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152
Multiobjective Optimization Using Nondominated Sorting in Genetic Algorithms
 Evolutionary Computation
, 1994
"... In trying to solve multiobjective optimization problems, many traditional methods scalarize the objective vector into a single objective. In those cases, the obtained solution is highly sensitive to the weight vector used in the scalarization process and demands the user to have knowledge about t ..."
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Cited by 524 (4 self)
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In trying to solve multiobjective optimization problems, many traditional methods scalarize the objective vector into a single objective. In those cases, the obtained solution is highly sensitive to the weight vector used in the scalarization process and demands the user to have knowledge about the underlying problem. Moreover, in solving multiobjective problems, designers may be interested in a set of Paretooptimal points, instead of a single point. Since genetic algorithms(GAs) work with a population of points, it seems natural to use GAs in multiobjective optimization problems to capture a number of solutions simultaneously. Although a vector evaluated GA (VEGA) has been implemented by Schaffer and has been tried to solve a number of multiobjective problems, the algorithm seems to have bias towards some regions. In this paper, we investigate Goldberg's notion of nondominated sorting in GAs along with a niche and speciation method to find multiple Paretooptimal points sim...
Direct least Square Fitting of Ellipses
, 1998
"... This work presents a new efficient method for fitting ellipses to scattered data. Previous algorithms either fitted general conics or were computationally expensive. By minimizing the algebraic distance subject to the constraint 4ac  b² = 1 the new method incorporates the ellipticity constraint ..."
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Cited by 421 (3 self)
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This work presents a new efficient method for fitting ellipses to scattered data. Previous algorithms either fitted general conics or were computationally expensive. By minimizing the algebraic distance subject to the constraint 4ac  b² = 1 the new method incorporates the ellipticity constraint into the normalization factor. The proposed method combines several advantages: (i) It is ellipsespecific so that even bad data will always return an ellipse; (ii) It can be solved naturally by a generalized eigensystem and (iii) it is extremely robust, efficient and easy to implement.
A Combined Genetic Adaptive Search (GeneAS) for Engineering Design
 Computer Science and Informatics
, 1996
"... In this paper, a flexible yet efficient algorithm for solving engineering design optimization problems is presented. The algorithm is developed based on both binarycoded and realcoded genetic algorithms (GAs). Since both GAs are used, the variables involving discrete, continuous, and zeroone varia ..."
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Cited by 50 (8 self)
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In this paper, a flexible yet efficient algorithm for solving engineering design optimization problems is presented. The algorithm is developed based on both binarycoded and realcoded genetic algorithms (GAs). Since both GAs are used, the variables involving discrete, continuous, and zeroone variables are handled quite efficiently. The algorithm restricts its search only to the permissible values of the variables, thereby reducing the search effort in converging to the optimum solution. The efficiency and ease of application of the proposed method is demonstrated by solving three different mechanical component design problems borrowed from the optimization literature. The proposed technique is compared with binarycoded genetic algorithms, Augmented Lagrange multiplier method, Branch and Bound method and Hooke and Jeeves pattern search method. In all cases, the solutions obtained using the proposed technique are superior than those obtained with other methods. These results are encour...
Gate Sizing for Constrained delay/power/area optimization
 in IEEE Transcation on VLSI Design
, 1997
"... Abstract—Gate sizing has a significant impact on the delay, power dissipation, and area of the final circuit. It consists of choosing for each node of a mapped circuit a gate implementation in the library so that a cost function is optimized under some constraints. For instance, one wants to mini ..."
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Cited by 42 (1 self)
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Abstract—Gate sizing has a significant impact on the delay, power dissipation, and area of the final circuit. It consists of choosing for each node of a mapped circuit a gate implementation in the library so that a cost function is optimized under some constraints. For instance, one wants to minimize the power consumption and/or the area of a circuit under some userdefined delay constraints, or to obtain the fastest circuit within a given power budget. Although this technologydependent optimization has been investigated for years, the proposed approaches sometimes rely on assumptions, cost models, or algorithms that make them unrealistic or impossible to apply on reallife large circuits. We discusse here a gate sizing algorithm (GS), and show how it is used to achieve constrained optimization. It can be applied on large circuits within a reasonable CPU time, e.g., minimizing the power of a 10000 nodes circuit under some delay constraint in 2 hours. Keywords—Gate sizing, discrete constrained optimization, delay/power/area tradeoff I.
New Algorithms for Gate Sizing: A Comparative Study
 IN DAC
, 1996
"... Gate sizing consists of choosing for each node of a mapped network a gate implementation in the library so that some cost function is optimized under some constraints. It has a significant impact on the delay, power dissipation, and area of the final circuit. This paper compares five gate sizing alg ..."
