Pipes have been using for different construction purposes, such as tube wells, oil wells, gas wells, and other sanitary purposes. These pipes have different sizes that can be used according to the need. In a particular construction, most of them can be used but some of them are left unused, which are known as leftovers. There are some usable leftovers (standards), whereas others are nonusable (nonstandards) leftovers. These leftovers could be difficult to manage to know which of them could be reused. The reuse of such leftovers become difficult for the construction companies to use them properly. On the other hand, these leftovers would be useful for other construction purposes rather than throw them into the bin. In this paper, we have presented a model and used a heuristic approach to make sure that the leftovers after different constructions could be reused according to the given demand. For this purpose, a genetic-based decision support system is applied to validate the solution feasibility of the problem. Experimental results validate the effectiveness of this novel proposed model by numerical experiments, and the leftovers are minimized up to a high extent.

We identify a class of root-searching methods that surprisingly outperform the bisection method on the average performance while retaining minmax optimality. The improvement on the average applies for any continuous distributional hypothesis. We also pinpoint one specific method within the class and show that under mild initial conditions it can attain an order of convergence of up to 1.618, i.e., the same as the secant method. Hence, we attain both an improved average performance and an improved order of convergence with no cost on the minmax optimality of the bisection method. Numerical experiments show that, on regular functions, the proposed method requires a number of function evaluations similar to current state-of-the-art methods, about 24% to 37% of the evaluations required by the bisection procedure. In problems with non-regular functions, the proposed method performs significantly better than the state-of-the-art, requiring on average 82% of the total evaluations required for the bisection method, while the other methods were outperformed by bisection. In the worst case, while current state-of-the-art commercial solvers required two to three times the number of function evaluations of bisection, our proposed method remained within the minmax bounds of the bisection method.

In the last decade, it has become apparent that the performance of Pareto-dominance-based evolutionary multiobjective optimization algorithms degrades as the number of objective functions of the problem, given by n, grows. This performance degradation has been the subject of several studies in the last years, but the exact mechanism behind this phenomenon has not been fully understood yet. This paper presents an analytical study of this phenomenon under problems with continuous variables, by a simple setup of quadratic objective functions with spherical contour curves and a symmetrical arrangement of the function minima location. Within such a setup, some analytical formulas are derived to describe the probability of the optimization progress as a function of the distance λ to the exact Pareto-set. A main conclusion is stated about the nature and structure of the performance degradation phenomenon in many-objective problems: when a current solution reaches a λ that is an order of magnitude smaller than the length of the Pareto-set, the probability of finding a new point that dominates the current one is given by a power law function of λ with exponent (n - 1). The dimension of the space of decision variables has no influence on that exponent. Those results give support to a discussion about some general directions that are currently under consideration within the research community.

This manuscript presents a comparative study between three Multiobjective Evolutionary Algorithms (NSGA-II, GDE3, and MOEA/D-DE) on Wireless Local Area Networks design. The considered problem consists on defining the positions, quantity, channels, and load balance of access points to be installed. Problem features such as equipment limitations, traffic demand, and minimum coverage level required are modeled as constraints. The used algorithms were tested in two scenarios, considering different network profiles. The results show that the developed approach for WLAN planning can help a network designer to define good Wi-Fi projects, improving the signal level, network balance, and reducing interference.

A new approach for the problem of optimal task scheduling in flexible manufacturing systems is proposed in this work, as a combination of metaheuristic optimization techniques with the supervisory control theory of discrete-event systems. A specific encoding, the word-shuffling encoding, which avoids the generation of a large number of infeasible sequences, is employed. A metaheuristic method based on a Variable Neighborhood Search is then built using such an encoding. The optimization algorithm performs the search for the optimal schedules, while the supervisory control has the role of codifying all the problem constraints, allowing an efficient feasibility correction procedure , and avoiding schedules that are sensitive to uncertainties in the execution times associated with the plant operation. In this way, the proposed methodology achieves a system performance which is typical from model-predictive scheduling, combined with the robustness which is required from a structural control.

