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Ant Colony Optimization (ACO) encompasses a family of metaheuristics inspired by the foraging behaviour of ants. Since the introduction of the first ACO algorithm, called Ant System (AS), several ACO variants have been proposed in the literature. Owing to their superior performance over other alternatives, the most popular ACO algorithms are Rank-based Ant System (AS R a n k ), Max-Min Ant System (MMAS) and Ant Colony System (ACS). While AS R a n k shows a fast convergence to high-quality solutions, its performance is improved by other more widely used ACO variants such as MMAS and ACS, which are currently considered the state-of-the-art ACO algorithms for static combinatorial optimization problems. With the purpose of diversifying the search process and avoiding early convergence to a local optimal, the proposed approach extends AS R a n k with an originality reinforcement strategy of the top-ranked solutions and a pheromone smoothing mechanism that is triggered before the algorithm reaches stagnation. The approach is tested on several symmetric and asymmetric Traveling Salesman Problem and Sequential Ordering Problem instances from TSPLIB benchmark. Our experimental results show that the proposed method achieves fast convergence to high-quality solutions and outperforms the current state-of-the-art ACO algorithms A S R a n k , MMAS and ACS, for most instances of the benchmark. [ABSTRACT FROM AUTHOR]

This work addresses the IFS-based image reconstruction problem for binary images. Given a binary image as the input, the goal is to obtain all the parameters of an iterated function system whose attractor approximates the input image accurately; the quality of this approximation is measured according to a similarity function between the original and the reconstructed images. This paper introduces a new method to tackle this issue. The method is based on functional networks, a powerful extension of neural networks that uses functions instead of the scalar weights typically found in standard neural networks. The method relies on an artificial network comprised of several functional networks, one for each of the contractive affine maps forming the IFS. The method is applied to an illustrative and challenging example of a fractal binary image exhibiting a complicated shape. The graphical and numerical results show that the method performs very well and is able to reconstruct the input image using IFS with high accuracy. The results also show that the method is not yet optimal and offers room for further improvement. [ABSTRACT FROM AUTHOR]

The rapid development of computer science and telecommunications has brought new ways and practices to sport training. The artificial sport trainer, founded on computational intelligence algorithms, has gained momentum in the last years. However, artificial sport trainer usually suffers from a lack of automatisation in realization and control phases of the training. In this study, the Digital Twin is proposed as a framework for helping athletes, during realization of training sessions, to make the proper decisions in situations they encounter. The digital twin for artificial sport trainer is based on the cognitive model of humans. This concept has been applied to cycling, where a version of the system on a Raspberry Pi already exists. The results of porting the digital twin on the mentioned platform shows promising potential for its extension to other sport disciplines. [ABSTRACT FROM AUTHOR]

This paper concerns several important topics of the Symmetry journal, namely, computer-aided design, computational geometry, computer graphics, visualization, and pattern recognition. We also take advantage of the symmetric structure of the tensor-product surfaces, where the parametric variables u and v play a symmetric role in shape reconstruction. In this paper we address the general problem of global-support parametric surface approximation from clouds of data points for reverse engineering applications. Given a set of measured data points, the approximation is formulated as a nonlinear continuous least-squares optimization problem. Then, a recent metaheuristics called Cuckoo Search Algorithm (CSA) is applied to compute all relevant free variables of this minimization problem (namely, the data parameters and the surface poles). The method includes the iterative generation of new solutions by using the Lévy flights to promote the diversity of solutions and prevent stagnation. A critical advantage of this method is its simplicity: the CSA requires only two parameters, many fewer than any other metaheuristic approach, so the parameter tuning becomes a very easy task. The method is also simple to understand and easy to implement. Our approach has been applied to a benchmark of three illustrative sets of noisy data points corresponding to surfaces exhibiting several challenging features. Our experimental results show that the method performs very well even for the cases of noisy and unorganized data points. Therefore, the method can be directly used for real-world applications for reverse engineering without further pre/post-processing. Comparative work with the most classical mathematical techniques for this problem as well as a recent modification of the CSA called Improved CSA (ICSA) is also reported. Two nonparametric statistical tests show that our method outperforms the classical mathematical techniques and provides equivalent results to ICSA for all instances in our benchmark. [ABSTRACT FROM AUTHOR]

