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Hernández, Víctor Adrián Sosa; Schütze, Oliver; Trautmann, Heike; Rudolph, Günter
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In this paper we investigate some aspects of stochastic local search such as pressure toward and along the set of interest within parameter dependent multiobjective optimization problems. The discussions and initial computations indicate that the problem to compute an approximation of the entire solution set of such a problem via stochastic search algorithms is wellconditioned. The new insights may be helpful for the design of novel stochastic search algorithms such as specialized evolutionary approaches. The discussion in particular indicates that it might be beneficial to integrate the set of external parameters directly into the search instead of computing projections of the solution sets separately by fixing the value of the external parameter.
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RiveraLopez, Rafael; CanulReich, Juana; Gámez, José A.; Puerta, José M.
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This paper describes the application of a Differential Evolution based approach for inducing oblique decision trees in a recursive partitioning strategy. Considering that: (1) the task of finding an optimal hyperplane with realvalued coefficients is a complex optimization problem in a continuous space, and (2) metaheuristics have been successfully applied for solving this type of problems, in this work a differential evolution algorithm is applied with the aim of finding nearoptimal hyperplanes that will be used as test conditions of an oblique decision tree. The experimental results show that this approach induces more accurate classifiers than those produced by other proposed induction methods.
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RiveraLopez, Rafael; CanulReich, Juana
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2 Citations
This paper describes the application of a Differential Evolution based approach for inducing oblique decision trees in a global search strategy. By using both the number of attributes and the number of class labels in a dataset, this approach determines the size of the realvalued vector utilized for encoding the set of hyperplanes used as test conditions in the internal nodes of an oblique decision tree. Also a scheme of three steps to map the linear representation of candidate solutions into feasible oblique decision trees is described. Experimental results obtained show that this approach induces more accurate classifiers than those produced by other proposed induction methods.
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Cuate, Oliver; Uribe, Lourdes; Ponsich, Antonin; Lara, Adriana; Beltran, Fernanda; Sánchez, Alberto Rodríguez; Schütze, Oliver
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The recently proposed Pareto Tracer method is an effective numerical continuation technique which allows performing movements along the set of KKT points of a given multiobjective optimization problem. The nature of this predictorcorrector method leads to constructing solutions along the Pareto set/front numerically; it applies to higher dimensions and can handle box and equality constraints. We argue that the right hybridization of multiobjective evolutionary algorithms together with specific continuation methods leads to fast and reliable algorithms. Moreover, due to the continuation technique, the resulting hybrid algorithm could have a certain advantage when handling, in particular, equality constraints. In this paper, we make the first effort to hybridize NSGAII with the Pareto Tracer. To support our claims, we present some numerical results on continuously differentiable equality constrained biobjective optimization test problems, to show that the resulting hybrid NSGAII/PT is highly competitive against some stateoftheart algorithms for constrained optimization. Finally, we stress that the chosen approach could be applied to a more significant number of objectives with some adaptations of the algorithm, leading to a very promising research topic.
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Sergio Ordoñez, G.; Cesar Guerra, T.
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The present article exposes a prototype and a security system, which using Artificial Intelligence of Neural Networks, using different environments to train and learn attacks, seeking to optimize the overall average of threats, minimizing the percent of vulnerabilities using an evolutionary algorithm called EVONORM.
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MartínezPeñaloza, MaríaGuadalupe; MezuraMontes, Efrén; CruzRamírez, Nicandro; AcostaMesa, HéctorGabriel; RíosFigueroa, HomeroVladimir
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The multiobjective clustering with automatic determination of the number of clusters (MOCK) approach is improved in this work by means of an empirical comparison of three multiobjective evolutionary algorithms added to MOCK instead of the original algorithm used in such approach. The results of two different experiments using seven real data sets from UCI repository are reported: (1) using two multiobjective optimization performance metrics (hypervolume and twoset coverage) and (2) using the Fmeasure and the silhouette coefficient to evaluate the clustering quality. The results are compared against the original version of MOCK and also against other algorithms representative of the state of the art. Such results indicate that the new versions are highly competitive and able to deal with different types of data sets.
