ABSTRACT Failures in safety‐critical systems such as aircraft engines pose severe economic and societal risks. This study introduces a novel Remaining Useful Life (RUL) prediction method uniquely combining diverse techniques. Specifically, the proposed methodology integrates fuzzy time series analysis with sliding window segmentation and Multinomial Naive Bayes (MNB) classification. These techniques transform raw sensor data from NASA's C‐MAPSS turbofan engine datasets into a symbolic representation that effectively captures degradation patterns leading to system failure. Tested across the four subsets—FD001, FD002, FD003 and FD004—from the C‐MAPSS NASA dataset, the proposed approach achieved competitive RMSE values of 24.73, 36.03, 34.71 and 39.07, respectively, while demonstrating robust PHM score metrics of as low as 1508 for one of the datasets. By optimising key parameters to enhance accuracy and computational efficiency, this low‐computational‐cost alternative to conventional deep learning models significantly advances RUL prediction, offering a promising alternative prognostic strategy in environments where the balance between computational efficiency and accuracy is essential.

This paper introduces a motion planning approach for navigating in a dynamic environment. The path is represented using a Non-Uniform Rational B-Spline (NURBS) to ensure smoothness, curvature continuity, and proper orientation by adjusting its parameters. A Differential Evolution algorithm optimizes the curve parameters and traversal speed at each replanning interval, taking into account speed limits, maximum curvature, and obstacles in the environment. A constraintbased on Velocity Obstacle (VO) ensures collision-free motion, considering bounds provided by lower-level controllers. The feasibility of the approach is validated through simulations and real-world experiments with the Crazyflie 2.1 micro quadcopter.

Multistep ahead time series forecasting is essential in Internet of Things (IoT) applications in smart cities and smart homes to make accurate future predictions and precise decision making. Thus, this study introduces a novel multiple-input single-output (MISO) forecasting method called Multistep Embedding-based fuzzy time series (MS-EFTS), designed to predict high-dimensional nonstationary time series data. As a first-order approach, it employs a direct strategy that integrates an embedding transformation with a weighted multivariate FTS (WMVFTS) model. This combination allows for effective predictions over long-term horizons within low-dimensional, learned continuous representations. The effectiveness of the proposed MS-EFTS is assessed using three high-dimensional IoT time series in this investigation. The obtained results showcase the superior performance of the proposed method compared to some deep learning forecasting methods, including LSTM, BiLSTM, TCN, and CNN-LSTM, in terms of accuracy, parsimony, and efficiency.

Time series classification (TSC) is a supervised task in which time series data are associated with predefined classes. Time ordering and correlations of the samples should be considered and observations can have different lengths. Therefore, learning compact and useful representations is an important approach for TSC. Fuzzy time series (FTS) methods have the ability to find temporal patterns and transition rules. Probabilistic Weighted FTS (PWFTS) uses the empirical probabilities to find the model of a TS. Despite its good performance, this method has been used exclusively for forecasting problems. Therefore, in this study we propose a novel TSC method using the PWFTS representation learning weights as features in conjuction to a classifier algorithm. We show that PWFTS method is able to learn useful representations for time series in low computational time. Our algorithm was tested in 24 datasets available in the UCR Time Series Classification Archive and compared with state of the art methods: fuzzy cognitive maps (FCM), Rocket, and TS2Vec in combination to the classifiers random forest (RF) and support vector machine (SVM). The classification accuracy and execution time required to find the features were evaluated. The results show that our fuzzy-probabilistic representation learning method is similar in accuracy to the other methods, and the time consumption for PWFTS computation was two to five orders of magnitude faster than the other methods. The results suggest that our approach can be used in time sensitive applications and in systems with hardware limitations.

Fuzzy Cognitive Maps (FCMs) have demonstrated considerable success in time series forecasting and are adept at handling uncertainties and capturing the dynamics of complex systems. Nevertheless, challenges still remain in the handling of multivariate high-dimensional time series using a time-effective learning algorithm. This paper introduces MRHFCM, a new methodology for predicting high-dimensional time series in multiple-input multiple-output (MIMO) systems. MRHFCM represents a hybrid method that combines data embedding transformation, randomized high-order FCM (R-HFCM), and an echo state network (ESN). The core of MRHFCM involves a cascade of R-HFCMs termed the CR-HFCM model. Each CR-HFCM comprises three layers: the input layer, reservoir (internal layer), and output layer. Notably, only the output layer is trainable, employing the least squares minimization algorithm. The weights within each sub-reservoir are randomly chosen and remain unchanged throughout the training procedure. Three real-world high-dimensional datasets are utilized to assess the performance of the proposed MRHFCM method. The results obtained reveal that our approach outperforms some existing baseline and state-of-the-art machine learning and deep learning forecasting techniques in terms of both accuracy and parsimony.

