This paper deals with Maximally Balanced Connected Partition (MBCP) problem. It introduces a mixed integer linear programming (MILP) formulation of the problem with polynomial number of variables and constraints. Also...
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This paper deals with Maximally Balanced Connected Partition (MBCP) problem. It introduces a mixed integer linear programming (MILP) formulation of the problem with polynomial number of variables and constraints. Also, a variable neighborhood search (VNS) technique for solving this problem is presented. The VNS implements the suitable neighborhoods based on changing the component for an increasing number of vertices. An efficient implementation of the local search procedure yields a relatively short running time. The numerical experiments are made on instances known in the literature. Based on the MILP model, tests are run using two MILP solvers, CPLEX and Gurobi. It is shown that both solvers succeed in finding optimal solutions for all smaller and most of medium scale instances. Proposed VNS reaches most of the optimal solutions. The algorithm is also successfully tested on large scale problem instances for which optimal solutions are not known. (C) 2014 Elsevier Inc. All rights reserved.
Consideration was given to the a priori formulation of the multistage problem of stochastic programming with a quantile criterion which is reducible to the two-stage problem. Equivalence of the two-stage problems with...
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Consideration was given to the a priori formulation of the multistage problem of stochastic programming with a quantile criterion which is reducible to the two-stage problem. Equivalence of the two-stage problems with the quantile criterion in the a priori and a posteriori formulations was proved for the general case. The a posteriori formulation of the two-stage problem was in turn reduced to the equivalent problem of mixed integer linear programming. An example was considered.
Owing to the revolution in sustainable and green manufacturing the production planning and network design of closed loop supply chain concept has got the attention of researchers and managers. In this paper, a multi-p...
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Owing to the revolution in sustainable and green manufacturing the production planning and network design of closed loop supply chain concept has got the attention of researchers and managers. In this paper, a multi-product, multi-facility capacitated closed-loop supply chain framework is proposed in an uncertain environment including reuse, refurbish, recycle and disposal of parts. The uncertainty related to demand, fraction of parts recovered for different product recovery processes, product acquisition cost, purchasing cost, transportation cost, processing, and set-up cost is handled with fuzzy numbers. A fuzzy mixed integer linear programming model is proposed to decide optimally the location and allocation of parts at each facility and number of parts to be purchased from external suppliers in order to maximise the profit of organisation. The proposed solution methodology is able to generate a balanced solution between the feasibility degree and degree of satisfaction of the decision maker. The proposed model has been tested with an illustrative example.
This paper presents a hybrid simulated annealing (SA) and mixed integer linear programming (MILP) approach for static expansion planning of radial distribution networks with distributed generators (DGs). The expansion...
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This paper presents a hybrid simulated annealing (SA) and mixed integer linear programming (MILP) approach for static expansion planning of radial distribution networks with distributed generators (DGs). The expansion planning problem is first modeled as MILP optimization problem with the goal of minimizing the investment cost, cost of losses, cost of customer interruptions due to failures at the branches and at DGs and the cost of lost DG production due to failures at branches. In order to reduce the complexity of planning problems the decomposition of the original problem is proposed into a number of sequences of sub-problems (local networks) that are solved using the MILP model. The decomposition and solution process is iteratively guided and controlled by the proposed SA algorithm that employs the proper intensification and diversification mechanism to obtain the minimum total cost solution. (C) 2013 Elsevier B.V. All rights reserved.
In this paper, a two-stage solution methodology for distribution network planning considering reliability indices improvement is proposed. This methodology comprises optimal distribution network expansion and improves...
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In this paper, a two-stage solution methodology for distribution network planning considering reliability indices improvement is proposed. This methodology comprises optimal distribution network expansion and improves network reliability by allocating sectionalizing switches and interconnection circuits (tie line circuits). The optimal expansion problem of radial aerial distribution systems is formulated as a mixed binary linearprogramming (MILP) problem aiming to reduce the investment and operational costs, subject to physical and operational constraints. The allocation of controlled sectionalizing switches and interconnection circuits is also formulated as a MILP in order to improve the network reliability indices. A pseudo-dynamic planning method is used to solve planning and reliability models through a heuristic technique that first solves the planning model followed by the solution of the reliability model, in each stage of planning horizon. Numerical results are presented for a 54-bus distribution system from literature.
This article considers single hoist multi-degree cyclic scheduling problems with reentrance. Time window constraints are also considered. Firstly, a mixedintegerprogramming model is formulated for multi-degree cycli...