This paper presents a new method called multilayer embedded bat algorithm (ME-BAT) to solve the general curve reconstruction problem with free-form parametric B-splines. Opposed to previous approaches in the literature, this method computes the optimal values of all free variables (data parameters, breakpoints, and poles), a very difficult task because they are strongly intertwined in a highly nonlinear way. The method is based on the idea of applying the bat algorithm at different layers: a main bat algorithm at an upper layer to compute the breakpoints and a second bat algorithm at a lower layer to compute the data parameters. This second bat algorithm is embedded into the first one and executed for each breakpoint vector of the population and at each iteration step of the main algorithm. Then, the poles are calculated by least-squares minimization through SVD. The method has been applied to three real-world engineering examples. The experimental results show that the method performs very well, being able to recover the underlying shape of data with high accuracy. A comparison with eleven alternative methods (including six classical methods in the field and all the metaheuristic methods applied so far to this problem) shows that this method outperforms the previous approaches in the field for all instances in the benchmark. [ABSTRACT FROM AUTHOR]

Surface reconstruction is a very important issue with outstanding applications in fields such as medical imaging (computer tomography, magnetic resonance), biomedical engineering (customized prosthesis and medical implants), computer-aided design and manufacturing (reverse engineering for the automotive, aerospace and shipbuilding industries), rapid prototyping (scale models of physical parts from CAD data), computer animation and film industry (motion capture, character modeling), archaeology (digital representation and storage of archaeological sites and assets), virtual/augmented reality, and many others. In this paper we address the surface reconstruction problem by using rational Bézier surfaces. This problem is by far more complex than the case for curves we solved in a previous paper. In addition, we deal with data points subjected to measurement noise and irregular sampling, replicating the usual conditions of real-world applications. Our method is based on a memetic approach combining a powerful metaheuristic method for global optimization (the electromagnetism algorithm) with a local search method. This method is applied to a benchmark of five illustrative examples exhibiting challenging features. Our experimental results show that the method performs very well, and it can recover the underlying shape of surfaces with very good accuracy. [ABSTRACT FROM AUTHOR]

Fitting curves to noisy data points is a difficult problem arising in many scientific and industrial domains. Although polynomial functions are usually applied to this task, there are many shapes that cannot be properly fitted by using this approach. In this paper, we tackle this issue by using rational Bézier curves. This is a very difficult problem that requires computing four different sets of unknowns (data parameters, poles, weights, and the curve degree) strongly related to each other in a highly nonlinear way. This leads to a difficult continuous nonlinear optimization problem. In this paper, we propose two simulated annealing schemas (the all-in-one schema and the sequential schema) to determine the data parameterization and the weights of the poles of the fitting curve. These schemas are combined with least-squares minimization and the Bayesian Information Criterion to calculate the poles and the optimal degree of the best fitting Bézier rational curve, respectively. We apply our methods to a benchmark of three carefully chosen examples of 2D and 3D noisy data points. Our experimental results show that this methodology (particularly, the sequential schema) outperforms previous polynomial-based approaches for our data fitting problem, even in the presence of noise of low-medium intensity. [ABSTRACT FROM AUTHOR]

Data fitting with B-splines is a challenging problem in reverse engineering for CAD/CAM, virtual reality, data visualization, and many other fields. It is well-known that the fitting improves greatly if knots are considered as free variables. This leads, however, to a very difficult multimodal and multivariate continuous nonlinear optimization problem, the so-called knot adjustment problem. In this context, the present paper introduces an adapted elitist clonal selection algorithm for automatic knot adjustment of B-spline curves. Given a set of noisy data points, our method determines the number and location of knots automatically in order to obtain an extremely accurate fitting of data. In addition, our method minimizes the number of parameters required for this task. Our approach performs very well and in a fully automatic way even for the cases of underlying functions requiring identical multiple knots, such as functions with discontinuities and cusps. To evaluate its performance, it has been applied to three challenging test functions, and results have been compared with those from other alternative methods based on AIS and genetic algorithms. Our experimental results show that our proposal outperforms previous approaches in terms of accuracy and flexibility. Some other issues such as the parameter tuning, the complexity of the algorithm, and the CPU runtime are also discussed. [ABSTRACT FROM AUTHOR]

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 called cuckoo 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. [ABSTRACT FROM AUTHOR]

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 B'ezier 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]