficult combinatorial problem contains both the Bin Packing Problem and the Traveling Salesman Problem (TSP) as special cases and conceptually lies at the intersection of these two well-studied problems. The capacity constraints of the integer programming formulation of this routing model provide the link between the underlying routing and packing structures. We describe a decomposition-based separation methodology for the capacity constraints that takes advantage of our ability to solve small instances of the TSP efficiently. Specifically, when standard procedures fail to separate a candidate point, we attempt to decompose it into a convex combination of TSP tours; if successful, the tours present in this decomposition are examined for violated capacity constraints; if not, the Farkas Theorem provides a hyperplane separating the point from the TSP polytope. We present some extensions of this basic concept and a general framework within which it can be applied to other combinatorial models. Computational results are given for an implementation within the parallel branch, cut, and price framework SYMPHONY.
324 citations
TL;DR: Large scale benchmark test for fold recognition shows that RAPTOR significantly outperforms other programs at the fold similarity level, and also performs very well in recognizing the hard Homology Modeling (HM) targets.
Abstract: This paper presents a novel linear programming approach to do protein 3-dimensional (3D) structure prediction via threading. Based on the contact map graph of the protein 3D structure template, the protein threading problem is formulated as a large scale integer programming (IP) problem. The IP formulation is then relaxed to a linear programming (LP) problem, and then solved by the canonical branch-and-bound method. The final solution is globally optimal with respect to energy functions. In particular, our energy function includes pairwise interaction preferences and allowing variable gaps which are two key factors in making the protein threading problem NP-hard. A surprising result is that, most of the time, the relaxed linear programs generate integral solutions directly. Our algorithm has been implemented as a software package RAPTOR-RApid Protein Threading by Operation Research technique. Large scale benchmark test for fold recognition shows that RAPTOR significantly outperforms other programs at the fold similarity level. The CAFASP3 evaluation, a blind and public test by the protein structure prediction community, ranks RAPTOR as top 1, among individual prediction servers, in terms of the recognition capability and alignment accuracy for Fold Recognition (FR) family targets. RAPTOR also performs very well in recognizing the hard Homology Modeling (HM) targets. RAPTOR was implemented at the University of Waterloo and it can be accessed at http://www.cs.uwaterloo.ca/~j3xu/RAPTOR_form.htm.
273 citations
TL;DR: This work adopts a (quasi-)static view of the RWA problem and proposes new integer-linear programming formulations, which can be addressed with highly efficient linear programming methods and yield optimal or near-optimal RWA policies.
Abstract: The problem of routing and wavelength assignment (RWA) is critically important for increasing the efficiency of wavelength-routed all-optical networks. Given the physical network structure and the required connections, the RWA problem is to select a suitable path and wavelength among the many possible choices for each connection so that no two paths sharing a link are assigned the same wavelength. In work to date, this problem has been formulated as a difficult integer programming problem that does not lend itself to efficient solution or insightful analysis. In this work, we propose several novel optimization problem formulations that offer the promise of radical improvements over the existing methods. We adopt a (quasi-)static view of the problem and propose new integer-linear programming formulations, which can be addressed with highly efficient linear (not integer) programming methods and yield optimal or near-optimal RWA policies. The fact that this is possible is surprising, and is the starting point for new and greatly improved methods for RWA. Aside from its intrinsic value, the quasi-static solution method can form the basis for suboptimal solution methods for the stochastic/dynamic settings.
254 citations
TL;DR: Column generation based solution approaches to a pickup and delivery vehicle routing problem commonly encountered in real-world logistics operations that involves a set of practical complications that have received little attention in the vehicle routing literature are proposed.
Abstract: We consider a pickup and delivery vehicle routing problem commonly encountered in real-world logistics operations. The problem involves a set of practical complications that have received little attention in the vehicle routing literature. In this problem, there are multiple carriers and multiple vehicle types available to cover a set of pickup and delivery orders, each of which has multiple pickup time windows and multiple delivery time windows. Orders and carrier/vehicle types must satisfy a set of compatibility constraints that specify which orders cannot be covered by which carrier/vehicle types and which orders cannot be shipped together. Order loading and unloading sequence must satisfy the nested precedence constraint that requires that an order cannot be unloaded until all the orders loaded into the truck later than this order are unloaded. Each vehicle trip must satisfy the driver's work rules prescribed by the Department of Transportation which specify legal working hours of a driver. The cost of a trip is determined by several factors including a fixed charge, total mileage, total waiting time, and total layover time of the driver. We propose column generation based solution approaches to this complex problem. The problem is formulated as a set partitioning type formulation containing an exponential number of columns. We apply the standard column generation procedure to solve the linear relaxation of this set partitioning type formulation in which the resulting master problem is a linear program and solved very efficiently by an LP solver, while the resulting subproblems are computationally intractable and solved by fast heuristics. An integer solution is obtained by using an IP solver to solve a restricted version of the original set partitioning type formulation that only contains the columns generated in solving the linear relaxation. The approaches are evaluated based on lower bounds obtained by solving the linear relaxation to optimality by using an exact dynamic programming algorithm to solve the subproblems exactly. It is shown that the approaches are capable of generating near-optimal solutions quickly for randomly generated instances with up to 200 orders. For larger randomly generated instances with up to 500 orders, it is shown that computational times required by these approaches are acceptable.
