This paper considers the problem of optimally placing fixed and switched type capacitors in a radial distribution network. The aim of this problem is to minimize the costs associated with capacitor banks, peak power, ...
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This paper considers the problem of optimally placing fixed and switched type capacitors in a radial distribution network. The aim of this problem is to minimize the costs associated with capacitor banks, peak power, and energy losses whilst satisfying a pre-specified set of physical and technical constraints. The proposed solution is obtained using a two-phase approach. In phase-I, the problem is formulated as a conic program in which all nodes are candidates for placement of capacitor banks whose sizes are considered as continuous variables. A global solution of the phase-I problem is obtained using an interior-point based conic programming solver. Phase-II seeks a practical optimal solution by considering capacitor sizes as discrete variables. The problem in this phase is formulated as a mixed integer linear program based on minimizing the L1-norm of deviations from the phase-I state variable values. The solution to the phase-II problem is obtained using a mixed integer linear programming solver. The proposed method is validated via extensive comparisons with previously published results. (C) 2007 Elsevier B.V. All rights reserved.
The objective of this study was to develop valid statistical collision models for multilane highway segments to examine the safety of curbs. For this, road geometric traffic and collision data for 2001 to 2003 were co...
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The objective of this study was to develop valid statistical collision models for multilane highway segments to examine the safety of curbs. For this, road geometric traffic and collision data for 2001 to 2003 were collected. The data included 2,274 collisions and 885 injury collisions that occurred on 191.85 mi of 199 directional segments in North Carolina. The authors applied a new modeling method of introducing variables into the model one by one in a multiplicative form. A nonlinear optimizing algorithm for estimating parameters using a negative binomial log likelihood function was adopted for the modeling. The functional form of the variable to be introduced was determined on the basis of the relationship between the recorded number of collisions and the number of collisions predicted by the current model without the variable. The integrate-differentiate method was applied to find candidate functional forms for each variable. Model selections were based on the -2 log likelihood and Bayesian information criterion statistics, and the cumulative residuals plot method to check the goodness of fit of the models was adopted. As a result of the modeling efforts, the annual average daily traffic, access point density, shoulder width, and shoulder type (including curb presence) variables were introduced to the final model for total collisions. The same variables except the shoulder type variable were introduced to the injury collision model. Overall, then, it appears that curbs mean fewer total collisions and no change in injury collisions as compared to no curbs on the sampled road segments.
We propose a globalization strategy for nonlinear constrained optimization. The method employs a 'flexible' penalty function to promote convergence, where during each iteration the penalty parameter can be cho...
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We propose a globalization strategy for nonlinear constrained optimization. The method employs a 'flexible' penalty function to promote convergence, where during each iteration the penalty parameter can be chosen as any number within a prescribed interval, rather than a fixed value. This increased flexibility in the step acceptance procedure is designed to promote long productive steps for fast convergence. An analysis of the global convergence properties of the approach in the context of a line search sequential quadratic programming method and numerical results for the KNITRO software package are presented.
In a competitive electricity market two kinds of generating companies coexist;according to their market power it possible to classify them in price-taking generating companies and leader generating companies. The opti...
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In a competitive electricity market two kinds of generating companies coexist;according to their market power it possible to classify them in price-taking generating companies and leader generating companies. The optimal bidding of price-taking companies depends on the market clearing prices. On the other hand, the optimal bidding of leader companies depends on their corresponding residual demand curves, which capture how the market clearing price changes with the variation on the levels production of a particular generating company. The idea of this article is to assess the potential market power of a leader company when it decides to compete in quantities according to the Cournot model. A non-linear optimization problem has been used to model the lemel the dleader generating company. Finally, a realistic case study is presented and discussed.
We consider a procurement problem where suppliers offer concave quantity discounts. The resulting continuous knapsack problem involves the minimization of a sum of separable concave functions. We identify polynomially...
