A typical railroad hump yard contains multiple layers of complex operations. The railcars coming with inbound trains through the yard need to be humped into different classification tracks according to the destination...
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A typical railroad hump yard contains multiple layers of complex operations. The railcars coming with inbound trains through the yard need to be humped into different classification tracks according to the destination, and then assembled to generate the desired outbound trains. During this complex procedure, the processing time of railcars and various resource constraints at different railroad yard facilities could significantly affect the overall performance of yard operations, individually and in combination. It is theoretically challenging to represent a large number of practical operation rules through tractable mathematical programming models. This paper first presents a time-expanded multi-layer network flow model to describe the connection between different layers of yard operations. A mixed integer programming model is developed to optimize the overall performance by jointly considering tightly interconnected facilities. We adopt a cumulative flow count representation to model the spatial capacity constraints in terms of the number of railcars in classification yards. A novel lot-sizing modeling framework and related valid inequality formulations are introduced to model the assembling jobs for outbound trains. We also develop an aggregated flow assignment model and earliest due date-based heuristic rules to determine the humping jobs sequence for reducing the search space. Numerical experiments are conducted to examine the solution quality and computational efficiency under different types of formulation strategies. (C) 2015 Elsevier Ltd. All rights reserved.
A trust-region-based derivative free algorithm for solving bound constrained mixedinteger nonlinear programs is developed in this paper. The algorithm is proven to converge to a local minimum after a finite number of...
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A trust-region-based derivative free algorithm for solving bound constrained mixedinteger nonlinear programs is developed in this paper. The algorithm is proven to converge to a local minimum after a finite number of function evaluations. In addition, an improved definition of local minima of mixedinteger programs is proposed. Computational results showing the effectiveness of the derivative free algorithm are presented.
The thermal unit commitment (UC) problem is a large-scale mixedinteger quadratic programming (MIQP), which is difficult to solve efficiently, especially for large-scale instances. This paper presents a projected refo...
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The thermal unit commitment (UC) problem is a large-scale mixedinteger quadratic programming (MIQP), which is difficult to solve efficiently, especially for large-scale instances. This paper presents a projected reformulation for UC problem. After projecting the power output of unit onto [0,1], a novel MIQP reformulation, denoted as P-MIQP, can be formed. The obtained P-MIQP is tighter than traditional MIQP formulation of UC problem. And the reduced problem of P-MIQP, which is eventually solved by solvers such as CPLEX, is compacter than that of traditional MIQP. In addition, two mixedinteger linear programming (MILP) formulations can be obtained from traditional MIQP and our P-MIQP of UC by replacing the quadratic terms in the objective functions with a sequence of piece-wise perspective-cuts. Projected MILP is also tighter and compacter than the traditional MILP due to the same reason of MIQP. The simulation results for realistic instances that range in size from 10 to 200 units over a scheduling period of 24 h show that the projected reformulation yields tight and compact mixed integer programming UC formulations, which are competitive with currently traditional ones. (C) 2014 Elsevier Ltd. All rights reserved.
This paper concerns a method of selecting the best subset of explanatory variables for a linear regression model. Employing Mallows' C-p, as a goodness-of-fit measure, we formulate the subset selection problem as ...
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This paper concerns a method of selecting the best subset of explanatory variables for a linear regression model. Employing Mallows' C-p, as a goodness-of-fit measure, we formulate the subset selection problem as a mixedinteger quadratic programming problem. Computational results demonstrate that our method provides the best subset of variables in a few seconds when the number of candidate explanatory variables is less than 30. Furthermore, when handling datasets consisting of a large number of samples, it finds better-quality solutions faster than stepwise regression methods do. (C) 2014 Elsevier Ltd. All rights reserved.
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.
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
The mixed-integer quadratically constrained quadratic fractional programming(MIQCQFP)problem often appears in various fields such as engineering practice,management science and network ***,most of the solutions to suc...
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The mixed-integer quadratically constrained quadratic fractional programming(MIQCQFP)problem often appears in various fields such as engineering practice,management science and network ***,most of the solutions to such problems are often designed for their unique *** paper puts forward a new global optimization algorithm for solving the problem *** first convert the MIQCQFP into an equivalent generalized bilinear fractional programming(EIGBFP)problem with integer ***,we linearly underestimate and linearly overestimate the quadratic functions in the numerator and the denominator respectively,and then give a linear fractional relaxation technique for EIGBFP on the basis of non-negative *** that,combining rectangular adjustment-segmentation technique and midpointsampling strategy with the branch-and-bound procedure,an efficient algorithm for solving MIQCQFP globally is ***,a series of test problems are given to illustrate the effectiveness,feasibility and other performance of this algorithm.
This study targets an examination proctor assignment problem where faculties and academic staffs are assigned to examinations as proctors in the regular examination period at our university. In previous work, the auth...
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This study targets an examination proctor assignment problem where faculties and academic staffs are assigned to examinations as proctors in the regular examination period at our university. In previous work, the author formulated fundamental mathematical model for the assignment task in a mixed integer programming form and developed a prototype system based on spreadsheet software to derive an optimal assignment. In this study, the proposed mathematical model is extended and revised to deal with the conditions in the assignment task. Some solutions are discussed to improve practicality for system users.
Operational readiness and mission availability are two important standards in equipment supportability. To evaluate these two standards, an improved particle swarm optimization (PSO) algorithm to solve the mixed integ...
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ISBN:
(纸本)9781479986460
Operational readiness and mission availability are two important standards in equipment supportability. To evaluate these two standards, an improved particle swarm optimization (PSO) algorithm to solve the mixed integer programming (MIP) problems has been developed. The augmented Lagrange multiplier method is employed to deal with the constraints, and special update strategy employed to restrict the swarm particles to lies only in integer positions. Tests on the two former mathematical models have verified the effectiveness of the proposed mixed technique, and it can be easily applied to other mixed integer programming with Constraint problem.
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