The usual formulation of a linear program is max . The core part of this linear program is the matrix since the columns define the variables and the rows define the constraints. The matrix is constructed by populating...
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The usual formulation of a linear program is max . The core part of this linear program is the matrix since the columns define the variables and the rows define the constraints. The matrix is constructed by populating columns or populating rows, or some of both, depending on the nature of the data and how it is collected. This paper addresses the construction of the matrix and solution procedures when there are separate data sources for the columns and for the rows and, moreover, the data is uncertain. The matrices which are "realizable" are only those which are considered possible from both sources. These realizable matrices then form an uncertainty set for a robust linear program. We show how to formulate and solve linear programs which provide lower and upper bounds to the robust linear program defined by . We also show how to use ordinary linear programming duality to share and divide the "credit/responsibility" of the optimal value of the robust linear program between the two alternative data sources.
The goal of the research is to propose an optimization-based methodology for the evaluation of retrofit incentives, using as a benchmark the wide data collection reported by the ENEA Italian Agency since 2007. To dete...
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The goal of the research is to propose an optimization-based methodology for the evaluation of retrofit incentives, using as a benchmark the wide data collection reported by the ENEA Italian Agency since 2007. To determine the best mix of energy retrofit measures for different areas of Italy, two linear programming models are proposed. The first model maximizes energy savings and the second one minimizes retrofit costs. The results show a 17% reduction in the average cost for each MW h of saved energy. More importantly, the methodology can help decision-makers appreciate how energy efficiency incentives have been used so far and how effective they could be. Furthermore, the methodology can be used for setting future incentive distribution plans. (C) 2015 Elsevier B.V. All rights reserved.
In this paper, a new linear programming formulation of a 1-norm support vector regression (SVR) is proposed whose solution is obtained by solving an exterior penalty problem in the dual space as an unconstrained minim...
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In this paper, a new linear programming formulation of a 1-norm support vector regression (SVR) is proposed whose solution is obtained by solving an exterior penalty problem in the dual space as an unconstrained minimization problem using Newton method. The solution of modified unconstrained minimization problem reduces to solving just system of linear equations as opposed to solving quadratic programming problem in SVR, which leads to extremely simple and fast algorithm. The algorithm converges from any starting point and can be easily implemented in MATLAB without using any optimization packages. The main advantage of the proposed approach is that it leads to a robust and sparse model representation meaning that many components of the optimal solution vector will become zero and therefore the decision function can be determined using much less number of support vectors in comparison to SVR, smooth SVR (SSVR) and weighted SVR (WSVR). To demonstrate its effectiveness, experiments were performed on well-known synthetic and real-world benchmark datasets. Similar or better generalization performance of the proposed method in less training time in comparison with SVR, SSVR and WSVR clearly exhibits its suitability and applicability. (C) 2015 Elsevier B.V. All rights reserved.
In this paper we propose a novel two-step linear optimization model to calculate energy efficient timetables in metro railway networks. The resultant timetable minimizes the total energy consumed by all trains and max...
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In this paper we propose a novel two-step linear optimization model to calculate energy efficient timetables in metro railway networks. The resultant timetable minimizes the total energy consumed by all trains and maximizes the utilization of regenerative energy produced by braking trains, subject to the constraints in the railway network. In contrast to other existing models, which are NP-hard, our model is computationally the most tractable one being a linear program. We apply our optimization model to different instances of service PES2-SFM2 of line 8 of Shanghai Metro network spanning a full service period of one day (18 h) with thousands of active trains. For every instance, our model finds an optimal timetable very quickly (largest runtime being less than 13 s) with significant reduction in effective energy consumption (the worst case being 19.27%). Code based on the model has been integrated with Thales Timetable Compiler - the industrial timetable compiler of Thales Inc that has the largest installed base of communication based train control systems worldwide. (C) 2016 Elsevier Ltd. All rights reserved.
When municipal waste scenarios are compared by using Life Cycle Assessment, the comparison is usually carried out among a limited number of alternative scenarios identified in advance. Therefore, however accurate and ...
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When municipal waste scenarios are compared by using Life Cycle Assessment, the comparison is usually carried out among a limited number of alternative scenarios identified in advance. Therefore, however accurate and broad the scenario definition may be, the scenario actually generating the lowest environmental impacts might just not be included among the alternatives proposed and analysed. To overcome this limitation, this paper proposes linear programming models developed to identify, among all the potential scenarios, the waste management scenario that minimises one particular environmental impact or a set of impacts at the same time, using environmental data from Life Cycle Assessment. Besides describing the proposed models, a concise overview of solution methods for multi-objective linear programming is provided. These models were tested in a case study and the results obtained are here presented and analysed. As a case-study, a suitable waste management system in the Abruzzo Region, Italy, was identified. In addition, a further hypothetical waste management context, also including an incinerator plant, was considered. Moreover, a sensitivity analysis was carried out to identify how changing distances to plants may affect optimal scenarios. As a result, different best-performing scenarios for the analysed waste management system were obtained, one for each single impact category considered, and one for each solution method adopted. Furthermore, the analysis of the hypothetical context shows how the introduction of an additional treatment plant could affect the system. Both distances and the solution methods used affect the results. The models developed could be used in decision-making processes to identify the best-performing scenario of a waste management system from the environmental point of view. The models are easy to apply and flexible, since they can be modelled according to the context to be analysed by introducing new factors. (C) 2015 Elsevier Ltd. Al
Component deployment is a combinatorial optimisation problem in software engineering that aims at finding the best allocation of software components to hardware resources in order to optimise quality attributes, such ...
