Let be a rational polyhedron, and let P (I) be the convex hull of . We define the integral lattice-free closure of P as the set obtained from P by adding all inequalities obtained from disjunctions associated with int...
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Let be a rational polyhedron, and let P (I) be the convex hull of . We define the integral lattice-free closure of P as the set obtained from P by adding all inequalities obtained from disjunctions associated with integral lattice-free polyhedra in . We show that the integral lattice-free closure of P is again a polyhedron, and that repeatedly taking the integral lattice-free closure of P gives P (I) after a finite number of iterations. Such results can be seen as a mixedinteger analogue of theorems by Chvatal and Schrijver for the pure integer case. One ingredient of our proof is an extension of a result by Owen and Mehrotra. In fact, we prove that for each rational polyhedron P, the split closures of P yield in the limit the set P (I) .
This paper describes parallel, non-shared-memory implementation of the classical general mixedinteger branch and bound algorithm, with experiments on the CM-5 family of parallel processors. The main issue in such an ...
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This paper describes parallel, non-shared-memory implementation of the classical general mixedinteger branch and bound algorithm, with experiments on the CM-5 family of parallel processors. The main issue in such an implementation is whether task scheduling and certain data-storage functions should be handled by a single processor, or spread among multiple processors. The centralized approach risks creating processing bottlenecks, while the more decentralized implementations differ more from the fundamental serial algorithm. Extensive computational tests on standard MIPLIB problems compare centralized, clustered, and fully decentralized task scheduling methods, using a novel combination of random work scattering and rendezvous-based global load balancing, along with a distributed ''control by token'' technique. Further experiments compare centralized and distributed schemes for storing heuristic ''pseudo-cost'' branching data. The distributed storage method is based on continual asynchronous reduction along a tree of redundant storage sites. On average, decentralized task scheduling appears at least as effective as central control, but pseudo-cost storage should be kept as centralized as possible.
Polygonal approximations of digital planar curves are very useful for a considerable number of applications in computer vision. A great interest in this area has generated a huge number of methods for obtaining polygo...
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Polygonal approximations of digital planar curves are very useful for a considerable number of applications in computer vision. A great interest in this area has generated a huge number of methods for obtaining polygonal approximations. A good measure to compare these methods is known as Rosin's merit. This measure uses the optimal polygonal approximation, but the state-of-the-art methods require a tremendous computation time for obtaining this optimal solution. We focus on the problem of obtaining the optimal polygonal approximation of a digital planar curve. Given N ordered points on a Euclidean plane, an efficient method to obtain M points that defines a polygonal approximation with the minimum distortion is proposed. The new solution relies on mixed integer programming techniques in order to obtain the minimum value of distortion. Results, show that computation time for the new method dramatically decreases in comparison with state-of-the-art methods for obtaining the optimal polygonal approximation. (C) 2015 Elsevier Inc. All rights reserved.
In addition to improved sanitation, hygiene, and better access to safe water, oral cholera vaccines can help to control the spread of cholera in the short term. However, there is currently no systematic method for det...
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In addition to improved sanitation, hygiene, and better access to safe water, oral cholera vaccines can help to control the spread of cholera in the short term. However, there is currently no systematic method for determining the best allocation of oral cholera vaccines to minimize disease incidence in a population where the disease is endemic and resources are limited. We present a mathematical model for optimally allocating vaccines in a region under varying levels of demographic and incidence data availability. The model addresses the questions of where, when, and how many doses of vaccines to send. Considering vaccine efficacies (which may vary based on age and the number of years since vaccination), we analyze distribution strategies which allocate vaccines over multiple years. Results indicate that, given appropriate surveillance data, targeting age groups and regions with the highest disease incidence should be the first priority, followed by other groups primarily in order of disease incidence, as this approach is the most life-saving and cost-effective. A lack of detailed incidence data results in distribution strategies which are not cost-effective and can lead to thousands more deaths from the disease. The mathematical model allows for what-if analysis for various vaccine distribution strategies by providing the ability to easily vary parameters such as numbers and sizes of regions and age groups, risk levels, vaccine price, vaccine efficacy, production capacity and budget. (C) 2015 Elsevier Ltd. All rights reserved.
This work addresses harvest planning problems that arise in the production of sugar and alcohol from sugar cane in Brazil. The planning is performed for two planning horizons, tactical and operational planning, such t...
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This work addresses harvest planning problems that arise in the production of sugar and alcohol from sugar cane in Brazil. The planning is performed for two planning horizons, tactical and operational planning, such that the total sugar content in the harvested cane is maximized. The tactical planning comprises the entire harvest season that averages seven months. The operational planning considers a horizon from seven to thirty days. Both problems are solved by mixed integer programming. The tactical planning is well handled. The model for the operational planning extends the one for the tactical planning and is presented in detail. Valid inequalities are introduced and three techniques are proposed to speed up finding quality solutions. These include pre-processing by grouping and filtering the distance matrix between fields, hot starting with construction heuristic solutions, and dividing and sequentially solving the resulting MIP program. Experiments are run over a set of real world and artificial instances. A case study illustrates the benefits of the proposed planning. (C) 2013 Elsevier B.V. All rights reserved.
