This paper considers the class scheduling and timetabling problem faced at Kuwait University (KU). The principal focus is to design efficient class offering patterns while taking into consideration newly imposed gende...
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This paper considers the class scheduling and timetabling problem faced at Kuwait University (KU). The principal focus is to design efficient class offering patterns while taking into consideration newly imposed gender policies. We formulate a mathematical programming model that assigns offered classes to time-slots and addresses gender issues by defining appropriate surrogate constraints along with objective penalty terms. The model aims to enhance existing manual scheduling and timetabling approaches that are often accompanied with arduous combinatorial tasks such as resolving class conflicts, dealing with parking and traffic congestion, and ensuring an efficient utilization of facility and human resources. This modeling approach emphasizes the generation of flexible class timetables for students, and the efficient utilization of available facility resources. Computational results based on a number of case studies related to Kuwait University reveal that this approach yields improved schedules in terms of offering patterns and class conflicts. (c) 2006 Elsevier B.V. All rights reserved.
As the development and population of North America continues to grow, the demand for environmentally friendly or clean energy generation is becoming more of an issue. We present a model that addresses the energy techn...
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As the development and population of North America continues to grow, the demand for environmentally friendly or clean energy generation is becoming more of an issue. We present a model that addresses the energy technologies that may continue to be used and new clean energy technologies that should be introduced in energy generation. The approach involves a Stochastic mixed-integer Program (SMIP) that minimizes cost and emission levels associated with energy generation while meeting energy demands of a given region. The results provide encouraging outcomes with respect to cost, emission levels, and energy-technologies that should be utilized for future generation. (C) 2011 Elsevier Ltd. All rights reserved.
An exact algorithm is developed for the chance-constrained multi-area reserve sizing problem in the presence of transmission network constraints. The problem can be cast as a two-stage stochastic mixedinteger linear ...
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An exact algorithm is developed for the chance-constrained multi-area reserve sizing problem in the presence of transmission network constraints. The problem can be cast as a two-stage stochastic mixedinteger linear program using sample approximation. Due to the complicated structure of the problem, existing methods attempt to find a feasible solution based on heuristics. Existing mixed-integer algorithms that can be applied directly to a two-stage stochastic program can only address small-scale problems that are not practical. We have found a minimal description of the projection of our problem onto the space of the first-stage variables. This enables us to directly apply more general integerprogramming techniques for mixing sets, that arise in chance-constrained problems. Combining the advantages of the minimal projection and the strengthening reformulation from IP techniques, our method can tackle real-world problems. We specifically consider a case study of the 10-zone Nordic network with 100,000 scenarios where the optimal solution can be found in approximately 5 minutes.
This paper presents a new data classification method based on mixed-integer programming. Traditional approaches that are based on partitioning the data sets into two groups perform poorly for multi-class data classifi...
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This paper presents a new data classification method based on mixed-integer programming. Traditional approaches that are based on partitioning the data sets into two groups perform poorly for multi-class data classification problems. The proposed approach is based on the use of hyper-boxes for defining boundaries of the classes that include all or some of the points in that set. A mixed-integer programming model is developed for representing existence of hyper-boxes and their boundaries. In addition, the relationships among the discrete decisions in the model are represented using propositional logic and then converted to their equivalent integer constraints using Boolean algebra. The proposed approach for multi-class data classification is illustrated on an example problem. The efficiency of the proposed method is tested on the well-known IRIS data set. The computational results on the illustrative example and the IRIS data set show that the proposed method is accurate and efficient on multi-class data classification problems. (c) 2005 Elsevier B.V. All rights reserved.
The parallel replacement problem under economies of scale (PRES) determines minimum cost replacement policies for each asset in a group of assets that operate in parallel and are subject to fixed and variable purchase...
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The parallel replacement problem under economies of scale (PRES) determines minimum cost replacement policies for each asset in a group of assets that operate in parallel and are subject to fixed and variable purchase costs. We study the mixed-integer programming formulation of PRES under technological change by incorporating capacity gains into the model such that newer, technologically advanced assets have higher capacity than assets purchased earlier. We provide optimal solution characteristics and insights about the economics of the problem and derive associated cutting planes for optimising the problem. Computational experiments illustrate that the inequalities are quite effective in solving PRES under technological change instances.
A new mixed-integer programming (MIP) formulation is presented for the production planning of single-stage multi-product processes. The problem is formulated as a multi-item capacitated lot-sizing problem in which (a)...