This paper proposes a new multiobjective evolutionary algorithm for handling the problem of distribution network restoration after failures. The problem is formulated as a bi-objective optimization problem considering the total load restored and the time required for restoration. A new encoding scheme is proposed, in which the variables that encode the switch operation are separated into six groups, according to their roles in the faulty system configuration. Employing the idea of defining subspaces of a combinatorial space, those groups are used in order to define subpermutations within which the crossover and mutation operations are performed. In this way, the dimensionality of the search space becomes reduced, allowing a much more efficient search. The proposed encoding scheme also makes a single individual to encode several different solutions, leading to a further reduction of the search space dimensionality. Due to this peculiar feature of the encoding scheme, it becomes convenient to use an adaptation of the Strength Pareto Evolutionary Algorithm 2, in which the raw fitness is modified in order to allow the assignment of fitness to individuals that simultaneously encode several different solutions. The proposed algorithm was implemented such that good solutions are delivered within low processing times, of the order of some minutes for large real systems.

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.

Recent works raised the hypothesis that the assignment of a geometry to the decision variable space of a combinatorial problem could be useful both for providing meaningful descriptions of the fitness landscape and for supporting the systematic construction of evolutionary operators (the geometric operators) that make a consistent usage of the space geometric properties in the search for problem optima. This paper introduces some new geometric operators that constitute the realization of searches along the combinatorial space versions of the geometric entities descent directions and subspaces. The new geometric operators are stated in the specific context of the wireless sensor network dynamic coverage and connectivity problem (WSN-DCCP). A genetic algorithm (GA) is developed for the WSN-DCCP using the proposed operators, being compared with a formulation based on integer linear programming (ILP) which is solved with exact methods. That ILP formulation adopts a proxy objective function based on the minimization of energy consumption in the network, in order to approximate the objective of network lifetime maximization, and a greedy approach for dealing with the system's dynamics. To the authors' knowledge, the proposed GA is the first algorithm to outperform the lifetime of networks as synthesized by the ILP formulation, also running in much smaller computational times for large instances.

A new approach for the problem of optimal task scheduling in a manufacturing cell is proposed in this work, as a combination of a clonal algorithm with the supervisory control of discrete-event dynamical systems. Two methodologies are proposed. In the first one, the clonal selection algorithm (CSA) performs the search for the optimal solution, using randomized searches over permutations of sequences of operations. The supervisory control has the role of encoding all the problem constraints, allowing for the search to be conducted on the feasible solution set only. The second methodology is similar, but the CSA uses a local search 2-opt to improve the best individual of each generation. The preliminary results show that both methodologies can obtain significant gains in the total plant operation time in relation to the greedy control policy employed on an example system considered here. A better performance of the CSA + 2-opt methodology can also be observed, when compared with the Clonal Selection Algorithm alone. The proposed methodology provides robustness and flexibility to the solutions - these features are not usually present in most optimization-based solutions for those problems.

This work investigates the conjecture that the employment of geometry-based operators can be worthy for the construction of efficient and stable evolutionary algorithms for scheduling problems in parallel machines. The effort reported here is an instance of a broader study which investigates the role of geometric concepts in combinatorial problems. This work considers multiobjective versions of the scheduling problem, which are solved using a variation of the classical NSGA-II with the geometric operators. The achieved results are encouraging, showing a repeatable good performance in several problem instances of different sizes, for both identical and unrelated machines. It is also shown some empirical evidence that the proposed geometric operators are able to regularize the space, which is a possible explanation for the algorithm good performance.

A new approach for wireless local area network (WLAN) installation planning is proposed in this paper. This approach is based on a multiobjective genetic algorithm and on greedy algorithms, and it is composed of two steps: network structure design and channel assignment. In the first step, the quantity, position and load balance of the access points are planned taking into account a minimum coverage level, the AP capacity and the traffic demand in the WLAN. In the second step, the channel of each access point is assigned in such a way that the network presents minimal interference and high throughput. An approximation of the efficient solution set, taking into account two design criteria, is delivered by the proposed algorithm. These solutions can be used to provide cost reduction and quality improvement on WLAN design. Results obtained by the proposed algorithm in two reasonable scenarios are presented in order to evaluate its efficacy.