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This article considers single hoist multi-degree cyclic scheduling problems with reentrance. Time window constraints are also considered. Firstly, a mixedintegerprogramming model is formulated for multi-degree cyclic hoist scheduling without reentrance, referred to as basic lines in this article. Two valid inequalities corresponding to this problem are also presented. Based on the model for basic lines, an extended mixedintegerprogramming model is proposed for more complicated scheduling problems with reentrance. Phillips and Unger's benchmark instance and randomly generated instances are applied to test the model without reentrance, solved using the commercial software CPLEX. The efficiency of the model is analysed based on computational time. Moreover, an example is given to demonstrate the effectiveness of the model with reentrance.
This study proposes a mixed integer linear programming (MILP) model to optimize the spillways scheduling for reservoir flood control. Unlike the conventional reservoir operation model, the proposed MILP model specifie...
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This study proposes a mixed integer linear programming (MILP) model to optimize the spillways scheduling for reservoir flood control. Unlike the conventional reservoir operation model, the proposed MILP model specifies the spillways status (including the number of spillways to be open and the degree of the spillway opened) instead of reservoir release, since the release is actually controlled by using the spillway. The piecewise linear approximation is used to formulate the relationship between the reservoir storage and water release for a spillway, which should be open/closed with a status depicted by a binary variable. The control order and symmetry rules of spillways are described and incorporated into the constraints for meeting the practical demand. Thus, a MILP model is set up to minimize the maximum reservoir storage. The General Algebraic Modeling System (GAMS) and IBM ILOG CPLEX Optimization Studio (CPLEX) software are used to find the optimal solution for the proposed MILP model. The China's Three Gorges Reservoir, whose spillways are of five types with the total number of 80, is selected as the case study. It is shown that the proposed model decreases the flood risk compared with the conventional operation and makes the operation more practical by specifying the spillways status directly.
The performance of classification methods, such as Support Vector Machines, depends heavily on the proper choice of the feature set used to construct the classifier. Feature selection is an NP-hard problem that has be...
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The performance of classification methods, such as Support Vector Machines, depends heavily on the proper choice of the feature set used to construct the classifier. Feature selection is an NP-hard problem that has been studied extensively in the literature. Most strategies propose the elimination of features independently of classifier construction by exploiting statistical properties of each of the variables, or via greedy search. All such strategies are heuristic by nature. In this work we propose two different mixed integer linear programming formulations based on extensions of Support Vector Machines to overcome these shortcomings. The proposed approaches perform variable selection simultaneously with classifier construction using optimization models. We ran experiments on real-world benchmark datasets, comparing our approaches with well-known feature selection techniques and obtained better predictions with consistently fewer relevant features. (C) 2014 Elsevier Inc. All rights reserved.
Diffusion processes in semiconductor fabrication facilities (Fabs) refer to the series of processes from wafer cleaning processes to furnace processes. Most furnace tools are batch tools, with large batch sizes, and h...
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Diffusion processes in semiconductor fabrication facilities (Fabs) refer to the series of processes from wafer cleaning processes to furnace processes. Most furnace tools are batch tools, with large batch sizes, and have relatively long process times, when compared to the other processes. Strict time window constraints link cleaning processes with furnace processes for quality control. Those operational requirements for diffusion processes make their scheduling very difficult. This paper proposes an advanced scheduling approach based on a rolling horizon scheduling concept. Due to the combinatorial nature of the scheduling problem, the complexity of the problem increases exponentially, when the number of jobs and tools increase. However, the computation time allowed for the scheduler is limited in practice, because the variability in most Fabs requires schedulers to update the schedule in short intervals. We suggest an mixed integer linear programming model for diffusion processes, and propose an effective decomposition method to deal with this complexity problem. The decomposition method repeats multiple scheduling iterations, as it gradually extends the number of runs on tools, enabling the scheduler to generate near-optimal schedules in limited time intervals. The scheduler could make large improvements on key performance indicators, such as time window violation rates, batch sizes, throughput, etc. The software architecture of the scheduler implementation is also addressed in this paper.
In this paper, we present a novel algorithm for the solution of multiparametric mixed integer linear programming (mp-MILP) problems that exhibit uncertain objective function coefficients and uncertain entries in the r...
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In this paper, we present a novel algorithm for the solution of multiparametric mixed integer linear programming (mp-MILP) problems that exhibit uncertain objective function coefficients and uncertain entries in the right-hand side constraint vector. The algorithmic procedure employs a branch and bound strategy that involves the solution of a multiparametric linearprogramming sub-problem at leaf nodes and appropriate comparison procedures to update the tree. McCormick relaxation procedures are employed to overcome the presence of bilinear terms in the model. The algorithm generates an envelope of parametric profiles, containing the optimal solution of the mp-MILP problem. The parameter space is partitioned into polyhedral convex critical regions. Two examples are presented to illustrate the steps of the proposed algorithm.
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