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A new mixed-integer programming (MIP) formulation is presented for the production planning of single-stage multi-product processes. The problem is formulated as a multi-item capacitated lot-sizing problem in which (a) multiple items can be produced in each planning period, (b) sequence-independent set-ups can carry over from previous periods, (c) set-ups can cross over planning period boundaries, and (d) set-ups can be longer than one period. The formulation is extended to model time periods of non-uniform length, idle time, parallel units, families of products, backlogged demand, and lost sales. (C) 2007 Elsevier Ltd. All rights reserved.
In the smart grid environment, optimal placement and sizing of microgrids have attracted a great deal of attention. Here, we propose a multi-scale optimization model for determining microgrid configuration, capacity, ...
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In the smart grid environment, optimal placement and sizing of microgrids have attracted a great deal of attention. Here, we propose a multi-scale optimization model for determining microgrid configuration, capacity, and geographical location, and we apply it to a municipality in Southwestern Ontario. The proposed approach accounts for the net present value of the project, power balance of the grid, maximum capacity of the current substations, and the geographic availability for the installation of a microgrid. The problem is tackled in two stages. First, a geographic information system/multicriteria decision analysis (GIS/MCDA) is performed to determine the suitable locations for the installation of distributed energy resources (DERs). Then, a mixedinteger optimization model is used to determine the capacities and final installation locations of the DERs based on the results obtained in the GIS/MCDA. Finally, three different scenarios are evaluated to elucidate the influence that retail price, microgrids' minimum contribution to the demand, and available land have over the final architecture, cost, and allocation of a renewable energy project.
In this article, we consider a network of processors aiming at cooperatively solving mixed-integer convex programs subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint...
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In this article, we consider a network of processors aiming at cooperatively solving mixed-integer convex programs subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint set. We propose a randomized, distributed algorithm working under asynchronous, unreliable, and directed communication. The algorithm is based on a local computation and communication paradigm. At each communication round, nodes perform two updates: 1) A verification in which they check-in a randomized fashion-the robust feasibility of a candidate optimal point, and 2) an optimization step in which they exchange their candidate basis (the minimal set of constraints defining a solution) with neighbors and locally solve an optimization problem. As a main result, we show that processors can stop the algorithm after a finite number of communication rounds (either because verification has been successful for a sufficient number of rounds or because a given threshold has been reached) so that candidate optimal solutions are consensual. The common solution has proven to be-with high confidence-feasible and, hence, optimal for the entire set of uncertainty except a subset having an arbitrarily small probability measure. We show the effectiveness of the proposed distributed algorithm using two examples: a random, uncertain mixed-integer linear program and a distributed localization in wireless sensor networks. The distributed algorithm is implemented on a multicore platform in which the nodes communicate asynchronously.
In many countries civil engineers play a fundamental role in the processes through which the location and capacities of public facilities like medical centers, schools, sanitary landfills, libraries, swimming-pool, et...
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In many countries civil engineers play a fundamental role in the processes through which the location and capacities of public facilities like medical centers, schools, sanitary landfills, libraries, swimming-pool, etc., are decided. This paper describes a study aimed at evaluating the aptitude of general methods of mixed-integer programming (MIP) for solving public facility planning problems using PCs. The application of these methods is quite easy today, even for people with limited optimization and computing skills, thanks to the good, friendly MIP packages now available. The evaluation was performed on a collection of basic problems types involving both minimum-cost and maximum-accessibility objectives. The main, general conclusion of the study was that, at present, problems with up to 100 centers and 100 sites, like most real-world problems are, can be solved rather efficiently on many occasions.
In this paper, we propose a new framework for finding an initial feasible solution from a mixed-integer programming (MIP) model. We call it learn-and-construct since it first exploits the structure of the model and it...
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In this paper, we propose a new framework for finding an initial feasible solution from a mixed-integer programming (MIP) model. We call it learn-and-construct since it first exploits the structure of the model and its linear relaxation solution and then uses this knowledge to try to produce a feasible solution. In the learning phase, we use an unsupervised learning algorithm to cluster entities originating the MIP model. Such clusters are then used to decompose the original MIP in a number of easier sub-MIPs that are solved by using a black box solver. Computational results on three well-known problems show that our procedure is characterized by a success rate larger than both the feasibility pump heuristic and a state-of-the-art MIP solver. Furthermore, our approach is more scalable and uses less computing time on average.
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