In multiobjective optimization problems, Pareto dominance-based search techniques are known to lose their efficiency in problems with a large number of objective functions - the many-objective problems. This paper proposes an algorithm based on a stochastic differential equation approach combined with an evolutionary strategy for dealing with such problems. The proposed algorithm is intended to both allow the determination of tight Pareto-optimal solutions in many-objective problems (which is a difficult task for usual evolutionary algorithms) and to find a solution set that performs a relatively uniform sampling of the Pareto-optimal set (which is a deficiency of the known stochastic differential equation approach). The proposed algorithm is shown to attain such goals at a relatively low computational cost.

In this paper, a genetic algorithm is employed to plan the medium and long term expansion of electric power distribution systems. The expansion planning task is modeled as a single-objective optimization problem in which the objective function is the monetary cost of the network. A new procedure is proposed to perform substation location jointly with network topology design. Such a procedure is performed during function evaluation, and it requires low computational cost. Results for a real eight bus energy system are presented. These results show that reasonable solutions can be reached in a computational time considerably lower than the one required by former methods.

This work studies a multiobjective version of the Multi-mode Resource-Constrained Project Scheduling Problem (MRCPSP), in which both the total time of execution and the total cost of assignment are treated as objective functions. An NSGA-II based genetic algorithm is employed for the estimation of the Pareto-optimal solution set. An encoding/decoding scheme guarantees that only feasible individuals are represented in the population, and problem-specific mutation and crossover operators are employed in order to enhance the algorithm efficiency. A case study of the engineering design of the facilities of a new mining plant located in the northern Brazilian territory illustrates the application of the proposed methodology. In this case study, several scenarios of project task assignment to a team of workers with different skills and different hiring costs are generated by the proposed algorithm. This quantitative description of the trade-off between project term and project cost can be particularly useful in the preliminary stage of price negotiation between the engineering consulting firm that develops the project and the client mining company.

This paper proposes a method which is suitable for the estimation of the probability of occurrence of a syndrome, as a function of the geographical coordinates of the individuals under risk. The data describing the location of syndrome cases over the population suffers a moving-average filtering, and the resulting values are fitted by an RBF network performing a regression. Some contour curves of the RBF network are then employed in order to establish the boundaries between four kinds of regions: regions of high-incidence, regions of medium incidence, regions of slightly-abnormal incidence, and regions of normal prevalence. In each region, the risk is estimated with three indicators: a nominal risk, an upper bound risk and a lower bound risk. Those indicators are obtained by adjusting the probability employed for the Monte Carlo simulation of syndrome scenarios over the population. The nominal risk is the probability which produces Monte Carlo simulations for which the empirical number of syndrome cases corresponds to the median. The upper bound and the lower bound risks are the probabilities which produce Monte Carlo simulations for which the empirical values of syndrome cases correspond respectively to the 25% percentile and the 75% percentile. The proposed method constitutes an advance in relation to the currently known techniques of spatial cluster detection, which are dedicated to finding clusters of abnormal occurrence of a syndrome, without quantifying the probability associated to such an abnormality, and without performing a stratification of different sub-regions with different associated risks. The proposed method was applied on data which were studied formerly in a paper that was intended to find a cluster of dengue fever. The result determined here is compatible with the cluster that was found in that reference.

Local search techniques based on Convex Quadratic Approximation (CQA) of functions are studied here, in order to speed up the convergence and the quality of solutions in evolutionary multiobjective algorithms. The hybrid methods studied here pick up points from the nondominated population and determine a CQA for each objective function. Since the CQA of the functions and the respective weighted sums are convex, fast deterministic methods can be used in order to generate approximated Pareto-optimal solutions from the approximated functions. A new scheme is proposed in this paper, using a CQA model that represents a lower bound for the function points, which can be solved via linear programming. This scheme and also another one using the methodology of linear matrix inequality (LMI) for CQA are coupled with a canonical implementation of the NSGA-II. Comparison tests are performed, using Monte Carlo simulations, considering the S-metric with an equivalent final number of evaluated objective functions and the algorithm execution time. The results indicate that the proposed scheme is promising.

