scholarly journals Firefly Algorithm for Polynomial Bézier Surface Parameterization

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Akemi Gálvez ◽  
Andrés Iglesias
Keyword(s):  
Computer Animation ◽  
Computer Aided Design ◽  
Firefly Algorithm ◽  
Optimization Problems ◽  
Continuous Optimization ◽  
Well Being ◽  
Optimization Techniques ◽  
Surface Parameterization ◽  
Cad Cam ◽  
Data Points

A classical issue in many applied fields is to obtain an approximating surface to a given set of data points. This problem arises in Computer-Aided Design and Manufacturing (CAD/CAM), virtual reality, medical imaging, computer graphics, computer animation, and many others. Very often, the preferred approximating surface is polynomial, usually described in parametric form. This leads to the problem of determining suitable parametric values for the data points, the so-called surface parameterization. In real-world settings, data points are generally irregularly sampled and subjected to measurement noise, leading to a very difficult nonlinear continuous optimization problem, unsolvable with standard optimization techniques. This paper solves the parameterization problem for polynomial Bézier surfaces by applying the firefly algorithm, a powerful nature-inspired metaheuristic algorithm introduced recently to address difficult optimization problems. The method has been successfully applied to some illustrative examples of open and closed surfaces, including shapes with singularities. Our results show that the method performs very well, being able to yield the best approximating surface with a high degree of accuracy.

scholarly journals From Nonlinear Optimization to Convex Optimization through Firefly Algorithm and Indirect Approach with Applications to CAD/CAM

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Akemi Gálvez ◽  
Andrés Iglesias
Keyword(s):  
Convex Optimization ◽  
Nonlinear Optimization ◽  
Firefly Algorithm ◽  
Optimization Problem ◽  
Continuous Optimization ◽  
Optimization Techniques ◽  
Continuous Variables ◽  
Indirect Approach ◽  
Nonlinear Optimization Problem ◽  
Cad Cam

Fitting spline curves to data points is a very important issue in many applied fields. It is also challenging, because these curves typically depend on many continuous variables in a highly interrelated nonlinear way. In general, it is not possible to compute these parameters analytically, so the problem is formulated as a continuous nonlinear optimization problem, for which traditional optimization techniques usually fail. This paper presents a new bioinspired method to tackle this issue. In this method, optimization is performed through a combination of two techniques. Firstly, we apply the indirect approach to the knots, in which they are not initially the subject of optimization but precomputed with a coarse approximation scheme. Secondly, a powerful bioinspired metaheuristic technique, the firefly algorithm, is applied to optimization of data parameterization; then, the knot vector is refined by using De Boor’s method, thus yielding a better approximation to the optimal knot vector. This scheme converts the original nonlinear continuous optimization problem into a convex optimization problem, solved by singular value decomposition. Our method is applied to some illustrative real-world examples from the CAD/CAM field. Our experimental results show that the proposed scheme can solve the original continuous nonlinear optimization problem very efficiently.

scholarly journals A Modified Artificial Bee Colony Algorithm with Firefly Algorithm Strategy for Continuous Optimization Problems

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Amnat Panniem ◽  
Pikul Puphasuk
Keyword(s):  
Firefly Algorithm ◽  
Artificial Bee Colony ◽  
Optimization Problems ◽  
Continuous Optimization ◽  
Control Parameters ◽  
Exploration And Exploitation ◽  
Bee Colony ◽  
Continuous Problems ◽  
Local Solutions ◽  
Continuous Optimization Problems

Artificial Bee Colony (ABC) algorithm is one of the efficient nature-inspired optimization algorithms for solving continuous problems. It has no sensitive control parameters and has been shown to be competitive with other well-known algorithms. However, the slow convergence, premature convergence, and being trapped within the local solutions may occur during the search. In this paper, we propose a new Modified Artificial Bee Colony (MABC) algorithm to overcome these problems. All phases of ABC are determined for improving the exploration and exploitation processes. We use a new search equation in employed bee phase, increase the probabilities for onlooker bees to find better positions, and replace some worst positions by the new ones in onlooker bee phase. Moreover, we use the Firefly algorithm strategy to generate a new position replacing an unupdated position in scout bee phase. Its performance is tested on selected benchmark functions. Experimental results show that MABC is more effective than ABC and some other modifications of ABC.

scholarly journals Cuckoo Search with Lévy Flights for Weighted Bayesian Energy Functional Optimization in Global-Support Curve Data Fitting

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Akemi Gálvez ◽  
Andrés Iglesias ◽  
Luis Cabellos
Keyword(s):  
Optimization Problems ◽  
Cuckoo Search ◽  
Parameter Tuning ◽  
Well Being ◽  
Data Fitting ◽  
Energy Functional ◽  
Simple Task ◽  
Cad Cam ◽  
Two Parameters ◽  
Applied Fields

The problem of data fitting is very important in many theoretical and applied fields. In this paper, we consider the problem of optimizing a weighted Bayesian energy functional for data fitting by using global-support approximating curves. By global-support curves we mean curves expressed as a linear combination of basis functions whose support is the whole domain of the problem, as opposed to other common approaches in CAD/CAM and computer graphics driven by piecewise functions (such as B-splines and NURBS) that provide local control of the shape of the curve. Our method applies a powerful nature-inspired metaheuristic algorithm calledcuckoo search, introduced recently to solve optimization problems. A major advantage of this method is its simplicity: cuckoo search requires only two parameters, many fewer than other metaheuristic approaches, so the parameter tuning becomes a very simple task. The paper shows that this new approach can be successfully used to solve our optimization problem. To check the performance of our approach, it has been applied to five illustrative examples of different types, including open and closed 2D and 3D curves that exhibit challenging features, such as cusps and self-intersections. Our results show that the method performs pretty well, being able to solve our minimization problem in an astonishingly straightforward way.