243 citations
TL;DR: An integration of multi-criteria decision analysis (MCDA) and inexact mixed integer linear programming (IMILP) methods to support selection of an optimal landfill site and a waste-flow-allocation pattern such that the total system cost can be minimized.
241 citations
TL;DR: A new methodology for reliably solving the correspondence problem between sparse sets of points of two or more images is proposed, which performs correspondence and outlier rejection in a single step and achieves global optimality with feasible computation.
Abstract: We propose a new methodology for reliably solving the correspondence problem between sparse sets of points of two or more images. This is a key step inmost problems of computer vision and, so far, no general method exists to solve it. Our methodology is able to handle most of the commonly used assumptions in a unique formulation, independent of the domain of application and type of features. It performs correspondence and outlier rejection in a single step and achieves global optimality with feasible computation. Feature selection and correspondence are first formulated as an integer optimization problem. This is a blunt formulation, which considers the whole combinatorial space of possible point selections and correspondences. To find its global optimal solution, we build a concave objective function and relax the search domain into its convex-hull. The special structure of this extended problem assures its equivalence to the original one, but it can be optimally solved by efficient algorithms that avoid combinatorial search. This methodology can use any criterion provided it can be translated into cost functions with continuous second derivatives.
TL;DR: This paper proposes a strategic production-distribution model for supply chain design with consideration of bills of materials, and shows how these relationships are formulated as logical constraints in a mixed integer programming (MIP) model, thus capturing the role of BOM in the selection of suppliers in the strategic design of a supply chain.
TL;DR: It is shown that the linear programming relaxation of three textbook mixed-integer programming formulations each approximates the cost function by its lower convex envelope, and a relationship between this result and classical Lagrangian duality theory is shown.
Abstract: We study a generic minimization problem with separable nonconvex piecewise linear costs, showing that the linear programming (LP) relaxation of three textbook mixed-integer programming formulations each approximates the cost function by its lower convex envelope. We also show a relationship between this result and classical Lagrangian duality theory.
TL;DR: In this article, a lane-based optimization method for the integrated design of lane markings and signal settings for isolated junctions is presented, where both traffic and pedestrian movements are considered in a unified framework.
Abstract: This paper presents a lane-based optimization method for the integrated design of lane markings and signal settings for isolated junctions. Both traffic and pedestrian movements are considered in a unified framework. Capacity maximization and cycle length minimization problems are considered. The problems are formulated as Binary-Mix-Integer-Linear-Programs (BMILP), which are solvable by any standard branch-and-bound routine. The integer variables include the permitted movements on traffic lanes and successor functions to govern the order of signal displays, whereas the continuous variables include the assigned lane flows, common flow multiplier, cycle length, and starts and durations of green for traffic movements and lanes and pedestrian crossings. A set of constraints are set up to ensure feasibility and safety of the resulting optimal lane markings and signal settings. Numerical examples are given to demonstrate the effectiveness of the proposed method.
04 Jun 2003
TL;DR: A formulation for model predictive control is presented for application to vehicle maneuvering problems in which the target regions need not contain equilibrium points, allowing the inclusion of non-convex avoidance constraints.
Abstract: A formulation for model predictive control is presented for application to vehicle maneuvering problems in which the target regions need not contain equilibrium points. Examples include a spacecraft rendezvous approach to a radial separation form the target and a UAV required to fly through several waypoints. Previous forms of MPC are not applicable to this class of problems because they are tailored to the control of plants about steady-state conditions. Mixed-integer linear programming is used to solve the trajectory optimizations, allowing the inclusion of non-convex avoidance constraints. Analytical proofs are given to show that the problem will always be completed in finite time and that, subject to initial feasibility, the optimization solved at each step will always be feasible in the presence of a bounded disturbance. The formulation is demonstrated in several simulations, including both aircraft and spacecraft, with extension to multiple vehicle programs.