Recent technological breakthroughs have allowed unmanned aerial vehicles (UAVs) to be utilized in a broad range of new operations. Among these various applications, herein, we focus on the use of UAVs for search and rescue missions in emergency and postdisaster scenarios. In this context, self-charging technologies for drones create new challenges in the routing of UAVs with charging stations. We present a variant of the vehicle routing problem (VRP) to address the integrated use of UAVs and mobile charging stations and define the VRP with synchronized networks (VRPSN), a new class of VRPs involving the routing of UAVs whose recharge platforms can travel to different locations during an operation. This leads to two networks within the VRP that must be integrated and synchronized. This research develops a mixed-integer linear program model for the VRPSN that considers the use of UAVs and mobile charging stations in a synchronized manner. To overcome the computational limits of the MILP model, this research presents a construct-and-adjust heuristic method integrated with a genetic algorithm. As a numerical example, we test the proposed model on the Córrego do Feijão Mine located in Minas Gerais, Brazil, where a dam recently collapsed, killing many workers. Numerical tests show that the new methodology is an attractive planning method for providing efficient and rapid responses in search and rescue missions.

Multi-objective algorithms based on decomposition have become popular for the reason that a uniform distribution of weight vectors may result in a better distribution of solutions along the Pareto front. However, for more complex Pareto fronts with irregular shapes, the initial weight vectors may not be adequate. One alternative to overcome this problem, is to adapt the weight vectors during the evolutionary process. In this paper an adaptive version of Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) is proposed to change the weight vectors based on the concept of local neighborhoods. The proposed method is called MOEA/D with local-neighborhood-based adaptation (MOEA/D-LNA). The proposed method is compared against a number of famous variants of MOEA/D in the literature. Initial experimental results have shown promising effectiveness on problems with irregular Pareto shapes.

Time series forecasting is an essential research field that provides significant data to help professionals in several areas. Thus, growing research and development in this area have been conducted, aiming at developing new forecasting methods with higher performance levels, but always also with low processing costs. One of this methods is Fuzzy Time Series - FTS. However, one great problem of FTS prediction is how to properly deal with the uncertainty associated to the time series and to model's design. Thus, in this paper we propose a univariate interval type-2 fuzzy time series model combined with the concept of Self-organised Direction Aware Data Partitioning Algorithm (SODA) for universe of discourse partitioning. All experiments were performed using the TAIEX data set and the results were then compared to other forecasting models from literature. A sliding window methodology was applied and the forecast error metric chosen was the Root Mean Squared Error (RMSE) for all methods. SODA-T2FTS results show that it outperformed other forecasting methods confirming that interval type-2 fuzzy logic can be a reliable tool for time series prediction.

Machine learning models that follow the FTS (Fuzzy Time Series) approach stand out as data-driven non-parametric models of easy implementation and high accuracy, which can be applied to uni-variate and multivariate time series. However, this approach encounters difficulties when dealing with databases of many variables, given the explosion of rules that are generated for the construction of models. Usually filter and wrapper techniques (e.g. Boruta test) and data projection techniques (e.g. Principal Component Analysis) are used. The present work proposes a methodology for tackling this issue by projecting the original high-dimensional data into a low dimensional embedding space using self-organizing Kohonnen maps and later using the Weighted Multivariate FTS method (WMVFTS) for rule discovery and forecasting. The results obtained showed good values of RMSE and MAPE, illustrating the validity and potential of the method.

In the present work we extend the traditional C4.5 decision tree method for regression and forecasting of multivariate time series. In the proposed method, time series data is first fuzzified leading to a fuzzy time series (FTS) representation of the data. A fuzzy decision tree (FDT) based on C4.5 is employed to form the knowledge base of the FTS model. The method can deal with high-order and multivariate fuzzy time series, offering an explainable model. The FDT-FTS method is tested with data from IBOVESPA stock market index, which tracks the performance of around 50 most liquid stocks traded on the Sao Paulo Stock Exchange in Brazil. The method is applied to the IBOVESPA mini future contract time series in order to forecast future values using a mix of historical values and technical analysis indicators. This method is compared with Support Vector Regression (SVR) and Random Forest Regression (RFR), both methods implemented in the Scikit-Learn open-source library. The FDT-FTS model was implemented in Python programming language in the open-source pyFTS library. Although all three methods have similar performance, according to the MAPE, SMAPE, RMSE, NRMSE and MAE metrics, the proposed method is computationally faster and explainable.

Explainable Artificial Intelligence (or xAI) has become an important research topic in the fields of Machine Learning and Deep Learning. In this paper, we propose a Genetic Programming (GP) based approach, name Genetic Programming Explainer (GPX), to the problem of explaining decisions computed by AI systems. The method generates a noise set located in the neighborhood of the point of interest, whose prediction should be explained, and fits a local explanation model for the analyzed sample. The tree structure generated by GPX provides a comprehensible analytical, possibly non-linear, expression which reflects the local behavior of the complex model. We considered three machine learning techniques that can be recognized as complex black-box models: Random Forest, Deep Neural Network and Support Vector Machine in twenty data sets for regression and classifications problems. Our results indicate that the GPX is able to produce more accurate understanding of complex models than the state of the art. The results validate the proposed approach as a novel way to deploy GP to improve interpretability.

