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.
When electricity supply is interrupted due to a fault, it is essential that the power system be restored promptly according to an adequately planned restoration procedure. A problem of obtaining an appropriate target ...
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When electricity supply is interrupted due to a fault, it is essential that the power system be restored promptly according to an adequately planned restoration procedure. A problem of obtaining an appropriate target system for restoration is referred to as a power system restoration problem. The authors have already proposed a very efficient method based on the network simplex method which is in the category of mathematical programming approaches. Although the method is effective for most system conditions, it is likely to give an undesirable result in the case of abnormal network conditions. This paper proposes an effective and computationally fast solution algorithm based on the mixed integer programming approach, which can resolve the shortcoming of the former method. The solution speed is improved greatly by incorporating the restoration strategies of system operators. The following assumptions are postulated in this approach: (1) 0 - 1 variables are allocated to branches and loads to present their status;(2) continuous variables are taken to represent branch flows;and (3) costs are assigned to branches to represent their priorities during restorative operations and power flow limits. The proposed approach can be used to complement the former approach. The new approach has been applied to restoration problems of practical size, and simulation results demonstrate its advantage over the former method for intricate operating conditions.
Multi-biomarker panels can capture the nonlinear synergy among biomarkers and they are important to aid in the early diagnosis and ultimately battle complex diseases. However, identification of these multi-biomarker p...
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Multi-biomarker panels can capture the nonlinear synergy among biomarkers and they are important to aid in the early diagnosis and ultimately battle complex diseases. However, identification of these multi-biomarker panels from case and control data is challenging. For example, the exhaustive search method is computationally infeasible when the data dimension is high. Here, we propose a novel method, MILP_k, to identify serum-based multi-biomarker panel to distinguish colorectal cancers (CRC) from benign colorectal tumors. Specifically, the multi-biomarker panel detection problem is modeled by a mixed integer programming to maximize the classification accuracy. Then we measured the serum profiling data for 101 CRC patients and 95 benign patients. The 61 biomarkers were analyzed individually and further their combinations by our method. We discovered 4 biomarkers as the optimal small multi-biomarker panel, including known CRC biomarkers CEA and IL-10 as well as novel biomarkers IMA and NSE. This multi-biomarker panel obtains leave-one-out cross-validation (LOOCV) accuracy to 0.7857 by nearest centroid classifier. An independent test of this panel by support vector machine (SVM) with threefold cross validation gets an AUC 0.8438. This greatly improves the predictive accuracy by 20% over the single best biomarker. Further extension of this 4-biomarker panel to a larger 13-biomarker panel improves the LOOCV to 0.8673 with independent AUC 0.8437. Comparison with the exhaustive search method shows that our method dramatically reduces the searching time by 1000-fold. Experiments on the early cancer stage samples reveal two panel of biomarkers and show promising accuracy. The proposed method allows us to select the subset of biomarkers with best accuracy to distinguish case and control samples given the number of selected biomarkers. Both receiver operating characteristic curve and precision-recall curve show our method's consistent performance gain in accuracy. Our method
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