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Cited by 40 (1 self)
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Gate sizing consists of choosing for each node of a mapped network a gate implementation in the library so that some cost function is optimized under some constraints. It has a significant impact on the delay, power dissipation, and area of the final circuit. This paper compares five gate sizing algorithms targeting discrete, nonlinear, nonunimodal, constrained optimization. The goal is to overcome the nonlinearity and nonunimodality of the delay and the power to achieve good quality results within a reasonable CPU time, e.g., handling a 10000 node network in 2 hours. We compare the five algorithms on constraint free delay optimization and delay constrained power optimization, and show that one method is superior to the others.
Power control and rate management for wireless multimedia CDMA systems
 IEEE Trans. Commun
, 2001
"... Abstract—We consider a wireless multimedia codedivision multipleaccess system, in which the terminals transmit at different rates. We formulate the problem as a constrained optimization problem, with the objective of maximizing the total effective rate. An optimal power control strategy is derived ..."
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Cited by 33 (0 self)
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Abstract—We consider a wireless multimedia codedivision multipleaccess system, in which the terminals transmit at different rates. We formulate the problem as a constrained optimization problem, with the objective of maximizing the total effective rate. An optimal power control strategy is derived. When the scale of the system is large, the optimal solution takes a simple form, which is easy to be applied practically. Furthermore, our basic model can be extended to include delaysensitive traffic. Index Terms—Multimedia CDMA, multirate CDMA, power control.
A Methodology for Feature Selection Using MultiObjective Genetic Algorithms for Handwritten Digit String Recognition
 International Journal of Pattern Recognition and Artificial Intelligence
, 2003
"... In this paper a methodology for feature selection for the handwritten digit string recognition is proposed. Its novelty lies in the use of a multiobjective genetic algorithm where sensitivity analysis and neural network are employed to allow the use of a representative database to evaluate tness ..."
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Cited by 32 (8 self)
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In this paper a methodology for feature selection for the handwritten digit string recognition is proposed. Its novelty lies in the use of a multiobjective genetic algorithm where sensitivity analysis and neural network are employed to allow the use of a representative database to evaluate tness and the use of a validation database to identify the subsets of selected features that provide a good generalization. Some advantages of this approach include the ability to accommodate multiple criteria such as number of features and accuracy of the classier, as well as the capacity to deal with huge databases in order to adequately represent the pattern recognition problem. Comprehensive experiments on the NIST SD19 demonstrate the feasibility of the proposed methodology.
MultiSpeed Gearbox Design Using MultiObjective Evolutionary Algorithms
 JOURNAL OF MECHANICAL DESIGN, VOLUME 125, ISSUE
, 2002
"... Optimal design of a multispeed gearbox involves different types of decision variables and objectives. Due to lack of efficient classical optimization techniques, such problems are usually decomposed into tractable subproblems and solved. Moreover, in most cases the explicit mathematical expressi ..."
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Cited by 16 (5 self)
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Optimal design of a multispeed gearbox involves different types of decision variables and objectives. Due to lack of efficient classical optimization techniques, such problems are usually decomposed into tractable subproblems and solved. Moreover, in most cases the explicit mathematical expressions of the problem formulation is exploited to arrive at the optimal solutions. In this paper, we demonstrate the use of a multiobjective evolutionary algorithm, which is capable of solving the original problem involving mixed discrete and realvalued parameters and more than one objectives, and is capable of finding multiple nondominated solutions in a single simulation run. On a number of instantiations of the problem having different complexities, the efficacy of NSGAII in handling different types of decision variables, constraints, and multiple objectives are demonstrated. An investigation of multiple obtained solutions provides a number of interesting insights to the gearbox design problem, which are otherwise dicult to obtain using existing optimization techniques.
Global optimization in geometry — Circle packing into the square
 Essays and Surveys in Global Optimization
, 2005
"... ..."
An efficient constrained learning algorithm with momentum acceleration
 Neural Networks 8 Ž 1995
"... AbstractAn algorithm for efficient learning in feedforward networks is presented. Momentum acceleration is achieved by solving a constrained optimization problem using nonlinear programming techniques. In particular, minimization of the usual mean square error cost function is attempted under an a ..."
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Cited by 12 (4 self)
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AbstractAn algorithm for efficient learning in feedforward networks is presented. Momentum acceleration is achieved by solving a constrained optimization problem using nonlinear programming techniques. In particular, minimization of the usual mean square error cost function is attempted under an additional condition for which the purpose is to optimize the alignment of the weight update vectors in successive epochs. The algorithm is applied to several benchmark training tasks (exclusiveor, encoder, multiplexer, and counter problems). Its performance, in terms of learning speed and scalability properties, is evaluated and found superior to the performance of reputedly fast variants of the backpropagation algorithm in the above benchmarks.