Various studies indicate that Fuzzy Time Series (FTS) methods can obtain high accuracy in a variety of forecasting applciations. However, weighted FTS methods tend to show superiority in contrast to weightless ones. This study exploits the use of Fuzzy Cognitive Map (FCM) technique to generate the rules in the knowledge base for the FTS forecasting method. The proposed hybrid method, named HFCM-FTS, combines High Order Fuzzy Cognitive Maps (HFCM) and High Order Fuzzy Time Series (HOFTS), where the weight matrices associated with the state transitions are learned via the genetic algorithm from the data. The objective of FCM is to find the weight matrices that model the causal relations among the concepts defined in the Universe of Discourse. As a case study, we consider solar energy forecasting with public data for Brazilian solar stations from the year 2012 to 2015. The proposed HFCM-FTS is compared with HOFTS, Weighted High Order FTS (WHOFTS), and Probabilistic Weighted FTS (PWFTS) methods. The experiments also cover the influence of three modeling elements on the accuracy of the presented model including the number of concepts, activation function, and bias. The results show that the HFCM-FTS is able to achieve the best results with a low number of concepts.

In recent years, the demand for developing low computational cost methods to deal with uncertainties in forecasting has been increased. Probabilistic forecasting is a class of forecasting in which the method provides intervals or probability distributions as outcomes of its forecasting. The aim of this paper is, therefore, proposing a new forecasting approach based on fuzzy time series (FTS) that takes advantage of fuzzy and stochastic patterns on data and is capable to deal with point, interval, and distribution forecasts. The method proposed was empirically tested with typical financial time series, and the results were compared with other standard FTS and statistical methods. The results show that the proposed method obtained accurate results and outperformed standard FTS methods. The proposed method also combines versatility, scalability, and low computational cost, making it useful on a wide range of application scenarios.

Technological advances have opened up the possibility of using unmanned aerial vehicles (UAVs) in diverse environments. The mining industry has been looking for solutions to handle periodic inspections of the belt conveyors that transport iron ore. The state of the art indicates the use of UAVs for this task as an attractive, low-cost and safe alternative, allowing for a significant increase in security. A new concise mixed-integer linear programming (MILP) model is developed to address UAV routing and charging station planning for belt conveyor inspection. We conduct computational tests covering a real conveyor belt system in Brazil to validate the model in practical applications. The loading terminal possesses approximately 120 km of belt conveyors, leading to 230 inspection points. Instances of different sizes were generated by randomly sampling a subset of these points and using two different drone specifications. The results show that the new optimization modeling satisfies the problem requirements and is a significant contribution to the automation of inspection in the mining industry.

Time series forecasting is an essential task in the management of Smart Cities and Smart Grids, becoming even more challenging when it needs to deal with big data time series. The development of highly accurate machine learning models is yet harder when considering the optimization of hyperparameters, which is an expensive computational task. To tackle these challenges this work proposes the Distributed Evolutionary Hyperparameter Optimization (DEHO) for the Weighted Multivariate Fuzzy Time Series method (WMVFTS), a simple and non-parametric forecasting method with high scalability and accuracy, comprising a sequential training and forecasting procedure and a MapReduce extension for distributed processing. The proposed methods were evaluated using a cluster with commodity hardware and two big time series, showing increasing speed up for training and test times as new CPU cores are added to cluster. Then the DEHO method was executed in the computational cluster, achieving fast convergence and feasible processing time and generating highly accurate WMVFTS models.

The visualization gap is one of the important challenges posed by many-objective optimization problems (MaOPs). In this paper, we present an integrated data visualization method for MaOPs, called CAP-vis plot, combining the Chord diagram, the Angular mapping and the Parallel coordinates in the same visualization. The method follows the circular design layout, showing different levels of information. This new approach allows the spatial location of points in high dimensional spaces, the visualization of harmony and conflict between objectives, as well as the comparison of the approximation sets provided by different algorithms. With this work, we try to fill the visualization gap and bring information to the eye of the decision-maker and the optimizer, with an intuitive overview of the obtained results. Some experiments were performed using the Benchmark Functions proposed for the IEEE-CEC 2018 Competition on Many-Objective Optimization. We used the tool to visualize the results obtained by NSGA-III, HypE, RVEA, MOEA/DD, PICEA-g, using the PlatEMO MATLAB platform, with the same parameter settings of the competition. The results on the Benchmark Problems show the importance of the qualitative analysis of the data. The experiments show how visualization can help interpretation of the results and identification of strengths and drawbacks of MOEA.