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Component deployment is a combinatorial optimisation problem in software engineering that aims at finding the best allocation of software components to hardware resources in order to optimise quality attributes, such as reliability. The problem is often constrained because of the limited hardware resources, and the communication network, which may connect only certain resources. Owing to the non-linear nature of the reliability function, current optimisation methods have focused mainly on heuristic or metaheuristic algorithms. These are approximate methods, which find near-optimal solutions in a reasonable amount of time. In this paper, we present a mixed integer linear programming (MILP) formulation of the component deployment problem. We design a set of experiments where we compare the MILP solver to methods previously used to solve this problem. Results show that the MILP solver is efficient in finding feasible solutions even where other methods fail, or prove infeasibility where feasible solutions do not exist.
Reserve requirements serve as a proxy for N-1 reliability in the security-constrained unit commitment (SCUC) problem. However, there is no guarantee that the reserve is deliverable for all scenarios (post-contingency ...
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Reserve requirements serve as a proxy for N-1 reliability in the security-constrained unit commitment (SCUC) problem. However, there is no guarantee that the reserve is deliverable for all scenarios (post-contingency states). One cheap way to improve reserve deliverability is to harness the flexibility of the transmission network. Flexible AC transmission system (FACTS) devices are able to significantly improve the transfer capability. However, FACTS utilization is limited today due to the complexities these devices introduce to the DC optimal power flow problem (DCOPF). With a linear objective, the traditional DCOPF is a linear program (LP);when variable impedance based FACTS devices are taken into consideration, the problem becomes a nonlinear program (NLP). A reformulation of the NLP to a mixed integer linear program, for day-ahead corrective operation of FACTS devices, is presented in this paper. Engineering insight is then introduced to further reduce the complexity to an LP. Although optimality is not guaranteed, the simulation studies on the IEEE 118-bus system show that the method finds the globally optimal solution in 98.8% of the cases. Even when the method did not find the optimal solution, it was able to converge to a near-optimal solution, which substantially improved the reliability, very quickly.
This paper presents a hybrid algorithm of linear programming (LP), max-min ant system, and local search for solving large instances of the k-covering problem (SCkP). This algorithm exploits the LP-relaxation solution ...
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This paper presents a hybrid algorithm of linear programming (LP), max-min ant system, and local search for solving large instances of the k-covering problem (SCkP). This algorithm exploits the LP-relaxation solution by classifying the columns, based on their reduced costs, into three sets, such that two of these sets have the columns that need to be included or excluded from any solution while ants search the third set, the selection set, to construct their feasible solutions. Moreover, to choose high-quality columns from the selection set, ants rely on heuristic information derived from the rows' dual costs, which we obtain from the LP-relaxation solution as well. To benchmark our algorithm, we solve a set of 135 instances and compare the results with those of the state-of-the-art algorithm, in addition to the best-known solutions obtained using a branch and bound algorithm. Our algorithm shows superior results in terms of solution quality and computation time. Moreover, it can identify two new best-known solutions. (C) 2016 Elsevier Ltd. All rights reserved.
We consider control design for positive compartmental systems in which each compartment's outflow rate is described by a concave function of the amount of material in the compartment. We address the problem of det...
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We consider control design for positive compartmental systems in which each compartment's outflow rate is described by a concave function of the amount of material in the compartment. We address the problem of determining the routing of material between compartments to satisfy time-varying state constraints while ensuring that material reaches its intended destination over a finite time horizon. We give sufficient conditions for the existence of a time-varying state-dependent routing strategy which ensures that the closed-loop system satisfies basic network properties of positivity, conservation and interconnection while ensuring that capacity constraints are satisfied, when possible, or adjusted if a solution cannot be found. These conditions are formulated as a linear programming problem. Instances of this linear programming problem can be solved iteratively to generate a solution to the finite horizon routing problem. Results are given for the application of this control design method to an example problem. Published by Elsevier Ltd.
In a carbon-constrained world, the continuing and rapid growth of gas-fired power generation (GPG) will lead to the increasing demand for natural gas. The reliable and affordable gas supply hence becomes an important ...
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In a carbon-constrained world, the continuing and rapid growth of gas-fired power generation (GPG) will lead to the increasing demand for natural gas. The reliable and affordable gas supply hence becomes an important factor to consider in power system planning. Meanwhile, the installation of GPG units should take into account not only the fuel supply constraints but also the capability of sending out the generated power. In this paper, a novel expansion co-planning (ECP) model is proposed, aiming to minimize the overall capital and operational costs for the coupled gas and power systems. Moreover, linear formulations are introduced to deal with the nonlinear nature of the objective functions and constraints. Furthermore, the physical and economic interactions between the two systems are simulated by an iterative process. The proposed linear co-planning approach is tested on a simple six-bus power system with a seven-node gas system and a modified IEEE 118-bus system with a 14-node gas system. Numerical results have demonstrated that our co-planning approach can allow systematic investigations on supporting cost-effective operating and planning decisions for power systems.
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