Petri nets, as an effective mathematical tool, have been intensively used in modeling and analyzing automated manufacturing systems (AMSs). Many deadlock control policies have been proposed for AMSs, but most of them ...
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Petri nets, as an effective mathematical tool, have been intensively used in modeling and analyzing automated manufacturing systems (AMSs). Many deadlock control policies have been proposed for AMSs, but most of them assume that resources never fail during product processing. However, resource failures may happen in a real world, which may invalidate existing control policies. This paper concentrates on robust liveness-enforcing supervisor design for a system of simple sequential processes with multiple unreliable resources. Recovery subnets model resource failure and recovery, which are added to the holders of unreliable resource places. The proposed method consists of two steps. At the first step, a mixed integer programming (MIP) problem is developed to detect a strict minimal siphon that can be emptied. At the second step, an extended constraint set derived by the complementary set of a siphon is constructed. The siphon is controlled through the extended constraint set by adding a control place. The above two steps are executed in an iterative way until no new empty siphon is found and a robust liveness-enforcing supervisor can be obtained. Examples are used to expose the advantages of the proposed method.
This letter presents a method for solving several linear equations in max-plus algebra. The essential part of these equations is reduced to constraint satisfaction problems compatible with mixed integer programming. T...
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This letter presents a method for solving several linear equations in max-plus algebra. The essential part of these equations is reduced to constraint satisfaction problems compatible with mixed integer programming. This method is flexible, compared with optimization methods, and suitable for scheduling of certain discrete event systems.
This letter focuses on the robust low-rank matrix recovery (RLRMR) in the presence of gross sparse outliers. Instead of using l(1)-norm to reduce or suppress the influence of anomalies, we aim to eliminate their impac...
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This letter focuses on the robust low-rank matrix recovery (RLRMR) in the presence of gross sparse outliers. Instead of using l(1)-norm to reduce or suppress the influence of anomalies, we aim to eliminate their impact. To this end, we model the RLRMR as a mixed integer programming (MIP) problem based on the l(0)-norm. Then, a block coordinate descent (BCD) algorithm is developed to iteratively solve the resultant MIP. At each iteration, the proposed approach first utilizes the l(0)-norm optimization theory to assign binary weights to all entries of the residual between the known and estimated matrices. With these binary weights, the optimization over the bilinear term is reduced to a weighted extension of the Frobenius norm. As a result, the optimization problem is decomposed into a group of row-wise and column-wise subproblems with closed-form solutions. Additionally, the convergence of the proposed algorithm is studied. Simulation results demonstrate that the proposed method is superior to five state-of-the-art RLRMR algorithms.
A two-step topology-finding method based on mixed integer programming and nonlinear programming is proposed for tensegrity structures. In the first step, feasible and symmetric strut connectivities are obtained throug...
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A two-step topology-finding method based on mixed integer programming and nonlinear programming is proposed for tensegrity structures. In the first step, feasible and symmetric strut connectivities are obtained through a ground structure method combined with mixed integer programming;in the second step, the cable connectivities are optimized through nonlinear programming to obtain a feasible tensegrity structure. The same ground structure used in the first step is adopted in the second step, which is beneficial to find a more symmetric cable layout. The independent continuous mapping method is used in the second step to convert the 0-1 binary variables of cable connectivities to continuous variables to transform the combinatorial optimization problem into a nonlinear programming problem. The number of strut lengths is adopted as a control parameter and a symmetry objective function is proposed to generate a variety of regular and symmetric tensegrity structures. A multi-stage computation scheme is proposed to improve the computational efficiency. Typical examples are carried out to validate the proposed method. The computational efficiency of the method is benchmarked with existing methods fully based on mixed integer programming. Results demonstrate that the computational efficiency of the proposed method is significantly improved compared to the existing methods.
A pair of symmetric dual multiobjective variational mixedinteger programs for the polars of arbitrary cones are formulated, which some primal and dual variables are constrained to belong to the set of integers. Under...
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A pair of symmetric dual multiobjective variational mixedinteger programs for the polars of arbitrary cones are formulated, which some primal and dual variables are constrained to belong to the set of integers. Under the separability with respect to integer variables and partial-invexity assumptions on the functions involved, we prove the weak, strong, converse and self-duality theorems to related minimax efficient solution. These results include some of available results. (c) 2006 Elsevier B.V. All rights reserved.
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