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Fernández de Vega, Francisco; Olague, Gustavo; Trujillo, Leonardo; Lombraña González, Daniel
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Evolutionary algorithms (EAs) consume large amounts of computational resources, particularly when they are used to solve realworld problems that require complex fitness evaluations. Beside the lack of resources, scientists face another problem: the absence of the required expertise to adapt applications for parallel and distributed computing models. Moreover, the computing power of PCs is frequently underused at institutions, as desktops are usually devoted to administrative tasks. Therefore, the proposal in this work consists of providing a framework that allows researchers to massively deploy EA experiments by exploiting the computing power of their instituions’ PCs by setting up a Desktop Grid System based on the BOINC middleware. This paper presents a new model for running unmodified applications within BOINC with a webbased centralized management system for available resources. Thanks to this proposal, researchers can run scientific applications without modifying the application’s source code, and at the same time manage thousands of computers from a single web page. Summarizing, this model allows the creation of ondemand customized execution environments within BOINC that can be used to harness unused computational resources for complex computational experiments, such as EAs. To show the performance of this model, a realworld application of Genetic Programming was used and tested through a centrallymanaged desktop grid infrastructure. Results show the feasibility of the approach that has allowed researchers to generate new solutions by means of an easy to use and manage distributed system.
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Oliva, Diego; Cuevas, Erik; Pajares, Gonzalo; Zaldivar, Daniel
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Template matching (TM) plays an important role in several imageprocessing applications such as feature tracking, object recognition, stereo matching, and remote sensing. The TM approach seeks for the bestpossible resemblance between a subimage known as template and its coincident region within a source image. TM involves two critical aspects: similarity measurement and search strategy. The simplest available TM method aims for the bestpossible coincidence between the images through an exhaustive computation of the normalized crosscorrelation (NCC) values (similarity measurement) for all elements of the source image (search strategy). Recently, several TM algorithms that are based on evolutionary approaches have been proposed to reduce the number of NCC operations by calculating only a subset of search locations. In this paper, a new algorithm based on the electromagnetismlike algorithm (EMO) is proposed to reduce the number of search locations in the TM process. The algorithm uses an enhanced EMO version, which incorporates a modification of the local search procedure to accelerate the exploitation process. As a result, the new EMO algorithm can substantially reduce the number of fitness function evaluations while preserving the good search capabilities of the original EMO. In the proposed approach, particles represent search locations, which move throughout the positions of the source image. The NCC coefficient, considered as the fitness value (charge extent), evaluates the matching quality presented between the template image and the coincident region of the source image, for a determined search position (particle). The number of NCC evaluations is also reduced by considering a memory, which stores the NCC values previously visited to avoid the reevaluation of the same search locations (particles). Guided by the fitness values (NCC coefficients), the set of candidate positions are evolved through EMO operators until the bestpossible resemblance is determined. The conducted simulations show that the proposed method achieves the best balance over other TM algorithms in terms of estimation accuracy and computational cost.
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Cuevas, Erik; Echavarría, Alonso; RamírezOrtegón, Marte A.
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47 Citations
The ability of an Evolutionary Algorithm (EA) to find a global optimal solution depends on its capacity to find a good rate between exploitation of foundsofar elements and exploration of the search space. Inspired by natural phenomena, researchers have developed many successful evolutionary algorithms which, at original versions, define operators that mimic the way nature solves complex problems, with no actual consideration of the explorationexploitation balance. In this paper, a novel natureinspired algorithm called the States of Matter Search (SMS) is introduced. The SMS algorithm is based on the simulation of the states of matter phenomenon. In SMS, individuals emulate molecules which interact to each other by using evolutionary operations which are based on the physical principles of the thermalenergy motion mechanism. The algorithm is devised by considering each state of matter at one different exploration–exploitation ratio. The evolutionary process is divided into three phases which emulate the three states of matter: gas, liquid and solid. In each state, molecules (individuals) exhibit different movement capacities. Beginning from the gas state (pure exploration), the algorithm modifies the intensities of exploration and exploitation until the solid state (pure exploitation) is reached. As a result, the approach can substantially improve the balance between exploration–exploitation, yet preserving the good search capabilities of an evolutionary approach. To illustrate the proficiency and robustness of the proposed algorithm, it is compared to other wellknown evolutionary methods including novel variants that incorporate diversity preservation schemes. The comparison examines several standard benchmark functions which are commonly considered within the EA field. Experimental results show that the proposed method achieves a good performance in comparison to its counterparts as a consequence of its better exploration–exploitation balance.