Optimization With Discrete Variables Via Recursive Quadratic Programming: Part 1—Concepts and Definitions

1989 ◽  
Vol 111 (1) ◽  
pp. 124-129 ◽  
Author(s):  
J. Z. Cha ◽  
R. W. Mayne
Keyword(s):  
Nonlinear Programming ◽  
Quadratic Programming ◽  
Optimization Problems ◽  
Continuous Optimization ◽  
Optimization Techniques ◽  
Discrete Variables ◽  
Convergence Criteria ◽  
Recursive Quadratic Programming ◽  
Analytical Properties ◽  
Discrete Optimization Problems

Although a variety of algorithms for discrete nonlinear programming have been proposed, the solution of discrete optimization problems is far from mature compared to continuous optimization techniques. This paper focuses on the recursive quadratic programming strategy which has proven to be efficient and robust for continuous optimization. The procedure is adapted to consider a class of mixed discrete nonlinear programming problems and utilizes the analytical properties of functions and constraints. This first part of the paper considers definitions, concepts, and possible convergence criteria. Part II includes the development and testing of the algorithm.

scholarly journals Firefly Algorithm for Explicit B-Spline Curve Fitting to Data Points

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Akemi Gálvez ◽  
Andrés Iglesias
Keyword(s):  
Firefly Algorithm ◽  
Optimization Problem ◽  
Nonlinear Least Squares ◽  
Well Being ◽  
B Spline ◽  
Spline Curve ◽  
Spline Fitting ◽  
Nature Inspired Algorithm ◽  
Data Points ◽  
High Degree

This paper introduces a new method to compute the approximating explicit B-spline curve to a given set of noisy data points. The proposed method computes all parameters of the B-spline fitting curve of a given order. This requires to solve a difficult continuous, multimodal, and multivariate nonlinear least-squares optimization problem. In our approach, this optimization problem is solved by applying the firefly algorithm, a powerful metaheuristic nature-inspired algorithm well suited for optimization. The method has been applied to three illustrative real-world engineering examples from different fields. Our experimental results show that the presented method performs very well, being able to fit the data points with a high degree of accuracy. Furthermore, our scheme outperforms some popular previous approaches in terms of different fitting error criteria.

Full-mouth Rehabilitation of Hypocalcified-type Amelogenesis Imperfecta With Chairside Computer-aided Design and Computer-aided Manufacturing: A Case Report

2019 ◽  
Vol 44 (3) ◽  
pp. E145-E158
Author(s):  
C Moussally ◽  
H Fron-Chabouis ◽  
A Charrière ◽  
L Maladry ◽  
E Dursun
Keyword(s):  
Case Report ◽  
Computer Aided Design ◽  
Functional Results ◽  
Well Being ◽  
Amelogenesis Imperfecta ◽  
Computer Aided Manufacturing ◽  
Patient Reported ◽  
Computer Aided ◽  
Cad Cam ◽  
Aided Design

SUMMARY Background: This case report describes the complete full-mouth treatment of hypocalcified amelogenesis imperfecta (AI) by chairside computer-aided design and computer-aided manufacturing (CAD/CAM). Case summary: After several years of interrupted dental care, a 17-year-old female patient presented with pain and also esthetic and functional discomfort. With loss of enamel and dyschromia affecting all teeth, the diagnosis was hypocalcified AI. Affected tissues were eliminated, gingivectomy with laser was performed, an indented jig was used to record the centric relationship during optical impressions, and 28 full ceramic crowns were created by chairside CAD/CAM in four sessions. The patient reported rapid pain relief and an overall improvement of well-being. Conclusion: AI sequelae can be treated promptly and conservatively with chairside CAD/CAM, obtaining esthetic and functional results.

Bounded, Multidimensional, Integrated Memetic Evolution for Character Recognition Based on Predictive Elimination Theory and Optimization Techniques

2019 ◽  
Vol 10 (1) ◽  
pp. 62-74
Author(s):  
Rashmi Welekar ◽  
Nileshsingh V. Thakur
Keyword(s):  
Character Recognition ◽  
Optimization Problems ◽  
General Structure ◽  
Continuous Optimization ◽  
Memetic Algorithms ◽  
Optimization Techniques ◽  
Elimination Theory ◽  
Combinatorial Optimization Problems ◽  
Optimization Parameters ◽  
Predictive Approaches

This article describes how inspired by the natural process of evolution in genetic algorithms, memetic algorithms (MAs) are a category of cultural evolution phenomenon. The very concept of MA has been discussed in the last few years and is adding newer dimensions to MA and computational skills of algorithms. There are many optimization algorithms which fully exploit the problem under consideration. This article presents a heuristic approach for an improvised algorithm which takes into consideration various optimization parameters in isolation and tries to integrate the self-learning technique of MA. A general structure of MA according to this article should be perfectly in-line with brain activities which are neurotically tested and given maximum emphasis on local search and context-based predictive approaches rather than mathematically computing every event and taking or picking solutions based on results of certain formula. This article goes one step beyond the conventional set of the variety of problem domains, ranging from discrete optimization, continuous optimization, constrained optimization and multi objective optimization in which MAs have been successfully implemented. These optimization techniques must be processed using outcomes of predictive optimization and using a method of elimination to make the search set smaller and smaller as we progress deeper into the search. There is a scarcity of literature and also lack of availability of comprehensive reviews on MAs. The proposed technique is a better approach for solving combinatorial optimization problems. This article gives an overview of various domains and problem types in which MA can be used. Apart from this, the problem of character recognition using predictive optimization and implementation of elimination theory MA is discussed.

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