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 Pareto-optimal 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 Pareto-optimal points sim...

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 ellipse-specific 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.

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, non-linear, non-unimodal, constrained optimization. The goal is to overcome the non-linearity 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. 1 Introduction Early work on gate sizing targeting area/delay optimization can be found in [20, 12]. Using a RC delay model, TILOS [8] expresses the delay and area as posynomials. Geometric programming or heuristics based greedy approaches can be used to so...

In this paper, a flexible yet efficient algorithm for solving engineering design optimization problems is presented. The algorithm is developed based on both binary-coded and realcoded genetic algorithms (GAs). Since both GAs are used, the variables involving discrete, continuous, and zero-one 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...

In this paper a methodology for feature selection for the handwritten digit string recognition is proposed. Its novelty lies in the use of a multi-objective 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.

Optimal design of a multi-speed 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 multi-objective evolutionary algorithm, which is capable of solving the original problem involving mixed discrete and real-valued parameters and more than one objectives, and is capable of finding multiple non-dominated solutions in a single simulation run. On a number of instantiations of the problem having different complexities, the efficacy of NSGA-II 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.

The recovery of generic solid parts is a fundamental step towards the realization of general-purpose vision systems. This thesis investigates issues in grouping, segmentation and recognition of parts from two-dimensional edge images.

We consider the problem of a learning mechanism (for example, a robot) locating a point on a line when it is interacting with an random environment which essentially informs it, possibly erroneously, which way it should move. In this paper we present a novel scheme by which the point can be learnt using some recently devised learning principles. The heart of the strategy involves discretizing the space and performing a controlled random walk on this space. The scheme is shown to be e-optimal and to converge with probability 1. Although the problem is solved in its generality, its application in non-linear optimization has also been suggested. Typically, an optimization process involves working one's way toward the maximum (minimum) using the local information that is available. However, the crucial issue in these strategies is that of determining the parameter to be used in the optimization itself. If the parameter is too small the convergence is sluggish. On the other hand, if the par...

The present review paper summarizes the research work done mostly by the authors on packing equal circles in the unit square in the last years. 1.

The choice of shape representation and the extraction of such representations from images is one of the great challenges of computer vision. This thesis addresses these issues by examining a number of topics in curve representations. Beginning with an examination of the conic fitting problem, a new linear ellipse fitter is developed. Previous ellipse-specific methods have been computationally expensive, and previous linear methods have fitted general conics, rather than ellipses, to the data. The new algorithm is compared with several others and is shown to be extremely stable and insensitive to noise. The comparison is itself of interest as it focusses on the behaviour of the algorithms under occlusion rather than noise, demonstrating that this is the parameter to which they are most sensitive. A comprehensive evaluation of conic fitting algorithms then follows, concluding that occlusion sensitivity is one of the key characteristics of the conic fitting problem. This survey is in itself of interest as it provides specific recommendations for practitioners in the field. The second part of the thesis deals with the question of deciding how well a model describes a given set of data. Two new techniques are discussed, both of which are independent of the noise level of the data, and which are therefore applicable to a wide range of automated processes. The run-distribution test of Chapter 5 is an effective method of determining a posteriori whether a given model accurately describes a data set. Comparisons with a number of standard tests indicate that the run-distribution test outperforms them unless the true noise level is known. The sum-of-variance metric of Chapter 6, on the other hand, provides a parameter-free method of segmenting a dataset into piecewise smooth segments. The behaviour of the metric is demonstrated