This work deals with the Unrelated Parallel Machine Scheduling Problem with Setup Times, with the objective of minimizing the makespan. It is proposed an Adaptive Large Neighborhood Search (ALNS) metaheuristic using Learning Automata (LA) to adapt the probabilities of using removal and insertion heuristics and methods. A computable function in the LA updates the probability vector for selecting the actions, corresponding to six removal and six insertion methods. We also propose a new insertion method based on Hungarian algorithm, which is applied to solve subproblems optimally. Computational experiments are performed to verify the performance of the proposed method. A set of instances available in the literature with problems up to 150 jobs and 10 machines is employed in the experiments. The proposed LA-ALNS is compared against three other algorithms from the literature. The results suggest that our algorithm has better performance in most of cases (88%) under the defined conditions of experiments. Statistical tests also suggest that LA-ALNS is better than the other algorithms from the literature. The proposed method is able to automatically choose the most suitable heuristics for the instance of the problem, through adaptation and learning in the Learning Automata.

The generation of weight vectors is the primary step in MOEA based on decomposition and aggregation methods, affecting the diversity of the Pareto approximation and overall performance of the algorithm. The basic methods, following the method proposed by Scheffé, have some limitations mainly when the number of objectives increases, because the number of weight vectors and hence the population size becomes very large. In this paper, we present a new method for weight vector generation that can create an arbitrary number of weight vectors, almost equally spaced, located in a surface in the first orthant of the objective space, with free choice of norm. The proposed evolutionary algorithm is able to prevent the creation of weight vectors along the border of the orthant, which is a region that contains solutions of little interest to the decision maker. With a small modification in the proposed method it is also possible to create cones of weight vectors, useful to explore specific regions of the decision space defined by preference directions. In our experiments, different sets of weight vectors were generated, varying the number of vectors and the dimension of the space. The validation of the results was given by the mean distance of each vector to its nearest neighbor, as well as the standard deviation and the Pearson coefficient of variation for this mean value. The results indicate that the proposed method is able to produce a distribution of vectors close to a uniform distribution, with no clustering of points, being useful for guiding decomposition-based MOEA.

Solar Photovoltaics is a source of energy very sensitive to climate variations. Therefore, it is very important to apply a forecasting method to a PV system. Solar forecasting provides extremely useful information for tasks such as management of electricity grids and solar energy trading, where good accuracy and good performance are desirable goals for a very short term forecasting model. In this paper, we propose the use of fuzzy time series (FTS) techniques to this problem. Specifically, Chen's first order and high-order FTS methods and the Weighted FTS method are compared with other forecasting models widely used to approach solar irradiance forecasting. We evaluate the performance of FTS methods and different forecasting techniques to solve very short-term solar forecasting problems. The results show that FTS methods are able to achieve significant improvements in forecasting accuracy and performance if compared to other forecasting methods. A discussion on how to improve the forecasting performance of FTS models is also provided.

The intensive use of electricity in life and modern society implies increasing demand and the need for increasingly high reliability. Smart Grids (SG) are the next technological breakthrough to be achieved for the generation, transmission and distribution of energy. Historically, it has been sought to automate each of these systems to perform main and ancillary services. Robust forecasting methodologies are essential for planning and operation of SG. However, SG data presents the characteristics of long memory time series, which are a kind of stationary processes in such a way that there is always a statistical long range dependency between the current value and values in different times of the series. Motivated by this, we introduce a new hybrid model combining Seasonal Auto Regressive Fractionally Integrated Moving Average with high order Fuzzy Time Series (SARFIMA-FTS). We present comparative results of SARFIMA-FTS with other two methodologies solutions in microgrid data. The computational results show that the performance of the proposed SARFIMA-FTS method is quite competitive with other presented methods in literature using less parameters, hence it is an important tool for prediction in smart grids.

Multi-Objective Optimization (MOO) problems might be subject to many modeling or manufacturing uncertainties that affect the performance of the solutions obtained by a multi-objective optimizer. The decision maker must perform an extra step of sensitivity analysis in which each solution should be verified for its robustness, but this post optimization procedure makes the optimization process expensive and inefficient. In order to avoid this situation, many researchers are developing Robust MOO, where uncertainties are incorporated in the optimization process, which seeks optimal robust solutions. We introduce a coevolutionary approach for robust MOO, without incorporating robustness measures neither in the objective function nor in the constraints. Two populations compete in the environment, one representing solutions and minimizing the objectives, another representing uncertainties and maximizing the objectives in a worst case scenario. The proposed coevolutionary method is a coevolutionary version of MOEA/D. The results clearly suggest that these competing co-evolving populations are able to identify robust solutions to multi-objective optimization problems.