Hydropower plants produce most of the electrical power generated in Brazil. Although the remaining potential is still large, most of it is located far from the industrialized south eastern states. In addition to that, the increasing opposition to the construction of new large reservoirs, for ecological and social reasons, highlights the need for the efficient operation of the existing system. In this work, a formulation recently developed by the authors, which has been shown to efficiently deal with the operational constraints of a single plant, is expanded to the multi-reservoir case. A multi-objective optimization of a system of five Brazilian hydropower plants is performed, with the objectives of increasing the mean power generation along a year and reducing the peak of demand of non-renewable energy sources. The optimization algorithm is taxed by the increase in the number of variables and by their unsual combination in the efficient solutions set, leading to problems that were found to be associated with the the simple Gaussian mutation operator employed.

This paper presents a statistical based comparison methodology for performing evolutionary algorithm comparison under multiple merit criteria. The analysis of each criterion is based on the progressive construction of a ranking of the algorithms under analysis, with the determination of significance levels for each ranking step. The multicriteria analysis is based on the aggregation of the different criteria rankings via a non-dominance analysis which indicates the algorithms which constitute the efficient set. In order to avoid correlation effects, a principal component analysis pre-processing is performed. Bootstrapping techniques allow the evaluation of merit criteria data with arbitrary probability distribution functions. The algorithm ranking in each criterion is built progressively, using either ANOVA or first order stochastic dominance. The resulting ranking is checked using a permutation test which detects possible inconsistencies in the ranking—leading to the execution of more algorithm runs which refine the ranking confidence. As a by-product, the permutation test also delivers$p$-values for the ordering between each two algorithms which have adjacent rank positions. A comparison of the proposed method with other methodologies has been performed using reference probability distribution functions (PDFs). The proposed methodology has always reached the correct ranking with less samples and, in the case of non-Gaussian PDFs, the proposed methodology has worked well, while the other methods have not been able even to detect some PDF differences. The application of the proposed method is illustrated in benchmark problems.

The need for the efficient operation of hidropower plants, which provides most of the electrical power consumed in Brazil, is related not only to the issue of energy conservation, but has also been highlighted by the increasing opposition to the construction of new large reservoirs, for ecological and social reasons. In this work, a multi-objective genetic algorithm is applied to problem of the optimization of a single Brazilian hydropower plant, with the objectives of increasing the net energy generation along the year and reducing the peak of demand of non-renewable energy sources. To increase the performance of the algorithm, two new formulations for the problem are proposed, with different ways of dealing with the operational constraints. In comparison with the more traditional approach, this results not only in efficiency gains, but also in an expanded Pareto front, which adds more flexibility to the system, by revealing new possible configurations of system operation.

The traditional Generalized Assignment Problem (GAP) problem consists of assigning n different tasks to m different agents, while minimizing a cost function. Additionally, it is necessary to ensure that each task is assigned to a single agent (indivisible task) and that the maximum resource capacity of the agents is honored. In this paper, the problem is extended to a bi-objective formulation, in which an equilibrium function is included in the problem statement. This formulation is motivated by situations in which it is important to distribute the tasks uniformly amongst the agents. An integer enhanced version of the Non-dominated Sorting Genetic Algorithm II (NSGA-II) algorithm is proposed for solving such a multiobjective problem. The results obtained using this algorithm show that it is possible to find solutions which are very close to the exact optimum of the single objective problem. The approach still allows to perform a trade-off analysis of the objectives, offering the possibility of choosing solutions with slightly higher cost and considerably better distribution of the tasks. Such a trade-off decision cannot be performed in the mono-objective approaches.

The evolution in the microelectronics and embedded systems has expanded the employment of Wireless Sensor Networks (WSNs). The energy limitation of the nodes is a very important restriction of those structures and should be always considered during the network design. The search for energy-efficient WSNs must take into account aspects which are essential for the proper operation of the network, such as area coverage and network connectivity. This paper proposes an evolutionary approach for performing the design of WSNs, considering the dynamic nature of the problem. A genetic algorithm, which aims to maximize the lifetime of the network, is employed for establishing the sequence in which the sensor nodes are activated, ensuring that the minimum coverage (established a priori) and the connectivity constraints are met. Results achieved by the proposed algorithm in a 81-sensor node instance are compared with a former work, in order to validate the approach which is presented here.