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VargasFelix, J. Miguel; BotelloRionda, Salvador
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We explore a structure optimization strategy that is analogous to how bones are formed in embryos, where shape and strength are mostly defined. The strategy starts with a rectangular grid of elements of uniform thickness with boundary displacements and force conditions. The thickness of each element can grow or shrink depending on the internal strain, this process is done iteratively. The internal strain is found using the finite element method solving a solid mechanics problem. The final shape depends only on five parameters (von Mises threshold, thickness grow and shrink factors, maximum and minimum thickness). An evolutionary algorithm is used to search an optimal combination of these five parameters that gives a shape that uses the minimal amount of material but also keeps the strain under a maximum threshold. This algorithm requires to test thousands of shapes, thus supercomputing is needed. Evaluation of shapes are done in a computer cluster. We will describe algorithms, software implementation and some results.
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Cuevas, Erik; ReynaOrta, Adolfo; DíazCortes, MargaritaArimatea
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The main objective of multimodal optimization is to find multiple global and local optima for a problem in only one execution. Detecting multiple solutions to a multimodal optimization formulation is especially useful in engineering, since the best solution could not represent the best realizable due to various practical restrictions. The States of Matter Search (SMS) is a recently proposed stochastic optimization technique. Although SMS is highly effective in locating single global optimum, it fails in providing multiple solutions within a single execution. To overcome this inconvenience, a new multimodal optimization algorithm called the Multimodal States of Matter Search (MSMS) in introduced. Under MSMS, the original SMS is enhanced with new multimodal characteristics by means of: (1) the definition of a memory mechanism to efficiently register promising local optima according to their fitness values and the distance to other probable high quality solutions; (2) the modification of the original SMS optimization strategy to accelerate the detection of new local minima; and (3) the inclusion of a depuration procedure at the end of each state to eliminate duplicated memory elements. The performance of the proposed approach is compared to several stateoftheart multimodal optimization algorithms considering a benchmark suite of fourteen multimodal problems. The results confirm that the proposed method achieves the best balance over its counterparts regarding accuracy and computational cost.
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AguilarRivera, Anton; ValenzuelaRendón, Manuel
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This work introduces a new algorithmic trading method based on evolutionary algorithms and portfolio theory. The limitations of traditional portfolio theory are overcome using a multiperiod definition of the problem. The model allows the inclusion of dynamic restrictions like transaction costs, portfolio unbalance, and inflation. A Monte Carlo method is proposed to handle these types of restrictions. The investment strategies method is introduced to make trading decisions based on the investor’s preference and the current state of the market. Preference is determined using heuristics instead of theoretical utility functions. The method was tested using real data from the Mexican market. The method was compared against buyandholds and singleperiod portfolios for metrics like the maximum loss, expected return, risk, the Sharpe’s ratio, and others. The results indicate investment strategies perform trading with less risk than other methods. Singleperiod methods attained the lowest performance in the experiments due to their high transaction costs. The conclusion was investment decisions that are improved when information providing from many different sources is considered. Also, profitable decisions are the result of a careful balance between action (transaction) and inaction (buyandhold).
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GuevaraSouza, Mauricio; Vallejo, Edgar E.
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1 Citations
This paper presents a new evolutionary algorithm for solving multiobjective optimization problems. The proposed algorithm simulates the infection of the endosymbiotic bacteria Wolbachia to improve the evolutionary search. We conducted a series of computational experiments to contrast the results of the proposed algorithm to those obtained by state of the art multiobjective evolutionary algorithms (MOEAs). We employed two widely used test problem benchmarks. Our experimental results show that the proposed model outperforms established MOEAs at solving most of the test problems.