The challenging problem of forecasting a given time series as accurately as possible is reality in different areas of expertise. The requirement of achieving reliable forecasts, for assisting the new generation of soft sensors, requests the development of novel smart mechanisms to be integrated into the available forecasting models. This current paper improves the previous work of Coelho et al. [1], [2], introduced in the 2014 WCCI, which introduced a Hybrid Self-adaptive Forecasting Model (HFM), calibrated using an evolutionary metaheuristic. Here, an expert input selection assisted by the use of Neighborhood Structures is used for learning the dataset provide in the CIF 2016 forecasting competition. Two different metaheuristic algorithms are used for training the HFM, computational experiments are conducted for optimizing both models. By selecting the maximum lag to be used by our model and, consequently, defining a rate of training cycles, we calibrate the HFM in order to minimize Symmetric Mean Absolute Percentage Errors. Blind forecasts generated by the model will be submit to the competition.

This article presents an Evolution Strategy (ES)--based algorithm, designed to self-adapt its mutation operators, guiding the search into the solution space using a Self-Adaptive Reduced Variable Neighborhood Search procedure. In view of the specific local search operators for each individual, the proposed population-based approach also fits into the context of the Memetic Algorithms. The proposed variant uses the Greedy Randomized Adaptive Search Procedure with different greedy parameters for generating its initial population, providing an interesting exploration-exploitation balance. To validate the proposal, this framework is applied to solve three different [Formula: see text]-Hard combinatorial optimization problems: an Open-Pit-Mining Operational Planning Problem with dynamic allocation of trucks, an Unrelated Parallel Machine Scheduling Problem with Setup Times, and the calibration of a hybrid fuzzy model for Short-Term Load Forecasting. Computational results point out the convergence of the proposed model and highlight its ability in combining the application of move operations from distinct neighborhood structures along the optimization. The results gathered and reported in this article represent a collective evidence of the performance of the method in challenging combinatorial optimization problems from different application domains. The proposed evolution strategy demonstrates an ability of adapting the strength of the mutation disturbance during the generations of its evolution process. The effectiveness of the proposal motivates the application of this novel evolutionary framework for solving other combinatorial optimization problems.

The Multi-Depot Vehicle Routing Problem (MDVRP) is an important variant of the classical Vehicle Routing Problem (VRP), where the customers can be served from a number of depots. This paper introduces a cooperative coevolutionary algorithm to minimize the total route cost of the MDVRP. Coevolutionary algorithms are inspired by the simultaneous evolution process involving two or more species. In this approach, the problem is decomposed into smaller subproblems and individuals from different populations are combined to create a complete solution to the original problem. This paper presents a problem decomposition approach for the MDVRP in which each subproblem becomes a single depot VRP and evolves independently in its domain space. Customers are distributed among the depots based on their distance from the depots and their distance from their closest neighbor. A population is associated with each depot where the individuals represent partial solutions to the problem, that is, sets of routes over customers assigned to the corresponding depot. The fitness of a partial solution depends on its ability to cooperate with partial solutions from other populations to form a complete solution to the MDVRP. As the problem is decomposed and each part evolves separately, this approach is strongly suitable to parallel environments. Therefore, a parallel evolution strategy environment with a variable length genotype coupled with local search operators is proposed. A large number of experiments have been conducted to assess the performance of this approach. The results suggest that the proposed coevolutionary algorithm in a parallel environment is able to produce high-quality solutions to the MDVRP in low computational time .

The channel allocation problem consists in defining the frequency used by Access Points (APs) in Wireless Local Area Networks (WLAN). An overlap of channels in a WLAN is the major factor of performance reduction for the users in a network. For this reason, we propose a new model for channel allocation that aims to maximize the total quality of the connection of the user by considering their marginal utility. The results show that an allocation model that does not take into account the total utility of each connection tends to prioritize the quality of connection of a few users and lead to a large unbalance in the distribution of connection speed between users. Thus, the new model can handle the importance of degradation caused by the levels of interference in the user connection separately.

The possibility of obtaining financial gain by investing in the Stock Markets is a hard task since it is under constant influence of economical, political and social factors. This paper aims to address the financial technical analysis of Stock Markets, focusing on time series data instead of subjective parameters. An algorithm based on genetic programming, named GoldMiner, has been proposed to perform retrospective study in order to get predictions about the best time for trading top stocks on the BOVESPA, the Brazilian stock exchange market.

Improving the use of energy resources has been a great challenge in the last years. A new complex scenario involving a decentralized bidirectional communication between energy suppliers, distribution system and consumption is nowadays becoming reality. Sometimes cited as the largest and most complex machine ever built, Electric Grids (EG) are been transformed into Smart Grids (SG). Hence, the load forecasting problem has become more difficulty and more autonomous load predictors are needed in this new conjecture. In this paper a novel method, so-called MSES, bio-inspired by Evolution Strategies (ES) combined with Multi-Start (MS) procedure is described. This procedure is mainly based on a self-adaptive algorithm to calibrate the parameters of the fuzzy rules. MSES was implemented in C++ via OptFrame framework. Our main goal is to evaluate the performance of this algorithm in a grid environment. Real data from an electric utility have been used in order to test the proposed methodology. The obtained results are fully described and analyzed.

