Home About us Contact
|
Home About us Contact | ||
|
|
||
Mixed Integer Program (mixed + integer_program)
Selected AbstractsAutomated application component placement in data centers using mathematical programmingINTERNATIONAL JOURNAL OF NETWORK MANAGEMENT, Issue 6 2008Xiaoyun Zhu In this article we address the application component placement (ACP) problem for a data center. The problem is defined as follows: for a given topology of a network consisting of switches, servers and storage devices with varying capabilities, and for a given specification of a component-based distributed application, decide which physical server should be assigned to each application component, such that the application's processing, communication and storage requirements are satisfied without creating bottlenecks in the infrastructure, and that scarce resources are used most efficiently. We explain how the ACP problem differs from traditional task assignment in distributed systems, or existing grid scheduling problems. We describe our approach of formalizing this problem using a mathematical optimization framework and further formulating it as a mixed integer program (MIP). We then present our ACP solver using GAMS and CPLEX to automate the decision-making process. The solver was numerically tested on a number of examples, ranging from a 125-server real data center to a set of hypothetical data centers with increasing size. In all cases the ACP solver found an optimal solution within a reasonably short time. In a numerical simulation comparing our solver to a random selection algorithm, our solver resulted in much more efficient use of scarce network resources and allowed more applications to be placed in the same infrastructure. Copyright © 2008 John Wiley & Sons, Ltd. [source] Optimization of energy usage for fleet-wide power generating system under carbon mitigation optionsAICHE JOURNAL, Issue 12 2009A. Elkamel Abstract This article presents a fleet-wide model for energy planning that can be used to determine the optimal structure necessary to meet a given CO2 reduction target while maintaining or enhancing power to the grid. The model incorporates power generation as well as CO2 emissions from a fleet of generating stations (hydroelectric, fossil fuel, nuclear, and wind). The model is formulated as a mixed integer program and is used to optimize an existing fleet as well as recommend new additional generating stations, carbon capture and storage, and retrofit actions to meet a CO2 reduction target and electricity demand at a minimum overall cost. The model was applied to the energy supply system operated by Ontario power generation (OPG) for the province of Ontario, Canada. In 2002, OPG operated 79 electricity generating stations; 5 are fueled with coal (with a total of 23 boilers), 1 by natural gas (4 boilers), 3 nuclear, 69 hydroelectric and 1 wind turbine generating a total of 115.8 TWh. No CO2 capture process existed at any OPG power plant; about 36.7 million tonnes of CO2 was emitted in 2002, mainly from fossil fuel power plants. Four electricity demand scenarios were considered over a span of 10 years and for each case the size of new power generation capacity with and without capture was obtained. Six supplemental electricity generating technologies have been allowed for: subcritical pulverized coal-fired (PC), PC with carbon capture (PC+CCS), integrated gasification combined cycle (IGCC), IGCC with carbon capture (IGCC+CCS), natural gas combined cycle (NGCC), and NGCC with carbon capture (NGCC+CCS). The optimization results showed that fuel balancing alone can contribute to the reduction of CO2 emissions by only 3% and a slight, 1.6%, reduction in the cost of electricity compared to a calculated base case. It was found that a 20% CO2 reduction at current electricity demand could be achieved by implementing fuel balancing and switching 8 out of 23 coal-fired boilers to natural gas. However, as demand increases, more coal-fired boilers needed to be switched to natural gas as well as the building of new NGCC and NGCC+CCS for replacing the aging coal-fired power plants. To achieve a 40% CO2 reduction at 1.0% demand growth rate, four new plants (2 NGCC, 2 NGCC+CCS) as well as carbon capture processes needed to be built. If greater than 60% CO2 reductions are required, NGCC, NGCC+CCS, and IGCC+CCS power plants needed to be put online in addition to carbon capture processes on coal-fired power plants. The volatility of natural gas prices was found to have a significant impact on the optimal CO2 mitigation strategy and on the cost of electricity generation. Increasing the natural gas prices resulted in early aggressive CO2 mitigation strategies especially at higher growth rate demands. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source] A mathematical programming approach for improving the robustness of least sum of absolute deviations regressionNAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 4 2006Avi Giloni Abstract This paper discusses a novel application of mathematical programming techniques to a regression problem. While least squares regression techniques have been used for a long time, it is known that their robustness properties are not desirable. Specifically, the estimators are known to be too sensitive to data contamination. In this paper we examine regressions based on Least-sum of Absolute Deviations (LAD) and show that the robustness of the estimator can be improved significantly through a judicious choice of weights. The problem of finding optimum weights is formulated as a nonlinear mixed integer program, which is too difficult to solve exactly in general. We demonstrate that our problem is equivalent to a mathematical program with a single functional constraint resembling the knapsack problem and then solve it for a special case. We then generalize this solution to general regression designs. Furthermore, we provide an efficient algorithm to solve the general nonlinear, mixed integer programming problem when the number of predictors is small. We show the efficacy of the weighted LAD estimator using numerical examples. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006 [source] Resource allocation with lumpy demand: To speed or not to speed?NAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 3 2004Bintong Chen Abstract In the classical EPQ model with continuous and constant demand, holding and setup costs are minimized when the production rate is no larger than the demand rate. However, the situation may change when demand is lumpy. We consider a firm that produces multiple products, each having a unique lumpy demand pattern. The decision involves determining both the lot size for each product and the allocation of resources for production rate improvements among the products. We find that each product's optimal production policy will take on only one of two forms: either continuous production or lot-for-lot production. The problem is then formulated as a nonlinear nonsmooth knapsack problem among products determined to be candidates for resource allocation. A heuristic procedure is developed to determine allocation amounts. The procedure decomposes the problem into a mixed integer program and a nonlinear convex resource allocation problem. Numerical tests suggest that the heuristic performs very well on average compared to the optimal solution. Both the model and the heuristic procedure can be extended to allow the company to simultaneously alter both the production rates and the incoming demand lot sizes through quantity discounts. Extensions can also be made to address the case where a single investment increases the production rate of multiple products. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004. [source] Shortest path network interdiction with asymmetric informationNETWORKS: AN INTERNATIONAL JOURNAL, Issue 3 2008Halil Bayrak Abstract We consider an extension of the shortest path network interdiction problem. In this problem an evader attempts to minimize the length of the shortest path between the origin and the destination in a network, while an interdictor attempts to maximize the length of this shortest path by interdicting network arcs using limited resources. We consider the case where there is asymmetric information, i.e., the evader and the interdictor have different levels of information about the network. We formulate this problem as a nonlinear mixed integer program and show that this formulation can be converted to a linear mixed integer program. Computational results demonstrate improvements in the objective function values over the shortest path network interdiction problem with symmetric information. © 2008 Wiley Periodicals, Inc. NETWORKS, 2008 [source] | ||||||||||