Solving Bilevel Multi-Objective Optimization Problems Using Evolutionary Algorithms

Deb, Kalyanmoy; Sinha, Ankur

doi:10.1007/978-3-642-01020-0_13

Cited by 976 publications

(1,653 citation statements)

References 12 publications

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“…However, the bilevel approach used here is a nested approach which was found to be computationally somewhat expensive in some cases. Recent efficient coevolutionary approaches for bilevel optimization (Deb and Sinha 2009) can be applied for a faster computation of the extreme points. The hybrid extreme-point-to-nadir approach seems to be a promising procedure for making a reliable and accurate estimate of the nadir point in linear and non-linear multi-objective optimization problems.…”

Section: Discussionmentioning

confidence: 99%

Nadir Point Estimation Using Evolutionary Approaches: Better Accuracy and Computational Speed Through Focused Search

Deb

Miettinen

2009

Lecture Notes in Economics and Mathematical Systems

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Estimation of the nadir objective vector representing worst objective function values in the set of Pareto-optimal solutions is an important task, particularly for multi-objective optimization problems having more than two conflicting objectives. Along with the ideal point, nadir point can be used to normalize the objectives so that multi-objective optimization algorithms can be used more reliably. The knowledge of the nadir point is also a pre-requisite to many multiple criteria decision making methodologies. Moreover, nadir point is useful for an aid in interactive methodologies and visualization softwares catered for multi-objective optimization. However, the computation of an exact nadir point for more than two objectives is not an easy matter, simply because the nadir point demands the knowledge of extreme Pareto-optimal solutions. In the past few years, researchers have proposed several nadir point estimation procedures using evolutionary optimization methodologies. In this paper, we review the past studies and reveal an interesting chronicle of events in this direction. To make the estimation procedure computationally faster and more accurate, the methodologies were refined one after the other by mainly focusing on finding smaller and still sufficient subset of Pareto-optimal solutions to facilitate estimating the nadir point. Simulation results on a number of numerical test problems demonstrate better efficacy of the approach which aims to find only the extreme Pareto-optimal points compared to other two approaches.

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Section: Discussionmentioning

confidence: 99%

Nadir Point Estimation Using Evolutionary Approaches: Better Accuracy and Computational Speed Through Focused Search

Deb

Miettinen

2009

Lecture Notes in Economics and Mathematical Systems

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“…The genetic algorithm is an optimization method based on evolution. 28 In each step, a certain population of solutions is created. The best of these solutions are selected as parents, which are used to create the input parameters for their children in the next generation.…”

Section: Genetic Algorithm Optimizationmentioning

confidence: 99%

Performance predictions of a focused ion beam from a laser cooled and compressed atomic beam

Haaf

Wouters

Geer

et al. 2014

Journal of Applied Physics

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Focused ion beams are indispensable tools in the semiconductor industry because of their ability to image and modify structures at the nanometer length scale. Here we report on performance predictions of a new type of focused ion beam based on photo-ionization of a laser cooled and compressed atomic beam. Particle tracing simulations are performed to investigate the effects of disorder-induced heating after ionization in a large electric field. They lead to a constraint on this electric field strength which is used as input for an analytical model which predicts the minimum attainable spot size as a function of amongst others the flux density of the atomic beam, the temperature of this beam and the total current. At low currents (I < 10 pA) the spot size will be limited by a combination of spherical aberration and brightness, while at higher currents this is a combination of chromatic aberration and brightness. It is expected that a nanometer size spot is possible at a current of 1 pA. The analytical model was verified with particle tracing simulations of a complete focused ion beam setup. A genetic algorithm was used to find the optimum acceleration electric field as a function of the current. At low currents the result agrees well with the analytical model while at higher currents the spot sizes found are even lower due to effects that are not taken into account in the analytical model.

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“…Crossovers for real parameter GAs have the interesting feature [14] of having tunable parameters that can be used to modify their exploration power. In this proposed approach each individual in the population consists of two types of variables: real and integer.…”

Section: B Crossover Schemementioning

confidence: 99%

Optimal Reactive Power Dispatch for Voltage Stability Enhancement Using Real Coded Genetic Algorithm

Jeyanthy¹,

Devaraj²

2010

IJCEE

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Abstract-This paper presents an algorithm for solving the multi-objective reactive power dispatch problem in a power system. Modal analysis of the system is used for static voltage stability assessment. Loss minimization and maximization of voltage stability margin are taken as the objectives. Generator terminal voltages, reactive power generation of the capacitor banks and tap changing transformer setting are taken as the optimization variables. An improved genetic algorithm which permits the control variables to be represented in their natural form is proposed to solve this combinatorial optimization problem. For effective genetic operation, crossover and mutation operators which can directly operate on floating point number and integers are used. The proposed method has been tested on IEEE 30 bus system and has resulted in loss which is less than the value reported earlier and is well suited for solving the mixed integer optimization problem.Index Terms-Modal analysis, optimal reactive power dispatch, loss minimization, genetic algorithm. I. INTRODUCTIONOptimal reactive power dispatch problem is one of the difficult optimization problems in power systems. The sources of the reactive power are the generators, synchronous condensers, capacitors, static compensators and tap changing transformers. The problem that has to be solved in a reactive power optimization is to determine the required reactive generation at various locations so as to optimize the objective function. Here the reactive power dispatch problem involves best utilization of the existing generator bus voltage magnitudes, transformer tap setting and the output of reactive power sources so as to minimize the loss and to enhance the voltage stability of the system. It involves a non linear optimization problem. Various mathematical techniques have been adopted to solve this optimal reactive power dispatch problem. These include the gradient method [1-2], Newton method [3] and linear programming [4][5][6][7].The gradient and Newton methods suffer from the difficulty in handling inequality constraints. To apply linear programming, the input-output function is to be expressed as a set of linear P. Aruna Jeyanthy is with the Electrical and Electronics Engineering Department, N.I. College of Engineering Kanyakumari District, India (corresponding author to provide phone: 91 9443174253. email: arunadarwin@yahoo.com) D.Devaraj is with the Electrical and Electronics Engineering Department, Kalasalingam University, Srivilliputhur, India.functions which may lead to loss of accuracy. Recently global optimization techniques such as genetic algorithms have been proposed to solve the reactive power flow problem [8,9]. A genetic algorithm is a stochastic search technique based on the mechanics of natural selection. In this paper, genetic algorithm is used to solve the voltage constrained reactive power dispatch problem. The proposed algorithm identifies the optimal values of generation bus voltage magnitudes, transformer tap setting and the output of the reactive p...

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Solving Bilevel Multi-Objective Optimization Problems Using Evolutionary Algorithms

Cited by 976 publications

References 12 publications

Nadir Point Estimation Using Evolutionary Approaches: Better Accuracy and Computational Speed Through Focused Search

Nadir Point Estimation Using Evolutionary Approaches: Better Accuracy and Computational Speed Through Focused Search

Performance predictions of a focused ion beam from a laser cooled and compressed atomic beam

Optimal Reactive Power Dispatch for Voltage Stability Enhancement Using Real Coded Genetic Algorithm

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