Join query optimization has a direct impact on the performance of a database system. This work presents an evolutionary multi-agent system applied to the join ordering problem related to database query planning. The proposed algorithm was implemented and embedded in the core of a database management system (DBMS). Parameters of the algorithm were calibrated by means of a factorial design and an analysis based on the variance. The algorithm was compared with the official query planner of the H2 DBMS, using a methodology based on benchmark tests. The results show that the proposed evolutionary multi-agent system was able to generate solutions associated with low execution costs in the majority of the cases.

Multiobjective optimization has been applied successfully to real-world optimization problems with few objectives. However, the performance of current algorithms for multiobjective optimization reduces exponentially as the number of objectives grows. In this paper we present a non-parametric harmony-based approach for objective reduction in order to deal with this issue in many-objective optimization problems. The proposed approach has many advantages such as the independence of the relationship between the objectives as long as they are harmonious and the possibility to visualize conflict and trade-off in the reductions performed.

This paper proposes a new Parallel Hybrid Genetic Algorithm approach for Vehicle Routing Problem with Time Windows. The algorithm was developed to be executed on cloud computing web services and serves as an online application for real world problems. A new parallel scheme was proposed with shared resources of candidate solutions accessed by many asynchronous tasks. The algorithm was tested over the classical well-known benchmark and presented excellent results for some instances in a low computational time. The algorithm reaches the best-known solutions for many instances and found high competitive solutions. The excellent performance of the proposed approach indicates its potential to be applied in real world applications, running on cloud computing servers.

In this paper, we analyze four dominance criteria in terms of their ability to adequately order sets of points in multi- and many-objective optimization problems. The use of relaxed and alternative dominance relationships has been an important tool for improving the performance of multiobjective evolutionary optimization algorithms, and their ordering ability is among the most important characteristics responsible for such improvement. Three relaxed formulations of dominance are investigated, along with the traditional Pareto ordering, in order to provide a comparison baseline. The results obtained show that all three relaxed dominance approaches presented greater robustness to the increase in the number of objectives, and are therefore more appropriate for use in many-objective optimization algorithms.

One of the greatest problems when using genetic algorithms to evolve melodies is creating an aesthetically conscious measure of fitness. In this paper, we describe a new approach with a minimum measure of fitness in which a set of good individuals is returned at the end of the process. Details about the implementation of a population of measures and some genetic operators are described in this work before an implicit way to evaluate fitness is given. We define a Takeover Matrix to measure the relationship between different generations and its compromise between originality and diversity. By means of this Takeover Matrix, the evolutionary process itself can be used as a criterion instead of using only ordinary individual measures of fitness. The results show the implications of using the proposed approach and demonstrate that the proposed algorithm is able to generate good sets of melodies. The algorithm can be used not only for developing new ideas but also to extend earlier created melodies with influence from the initial population.

We present a multiobjective hybrid technique for automatic orthogonal graph drawing. The new methodology combines the classical approach to automatic orthogonal graph drawings,the topology-shape-metric approach, and a multiobjective genetic algorithm based on the NSGA-II method. In the topology-shape-metric method, a fixed planar embedding is obtained in the planarization step and submitted to the orthogonalization and compaction steps, in this order. In the hybrid approach, a greater number of planar embeddings is explored by varying the order of edges insertion that forms the planar embedding in the planarization step. The problem is then formulated as a multiobjective permutationbased combinatorial optimization problem, considering the minimization of the number of crossings, the number of bends and the area of the drawing. Solutions on the estimated Pareto front represent different drawings, that can be stored and selected by the user in real-time. We illustrate a possible multicriteria decision making based on fuzzy decision. The results show that the hybrid methodology using NSGA-II is able to find good and diverse solutions, when compared to the traditional topology-shape-metric method.

The Differential Evolution (DE) algorithm is an efficient and powerful evolutionary algorithm (EA) for solving optimization problems. However the success of DE in solving a specific problem is closely related to appropriately choosing its control parameters. Parameter tuning leads to additional computational costs because of time-consuming trial-and-error tests. Self-adaptation, in contrast, allows the algorithm to reconfigure itself, automatically adapting to the problem being solved. There are in the literature some self-adaptive versions of differential evolution, however they do not align completely with self-adaptation concepts. In this paper, some self-adaptive versions of DE in the literature are described and discussed, and then a new Self-Adaptive Differential Evolution with multiple mutation strategies is proposed; it is called Self-adaptive Mutation Differential Evolution (SaMDE) and aims at preserving the essential characteristics of self-adaptation. Some computational experiments which illustrate algorithm behaviour and a comparative test with the classical DE and with an important self-adaptive DE are presented. The results suggest that SaMDE is a very promising algorithm.