TL;DR: In this article, the authors address the use of spatial optimization techniques for solving multi-site land-use allocation (MLUA) problems, where MLUA refers to the optimal allocation of multiple sites of different land uses to an area.
Abstract: Research in the area of spatial decision support (SDS) and resource allocation has recently generated increased attention for integrating optimization techniques with GIS. In this paper we address the use of spatial optimization techniques for solving multi-site land-use allocation (MLUA) problems, where MLUA refers to the optimal allocation of multiple sites of different land uses to an area. We solve an MLUA problem using four different integer programs (IP), of which three are linear integer programs. The IPs are formulated for a raster-based GIS environment and are designed to minimize development costs and to maximize compactness of the allocated land use. The preference for either minimizing costs or maximizing compactness has been made operational by including a weighting factor. The IPs are evaluated on their speed and their efficacy for handling large databases. All four IPs yielded the optimal solution within a reasonable amount of time, for an area of 8 × 8 cells. The fastest model was successfully applied to a case study involving an area of 30 × 30 cells. The case study demonstrates the practical use of linear IPs for spatial decision support issues.
25 Jun 2003
TL;DR: The results are that the Pure Parsimony problem can be solved efficiently in practice for a wide range of problem instances of current interest in biology.
Abstract: The next high-priority phase of human genomics will involve the development and use of a full Haplotype Map of the human genome [7]. A critical, perhaps dominating, problem in all such efforts is the inference of large-scale SNP-haplotypes from raw genotype SNP data. This is called the Haplotype Inference (HI) problem. Abstractly, input to the HI problem is a set of n strings over a ternary alphabet. A solution is a set of at most 2n strings over the binary alphabet, so that each input string can be "generated" by some pair of the binary strings in the solution. For greatest biological fidelity, a solution should be consistent with, or evaluated by, properties derived from an appropriate genetic model.
A natural model, that has been suggested repeatedly is called here the Pure Parsimony model, where the goal is to find a smallest set of binary strings that can generate the n input strings. The problem of finding such a smallest set is called the Pure Parsimony Problem. Unfortunately, the Pure Parsimony problem is NP-hard, and no paper has previously shown how an optimal Pure-parsimony solution can be computed efficiently for problem instances of the size of current biological interest. In this paper, we show how to formulate the Pure-parsimony problem as an integer linear program; we explain how to improve the practicality of the integer programming formulation; and we present the results of extensive experimentation we have done to show the time and memory practicality of the method, and to compare its accuracy against solutions found by the widely used general haplotyping program PHASE. We also formulate and experiment with variations of the Pure-Parsimony criteria, that allow greater practicality. The results are that the Pure Parsimony problem can be solved efficiently in practice for a wide range of problem instances of current interest in biology. Both the time needed for a solution, and the accuracy of the solution, depend on the level of recombination in the input strings. The speed of the solution improves with increasing recombination, but the accuracy of the solution decreases with increasing recombination.
TL;DR: This study addresses the routing and wavelength-assignment problem in a network with path protection under duct-layer constraints in a wavelength-division multiplexing (WDM) network in which failures occur due to fiber cuts.
Abstract: This study investigates the problem of fault management in a wavelength-division multiplexing (WDM)-based optical mesh network in which failures occur due to fiber cuts. In reality, bundles of fibers often get cut at the same time due to construction or destructive natural events, such as earthquakes. Fibers laid down in the same duct have a significant probability to fail at the same time. When path protection is employed, we require the primary path and the backup path to be duct-disjoint, so that the network is survivable under single-duct failures. Moreover, if two primary paths go through any common duct, their backup paths cannot share wavelengths on common links. This study addresses the routing and wavelength-assignment problem in a network with path protection under duct-layer constraints. Off-line algorithms for static traffic is developed to combat single-duct failures. The objective is to minimize total number of wavelengths used on all the links in the network. Both integer linear programs and a heuristic algorithm are presented and their performance is compared through numerical examples.
TL;DR: This work addresses the problem of identifying subsets of constraints which, when removed, lead to a consistent system and presents two algorithms to identify such subsets using mixed integer linear programming and linear programming.
TL;DR: This work identifies corresponding two- and multi-stage stochastic integer programs that are large-scale block-structured mixed-integer linear programs if the underlying probability distributions are discrete.
Abstract: Including integer variables into traditional stochastic linear programs has considerable implications for structural analysis and algorithm design. Starting from mean-risk approaches with different risk measures we identify corresponding two- and multi-stage stochastic integer programs that are large-scale block-structured mixed-integer linear programs if the underlying probability distributions are discrete. We highlight the role of mixed-integer value functions for structure and stability of stochastic integer programs. When applied to the block structures in stochastic integer programming, well known algorithmic principles such as branch-and-bound, Lagrangian relaxation, or cutting plane methods open up new directions of research. We review existing results in the field and indicate departure points for their extension.