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.

This paper proposes a normed-space vector representation of networks which allows defining evolutionary operators for network optimization that resemble continuous-space operators. These operators are employed here to build a genetic algorithm which becomes generic for the optimization of tree networks, without the requirement of any special encoding scheme. Such a genetic algorithm has been compared with several encoding-based genetic algorithms, on 25 and 50-node instances of the optimal communication spanning tree and of the quadratic minimum spanning tree, and has been shown to outperform all other algorithms in a stochastic dominance analysis. The proposed approach has also been applied to an electric power distribution network design (a multibranch problem), outperforming the results presented in a former reference (which have been obtained with an Ant Colony algorithm). The results of some landscape dispersion analysis suggest that the proposed normed-space network vector representation is analogous to some continuous-variable space dilation operations, which define favorable space coordinates for optimization.

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.

The increase in the demand for wireless sensor networks (WSNs) has intensified studies which aim to obtain energy-efficient solutions, since the energy storage limitation is critical in those systems. However, there are other aspects which usually must be ensured in order to provide an efficient design of WSNs, such as area coverage and network connectivity. This paper proposes a multiobjective hybrid approach for solving the dynamic coverage and connectivity problem (DCCP) in flat WSN subjected to node failures. It combines a multiobjective global on-demand algorithm (MGoDA), which improves the current DCCP solution using a genetic algorithm, with a local online algorithm (LoA), which is intended to restore the network coverage when one or more failures occur. The proposed approach is compared with an integer linear programming (ILP) based approach and a similar mono-objective approach with regard to coverage, energy consumption and residual energy of the solution provided by each method. Results achieved for a test instance show that the hybrid approach presented can obtain good solutions with a considerably smaller computational cost than ILP. The multiobjective approach still provides a feasible method for extending WSNs lifetime with slight decreasing in the network mean coverage.

This work presents an evolutionary approach for solving a difficult problem of combinatorial optimization, the DCMST (degree-constrained minimum spanning tree problem). Three genetic algorithms which embed candidate solutions in the continuous space are proposed here for solving the DCMST. The results achieved by these three algorithms have been compared with four other existing algorithms according to three merit criteria: i) quality of the best solution found; ii) computational effort spent by the algorithm, and; iii) convergence tendency of the population. The three proposed algorithms have provided better results for both solution quality and population convergence, with reasonable computational cost, in tests performed for 25-node and 50-node test instances. The results suggest that the proposed algorithms are well suited for dealing with the problem under study.

In this paper, we propose a multiobjective evolutionary approach to design a microwave heating device. The goal is to heat the maximum amount of water, above certain temperature, and spending the minimum energy. The device is modeled as a loss multilayer dielectric irradiated by microwave power. The resulting bi-objective problem is then solved using SPEA2 and a set of solutions is obtained. The results show that SPEA2 finds a higher number of non-dominated solution when compared with the traditional approaches used in this problem, within lower computational cost.

Support Vector Machines (SVMs) are considered state-of-the-art learning machines techniques for classification problems. This paper studies the training of SVMs in the special case of problems in which the raw data to be used for training purposes is composed of both labeled and unlabeled data - the semi-supervised learning problem. This paper proposes the definition of an intermediate problem of attributing labels to the unlabeled data as a multiobjective optimization problem, with the conflicting objectives of minimizing the classification error over the training data set and maximizing the regularity of the resulting classifier. This intermediate problem is solved using an evolutionary multiobjective algorithm, the SPEA2. Simulation results are presented in order to illustrate the suitability of the proposed technique.