We propose in this paper a new strategy for self-adaptation in multiobjective evolutionary algorithms, which is based on information obtained from the implicit distribution created by a chaotic differential mutation operator. This technique is used to develop a self-adaptive evolutionary algorithm for multiobjective optimisation, and its efficiency is evaluated by means of a comparative study using well-known benchmark problems. The statistical analysis of the results shows that the proposed algorithm was able to outperform the NSGA-II in fourteen of the seventeen problems used. These results represent evidence for the adequacy of the proposed technique in solving the classes of multiobjective optimisation problems represented in the benchmark suites used.

This paper presents a new approach for automatic graph drawing based on Genetic algorithms. The classical topology-shape-metric approach for orthogonal graph drawing keeps a fixed planar embedding obtained in its first step (planarization), using it for the next two steps (orthogonalization and compaction). However, each step is itself an NP-hard problem, and the choices made and heuristics used on previous stages have a direct impact on subsequent ones.

This work presents a Linear Matrix Inequality (LMI) formulation for training Radial Basis Function (RBF) neural networks, considering the context of multiobjective learning. The multiobjective learning approach treats the bias-variance dilemma in neural network modeling as a bi-objective optimization problem: the minimization of the empirical risk measured by the sum of squared error over the training data, and the minimization of the structure complexity measured by the norm of the weight vector. We transform the multiobjective problem into a constrained mono-objective one, using the ϵ-constraint method. This mono-objective problem can be efficiently solved using an LMI formulation. A procedure for choosing the width parameter of the radial basis functions is also presented. The results show that the proposed methodology provides generalization control and high quality solutions.

The Differential Evolution (DE) algorithm was initially proposed for continuous numerical optimization, but it has been applied with success in many combinatorial optimization problems, particularly permutation-based integer combinatorial problems. In this paper, a new and general approach for combinatorial optimization is proposed using the Differential Evolution algorithm. The proposed approach aims at preserving its interesting search mechanism for discrete domains, by defining the difference between two candidate solutions as a differential list of movements in the search space. Thus, a more meaningful and general differential mutation operator for the context of combinatorial optimization problems can be produced. We discuss three alternatives for using the differential list of movements within the differential mutation operation. We present results on instances of the Traveling Salesman Problem (TSP) and the N-Queen Problem (NQP) to illustrate the adequacy of the proposed approach for combinatorial optimization.

The Differential Evolution (DE) algorithm is a simple and efficient evolutionary algorithm that has been applied to solve many optimization problems mainly in continuous search domains. In the last few years, many implementations of multi-objective versions of DE have been proposed in the literature, combining the traditional differential mutation operator as the variation mechanism and some form of Pareto-ranking based fitness. In this paper, we propose the utilization of the differential mutation operator as an additional operator to be used within any multi-objective evolutionary algorithm that employs an archive (offline) population. The operator is applied for improving the high-quality solutions stored in the archive, working both as a local search operator and a diversity operator depending on the points selected to build the differential mutation. In order to illustrate the use of the operator, it is coupled with the NSGA-II and the multi-objective DE (MODE), showing promising results.

This paper presents the hierarchical cluster counting (HCC), a new quality metric for nondominated sets generated by multi-objective optimizers that is based on hierarchical clustering techniques. In the computation of the HCC, the samples in the estimate set are sequentially grouped into clusters. The nearest clusters in a given iteration are joined together until all the data is grouped in only one class. The distances of fusion used at each iteration of the hierarchical agglomerative clustering process are integrated into one value, which is the value of the HCC for that estimate set. The examples show that the HCC metric is able to evaluate both the extension and uniformity of the samples in the estimate set, making it suitable as a unary diversity metric for multiobjective optimization.

Uncertainties are commonly present in optimization systems, and when they are considered in the design stage, the problem usually is called a robust optimization problem. Robust optimization problems can be treated as noisy optimization problems, as worst case minimization problems, or by considering the mean and standard deviation values of the objective and constraint functions. The worst case scenario is preferred when the effects of the uncertainties on the nominal solution are critical to the application under consideration. Based on this worst case scenario, we developed the [I]RMOEA (Interval Robust Multi-Objective Evolutionary Algorithm), a hybrid method that combines interval analysis techniques to deal with the uncertainties in a deterministic way and a multi-objective evolutionary algorithm. We introduce [I]RMOEA and illustrate it on three robust test functions based on the ZDT problems. The results show that [I]RMOEA is an adequate way of tackling robust optimization problems with evolutionary techniques taking advantage of the interval analysis framework.