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We consider a procurement problem where suppliers offer concave quantity discounts. The resulting continuous knapsack problem involves the minimization of a sum of separable concave functions. We identify polynomially solvable special cases of. this NP-hard problem, and provide a fully polynomial-time approximation scheme for the general problem. (c) 2007 Elsevier B.V. All rights reserved.
Particle swarm optimization (PSO) is originally developed as an unconstrained optimization technique, therefore lacks an explicit mechanism for handling constraints. When solving constrained optimization problems (COP...
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Particle swarm optimization (PSO) is originally developed as an unconstrained optimization technique, therefore lacks an explicit mechanism for handling constraints. When solving constrained optimization problems (COPs) with PSO, the existing research mainly focuses on how to handle constraints, and the impact of constraints on the inherent search mechanism of PSO has been scarcely explored. Motivated by this fact, in this paper we mainly investigate how to utilize the impact of constraints (or the knowledge about the feasible region) to improve the optimization ability of the particles. Based on these investigations, we present a modified PSO, called self-adaptive velocity particle swarm optimization (SAVPSO), for solving COPs. To handle constraints, in SAVPSO we adopt our recently proposed dynamic-objective constraint-handling method (DOCHM), which is essentially a constituent part of the inherent search mechanism of the integrated SAVPSO, i.e., DOCHM + SAVPSO. The performance of the integrated SAVPSO is tested on a well-known benchmark suite and the experimental results show that appropriately utilizing the knowledge about the feasible region can substantially improve the performance of the underlying algorithm in solving COPs.
Mathematical programming models for telecommunications network design are prevalent in the literature, but little research has been reported on stochastic models for cellular networks. We present a stochastic revenue ...
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Mathematical programming models for telecommunications network design are prevalent in the literature, but little research has been reported on stochastic models for cellular networks. We present a stochastic revenue optimization model for CDMA networks inspired by bid pricing models from the airline industry. We describe the optimality conditions for the model and develop a supergradient algorithm to solve it. We provide computational results that show the effects of the distribution and variance of demand. Finally, we discuss areas of future research, including a method to optimize the locations of the towers. (c) 2007 Elsevier B.V. All rights reserved.
This paper addresses the problem of selecting a suitable failure-finding maintenance policy for repairable systems. We will consider hidden failures that do not interrupt aircraft operation when they occur, such as fa...
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This paper addresses the problem of selecting a suitable failure-finding maintenance policy for repairable systems. We will consider hidden failures that do not interrupt aircraft operation when they occur, such as failures of warning devices or backup components. We will study both corrective maintenance actions, carried out after item failure, and periodic failure finding, designed to check whether a system still works. Based on our probabilistic analytic developments, the optimal maintenance policy is then obtained as a solution of an optimization problem, in which the maintenance cost rate is the objective function and the risk of corrective maintenance is the constraint function. Finally, we will present an application of our methodology to a real-world case provided by Airbus Industries.
A standard Quadratic programming problem (StQP) consists in minimizing a (nonconvex) quadratic form over the standard simplex. For solving a SLQP we present an exact and a heuristic algorithm, that are based on new th...
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A standard Quadratic programming problem (StQP) consists in minimizing a (nonconvex) quadratic form over the standard simplex. For solving a SLQP we present an exact and a heuristic algorithm, that are based on new theoretical results for quadratic and convex optimization problems. With these results a StQP is reduced to a constrained nonlinear minimum weight clique problern in an associated graph. Such a Clique problem, which does not seem to have been Studied before, is then solved with all exact and a heuristic algorithm. Some computational experience shows that Our algorithms are able to solve StQP problems of at least one order of magnitude larger than those reported in the literature. (c) 2007 Elsevier B.V. All rights reserved.
We give several linear time algorithms for the continuous quadratic knapsack problem. In addition, we report cycling and wrong-convergence examples in a number of existing algorithms, and give encouraging computationa...
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We give several linear time algorithms for the continuous quadratic knapsack problem. In addition, we report cycling and wrong-convergence examples in a number of existing algorithms, and give encouraging computational results for large-scale problems.
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