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Silva Garza, Andrés Gómez
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Evolutionary algorithms (EAs) have been used in varying ways for design and other creative tasks. One of the main elements of these algorithms is the fitness function used by the algorithm to evaluate the quality of the potential solutions it proposes. The fitness function ultimately represents domain knowledge that serves to bias, constrain, and guide the algorithm’s search for an acceptable solution. In this paper, we explore the degree to which the fitness function’s implementation affects the search process in an evolutionary algorithm. To perform this, the reliability and speed of the algorithm, as well as the quality of the designs produced by it, are measured for different fitness function implementations. These measurements are then compared and contrasted.
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Hinojosa, Salvador; Oliva, Diego; Cuevas, Erik; Pajares, Gonzalo; Avalos, Omar; Gálvez, Jorge
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This paper presents two multicriteria optimization techniques: the MultiObjective Crow Search Algorithm (MOCSA) and an improved chaotic version called MultiObjective Chaotic Crow Search Algorithm (MOCCSA). Both methods MOCSA and MOCCSA are based on an enhanced version of the recently published Crow Search Algorithm. Crows are intelligent animals with interesting strategies for protecting their food hatches. This compelling behavior is extended into a MultiObjective approach. MOCCSA uses chaoticbased criteria on the optimization process to improve the diversity of solutions. To determinate if the performance of the algorithm is significantly enhanced, the incorporation of a chaotic operator is further validated by a statistical comparison between the proposed MOCCSA and its chaoticfree counterpart (MOCSA) indicating that the results of the two algorithms are significantly different from each other. The performance of MOCCSA is evaluated by a set of standard benchmark functions, and the results are contrasted with two wellknown algorithms: MultiObjective Dragonfly Algorithm and MultiObjective Particle Swarm Optimization. Both quantitative and qualitative results show competitive results for the proposed approach.
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Cuevas, Erik; González, Mauricio
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8 Citations
Hough transform (HT) has been the most common method for circle detection that delivers robustness but adversely demands considerable computational efforts and large memory requirements. As an alternative to HTbased techniques, the problem of shape recognition has also been handled through optimization methods. In particular, extracting multiple circle primitives falls into the category of multimodal optimization as each circle represents an optimum which must be detected within the feasible solution space. However, since all optimizationbased circle detectors focus on finding only a single optimal solution, they need to be applied several times in order to extract all the primitives which results on timeconsuming algorithms. This paper presents an algorithm for automatic detection of multiple circular shapes that considers the overall process as a multimodal optimization problem. In the detection, the approach employs an evolutionary algorithm based on the way in which the animals behave collectively. In such an algorithm, searcher agents emulate a group of animals which interact to each other using simple biological rules. These rules are modeled as evolutionary operators. Such operators are applied to each agent considering that the complete group maintains a memory which stores the optimal solutions seen sofar by applying a competition principle. The detector uses a combination of three noncollinear edge points as parameters to determine circle candidates (possible solutions). A matching function determines if such circle candidates are actually present in the image. Guided by the values of such matching functions, the set of encoded candidate circles are evolved through the evolutionary algorithm so that the best candidate (global optimum) can be fitted into an actual circle within the edgeonly image. Subsequently, an analysis of the incorporated memory is executed in order to identify potential local optima which represent other circles. Experimental results over several complex synthetic and natural images have validated the efficiency of the proposed technique regarding accuracy, speed and robustness.
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Escalante, Hugo Jair; MarinCastro, Maribel; MoralesReyes, Alicia; Graff, Mario; RosalesPérez, Alejandro; MontesyGómez, Manuel; Reyes, Carlos A.; Gonzalez, Jesus A.
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Prototype generation deals with the problem of generating a small set of instances, from a large data set, to be used by KNN for classification. The two key aspects to consider when developing a prototype generation method are: (1) the generalization performance of a KNN classifier when using the prototypes; and (2) the amount of data set reduction, as given by the number of prototypes. Both factors are in conflict because, in general, maximizing data set reduction implies decreasing accuracy and viceversa. Therefore, this problem can be naturally approached with multiobjective optimization techniques. This paper introduces a novel multiobjective evolutionary algorithm for prototype generation where the objectives are precisely the amount of reduction and an estimate of generalization performance achieved by the selected prototypes. Through a comprehensive experimental study we show that the proposed approach outperforms most of the prototype generation methods that have been proposed so far. Specifically, the proposed approach obtains prototypes that offer a better tradeoff between accuracy and reduction than alternative methodologies.
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