TL;DR: This computational study covers different types of resource-constrained project scheduling problems, based on several notoriously hard test sets, including practical problem instances from chemical production planning.
Abstract: In project scheduling, a set of precedence-constrained jobs has to be scheduled so as to minimize a given objective. In resource-constrained project scheduling, the jobs additionally compete for scarce resources. Due to its universality, the latter problem has a variety of applications in manufacturing, production planning, project management, and elsewhere. It is one of the most intractable problems in operations research, and has therefore become a popular playground for the latest optimization techniques, including virtually all local search paradigms. We show that a somewhat more classical mathematical programming approach leads to both competitive feasible solutions and strong lower bounds, within reasonable computation times. The basic ingredients of our approach are the Lagrangian relaxation of a time-indexed integer programming formulation and relaxation-based list scheduling, enriched with a useful idea from recent approximation algorithms for machine scheduling problems. The efficiency of the algorithm results from the insight that the relaxed problem can be solved by computing a minimum cut in an appropriately defined directed graph. Our computational study covers different types of resource-constrained project scheduling problems, based on several notoriously hard test sets, including practical problem instances from chemical production planning.
TL;DR: In this paper, a mixed integer linear programming (MILP) model that considers both the traditional reservoir rule curves and the hedging rules to manage and operate a multipurpose, multireservoir system was developed.
Abstract: This research develops a mixed integer linear programming (MILP) model that considers simultaneously both the traditional reservoir rule curves and the hedging rules to manage and operate a multipurpose, multireservoir system. During normal periods of operation, when inflows are plentiful, this optimization model efficiently distributes the available stored water from different reservoirs to meet the planned demands imposed by competing users. However, during periods of drought, or when anticipating a drought, the planned demands cannot be fully met, and a water shortage occurs. By considering the hedging rules along with the rule curves, guidelines are provided for reservoir releases. To minimize the impact of drought, the hedging rules effectively reduce the ongoing water supply to balance with the target storage requirement. The MILP model is applied to a multireservoir system in the southern region of Taiwan, where the results obtained demonstrate the applicability and utility of the model.
TL;DR: In this paper, a new transit operating strategy is presented in which service vehicles operate in pairs with the lead vehicle providing an all-stop local service and the following vehicle being allowed to skip some stops as an express service.
Abstract: A new transit operating strategy is presented in which service vehicles operate in pairs with the lead vehicle providing an all-stop local service and the following vehicle being allowed to skip some stops as an express service. The underlying scheduling problem is formulated as a nonlinear integer programming problem with the objective of minimizing the total costs for both operators and passengers. A sensitivity analysis using a real-life example is performed to identify the conditions under which the proposed operating strategy is most advantageous.
TL;DR: In this article, the authors consider the problem of train planning or scheduling for large, busy, complex train stations, which are common in Europe and elsewhere, though not in North America.
Abstract: We consider the problem of train planning or scheduling for large, busy, complex train stations, which are common in Europe and elsewhere, though not in North America. We develop the constraints and objectives for this problem, but these are too computationally complex to solve by standard combinatorial search or integer programming methods. Also, the problem is somewhat political in nature, that is, it does not have a clear objective function because it involves multiple train operators with conflicting interests. We therefore develop scheduling heuristics analogous to those successfully adopted by train planners using “manual” methods. We tested the model and algorithms by applying to a typical large station that exhibits most of the complexities found in practice. The results compare well with those found by traditional methods, and take account of cost and preference trade-offs not handled by those methods. With successive refinements, the algorithm eventually took only a few seconds to run, the time depending on the version of the algorithm and the scheduling problem. The scheduling models and algorithms developed and tested here can be used on their own, or as key components for a more general system for train scheduling for a rail line or network. Train scheduling for a busy station includes ensuring that there are no conflicts between several hundred trains per day going in and out of the station on intersecting paths from multiple in-lines and out-lines to multiple platforms, while ensuring that each train is allowed at least its minimum required headways, dwell time, turnaround time and trip time. This has to be done while minimizing (costs of) deviations from desired times, platforms or lines, allowing for conflicts due to through-platforms, dead-end platforms, multiple sub-platforms, and possible constraints due to infrastructure, safety or business policy.
TL;DR: A mixed integer programming approach which allows optimization over beamlet fluence weights as well as beam and couch angles and which consistently provides superior tumor coverage and conformity, aswell as dose homogeneity within the tumor region while maintaining a low irradiation to important critical and normal tissues is offered.