This paper proposes a local search optimizer that, employed as an additional operator in multiobjective evolutionary techniques, can help to find more precise estimates of the Pareto-optimal surface with a smaller cost of function evaluation. The new operator employs quadratic approximations of the objective functions and constraints, which are built using only the function samples already produced by the usual evolutionary algorithm function evaluations. The local search phase consists of solving the auxiliary multiobjective quadratic optimization problem defined from the quadratic approximations, scalarized via a goal attainment formulation using an LMI solver. As the determination of the new approximated solutions is performed without the need of any additional function evaluation, the proposed methodology is suitable for costly black-box optimization problems.

In this paper, we propose a local search methodology to be coupled with a Genetic Algorithm to solve optimization problems with non-linear constraints. This methodology uses quadratic approximations for both objective function and constraints. In the local search phase, these quadratic approximations define an associated problem that is solved using a linear matrix inequality (LMI) formulation. The number of function evaluations needed for finding the point of optimum is significantly reduced with this procedure, what makes the proposed methodology suitable for dealing with costly black-box optimization problems. A case study is presented: the well- known TEAM 22 benchmark problem, an expensive problem of electromagnetic design. The results show that the hybrid algorithm has a better performance when compared to the same Genetic Algorithm without the proposed local search operator.

Traditional shape optimization of engineering devices usually starts with an initial user-defined configuration of material. Optimization algorithms are then applied for optimizing objective functions of predefined parameters. While this approach can yield efficient results, it is essentially limited, since limitations in the initial design forbid the computational methods to explore different distributions of material as solutions for a given problem. In other words, the algorithms are not allowed to exhibit creativity in the design process. Topology optimization is a paradigm for optimization that allows such creativity to emerge. Instead of optimizing functions of user-defined parameters, this paradigm optimizes the material properties of each point of the design space, and its methods are theoretically able to describe all possible devices within a limited space. This work presents a new methodology for topology optimization, based on an evolutionary paradigm known as artificial immune systems. The proposed technique is capable of exploring the space locally as well as globally, efficiently searching for the optimal distribution of material. It also incorporates strategies for the evolution of smoother, more regular shapes, in order to generate physically feasible solutions for engineering problems.

The use of local search in evolutionary techniques is believed to enhance the performance of the algorithms, giving rise to memetic or hybrid algorithms. However, in many continuous optimization problems the additional cost required by local search may be prohibitive. Thus we propose the local learning of the objective and constraint functions prior to the local search phase of memetic algorithms, based on the samples gathered by the population through the evolutionary process. The local search operator is then applied over this approximated model. We perform some experiments by combining our approach with a real-coded genetic algorithm. The results demonstrate the benefit of the proposed methodology for costly black-box functions.

This paper studies the issue of defining the fitness function for ranking-based selection. Two families of parametric nonlinear functions are considered, for reaching different selection pressures, controlled by the function parameter. Both the static versions and some dynamic varying versions of such functions are considered. The usual linear fitness function is shown to be systematically outperformed by several instances of nonlinear fitness. After a multiobjective analysis, it seems to be possible to recommend the usage of a specific static nonlinear fitness function.

We devise in this paper a local search procedure for multiobjective genetic algorithms (GAs). The proposed local search process employs quadratic approximations for all objective functions involved in the optimization problem. The samples gathered by the algorithm along the evolutionary process are used to fit these quadratic approximations around the point selected to local search, therefore no extra cost of function evaluation is required. After that, a locally improved solution is easily estimated from the quadratic associated problem. We demonstrate the hybridization of our proposed procedure with SPEA 2.

This paper proposes a procedure for space coordinate change, inside genetic algorithms, based on convex quadratic approximations of the general nonlinear objective function. It is shown that in the transformed coordinates the genetic algorithm is able to And the problem optimum in less iterations and with greater proportion of successful attempts. The proposed procedure employs only the objective function samples that have already been obtained through the usual genetic algorithm operations. It means that there is no need of any additional function evaluation. The proposed procedure was tested with a set of benchmark problems. In all cases, the proposed algorithm has been able to repeatedly find solutions closer to the true solution than those found by the same genetic algorithm without coordinate change. The results suggest that the modification can enhance the convergence rate and accuracy of genetic algorithms.

This paper presents a new operator for genetic algorithms that enhances their convergence in the case of nonlinear problems with nonlinear equality constraints. The proposed operator, named CQA (constraint quadratic approximation), can be interpreted as both a local search engine (that employs quadratic approximations of both objective and constraint functions for guessing a solution estimate) and a kind of elitism operator that plays the role of 'fixing" the best estimate of the feasible set. The proposed operator has the advantage of not requiring any additional function evaluation per algorithm iteration, solely making use of the information that would be already obtained in the course of the usual genetic algorithm iterations. The test cases that were performed suggest that the new operator can enhance both the convergence speed (in terms of the number of function evaluations) and the accuracy of the final result.