Abstract: In intensity-modulated radiation therapy (IMRT) not only is the shape of the beam controlled, but combinations of open and closed multileaf collimators modulate the intensity as well. In this paper, we offer a mixed integer programming approach which allows optimization over beamlet fluence weights as well as beam and couch angles. Computational strategies, including a constraint and column generator, a specialized set-based branching scheme, a geometric heuristic procedure, and the use of disjunctive cuts, are described. Our algorithmic design thus far has been motivated by clinical cases. Numerical tests on real patient cases reveal that good treatment plans are returned within 30 minutes. The MIP plans consistently provide superior tumor coverage and conformity, as well as dose homogeneity within the tumor region while maintaining a low irradiation to important critical and normal tissues.
01 Jan 2003
TL;DR: In this paper, the authors consider a framework where decision makers interactively define a multicriteria evaluation model by providing imprecise information (i.e., a linear system of constraints to the models parameters) and analyze the consequences of the information provided.
Abstract: We consider a framework where decision makers (DMs) interactively define a multicriteria evaluation model by providing imprecise information (i.e., a linear system of constraints to the models parameters) and by analyzing the consequences of the information provided. DMs may introduce new constraints explicitly or implicitly (results that the model should yield). If a new constraint is incompatible with the previous ones, then the system becomes inconsistent and the DMs must choose between removing the new constraint or removing some of the older ones. We address the problem of identifying subsets of constraints which, when removed, lead to a consistent system. Identifying such subsets would indicate the reason for the inconsistent information given by DMs. There may exist several possibilities for the DMs to resolve the inconsistency. We present two algorithms to identify such possibilities, one using {0,1} mixed integer linear programming and the other one using linear programming. Both approaches are based on the knowledge that the system was consistent prior to introducing the last constraint. The output of these algorithms helps the DM to identify the conflicting pieces of information in a set of statements he/she asserted. The relevance of these algorithms for MCDA is illustrated by an application to an aggregation/disaggregation procedure for the Electre Tri method. � 2002 Elsevier Science B.V. All rights reserved.
TL;DR: In this article, an optimization-based approach to kinetic model reduction is presented, where the reaction-elimination problem is formulated as a linear integer program which can be solved to guaranteed global optimality.
TL;DR: The use of this model for the ground-holding problem improves upon prior models by allowing for easy integration into the newly developed ground-delay program procedures based on the Collaborative Decision-Making paradigm.
Abstract: In this paper, we analyze a generalization of a classic network-flow model. The generalization involves the replacement of deterministic demand with stochastic demand. While this generalization destroys the original network structure, we show that the matrix underlying the stochastic model is dual network. Thus, the integer program associated with the stochastic model can be solved efficiently using network-flow or linear-programming techniques. We also develop an application of this model to the ground-holding problem in air-traffic management. The use of this model for the ground-holding problem improves upon prior models by allowing for easy integration into the newly developed ground-delay program procedures based on the Collaborative Decision-Making paradigm.
TL;DR: This paper presents an approach to the wordlength allocation and optimization problem for linear digital signal processing systems implemented as custom parallel processing units and proposes a heuristic approach which guarantees an optimum set of wordlengths for each internal variable.
Abstract: This paper presents an approach to the wordlength allocation and optimization problem for linear digital signal processing systems implemented as custom parallel processing units. Two techniques are proposed, one which guarantees an optimum set of wordlengths for each internal variable, and one which is a heuristic approach. Both techniques allow the user to tradeoff implementation area for arithmetic error at system outputs. Optimality (with respect to the area and error estimates) is guaranteed through modeling as a mixed integer linear program. It is demonstrated that the proposed heuristic leads to area improvements of 6% to 45% combined with speed increases compared to the optimum uniform wordlength design. In addition, the heuristic reaches within 0.7% of the optimum multiple wordlength area over a range of benchmark problems.
09 Jul 2003
TL;DR: Three different integer programming models can be used for an optimal solution of the minimum power broadcast/multicast problem in wireless networks and is therefore most suited for networks where the locations of the nodes are fixed.
Abstract: Wireless multicast/broadcast sessions, unlike wired networks, inherently reach several nodes with a single transmission. For omnidirectional wireless broadcast to a node, all nodes closer will also be reached. Heuristic algorithms for constructing the minimum power tree in wireless networks have been proposed by Wieselthier et al. and Stojmenovic et al. Recently, an evolutionary search procedure has been proposed by Marks et al. In this paper, we present three different integer programming models which can be used for an optimal solution of the minimum power broadcast/multicast problem in wireless networks. The models assume complete knowledge of the distance matrix and is therefore most suited for networks where the locations of the nodes are fixed.