The increasing demand for Wireless Sensor Networks (WSN) has intensified studies which aim to obtain energy-efficient solutions, since the energy storage limitation is critical in those systems. However, there are other aspects which usually must be ensured in order to get an acceptable performance of WSNs, such as area coverage and network connectivity. This paper proposes a procedure for network performance enhancement: a multiobjective hybrid approach for solving the Dynamic Coverage and Connectivity Problem in flat WSN subjected to node failures.Results achieved for a test instance show that the hybrid approach can improve the performance of the WSN obtaining good solutions with a considerably smaller computational cost than ILP.

This work proposes an immune inspired memetic algorithm for the expansion planning of electric distribution systems. This algorithm is based on a clonal selection algorithm and a local search method which is built using network distance concepts abstracted from continuous spaces. The memetic algorithm is intended to find not only the optimal solution for the design conditions, but a whole set of viable solutions, that can be considered as alternatives under perturbed operation conditions. Those alternatives are used for handling with load evolution uncertainties, which are inherently related with long term evaluation of the distribution system. The post-optimization analysis of solutions has been made using a Monte Carlo simulation and a multiobjective sensitivity analysis, in order to estimate their robustness under perturbed load conditions. The results achieved by the proposed algorithm in a practical problem indicate that this method can be more suitable for designing distribution system under load evolution uncertainties.

The achievement of approximation models may constitute a complex computational task, in the cases of models with non-linear relation between parameters and data. This problem becomes even harder when the system to be modeled is subject to noisy data, since the simple minimization of error over a training data set can give rise to misleading models that fit both the system structure and the noise (the phenomenon of modeloverfit). This paper proposes a multiobjective genetic algorithm for guiding the training of ANFIS fuzzy networks. This algorithm considers the complexity of network jointly with the error over the training set as relevant objectives, that should be minimized. Results obtained in three regression problems are presented to show the generalization capacity of models constructed with the proposed methodology.

This paper presents an enhanced approach for comparing evolutionary algorithm. This approach is based on three statistical techniques: (a) Principal Component Analysis, which is used to make the data uncorrelated; (b) Bootstrapping, which is employed to build the probability distribution function of the merit functions; and (c) Stochastic Dominance Analysis, that is employed to make possible the comparison between two or more probability distribution functions. Since the approach proposed here is not based on parametric properties, it can be applied to compare any kind of quantity, regardless the probability distribution function. The results achieved by the proposed approach have provided more supported decisions than former approaches, when applied to the same problems.

This work studies the mGA operator (Micro Genetic Algorithm), that has been proposed in literature as a "local search" operator for optimization with Genetic Algorithm. A new interpretation for this operator behavior is proposed, showing the role that this operator can have in a "global search". Such interpretation will possibly allow the definition of some directives for this operator parameter tuning, leading to more efficient GA that reach the optima with greater probability, spending less objective function evaluations. Some preliminary tests, conducted over problems of nonlinear functions with continuous variables, are presented, leading to some specific conjectures about what should be such directives.

This paper studies the issue of space coordinate change in genetic algorithms, based on two methods: convex quadratic approximations, and principal component analysis. In both methods, the procedure employs only the objective function samples that have already been obtained through the usual genetic algorithm operations, without the need of any additional function evaluation. The two procedures have been tested over a set of benchmark problems, and the data has been analyzed via a stochastic dominance analysis procedure. In both cases, the results suggest that in the transformed coordinates the genetic algorithm can able to deal with ill-conditioned problems in less iterations and with greater proportion of successful attempts, in comparison to the genetic algorithm without coordinate transformation.

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.

This paper presents a novel approach for dealing with the structural risk minimization (SRM) applied to a general setting of the machine learning problem. The formulation is based on the fundamental concept that supervised learning is a bi-objective optimization problem in which two conflicting objectives should be minimized. The objectives are related to the empirical training error and the machine complexity. In this paper, one general Q-norm method to compute the machine complexity is presented, and, as a particular practical case, the minimum gradient method (MGM) is derived relying on the definition of the fat-shattering dimension. A practical mechanism for parallel layer perceptron (PLP) network training, involving only quasi-convex functions, is generated using the aforementioned definitions. Experimental results on 15 different benchmarks are presented, which show the potential of the proposed ideas.

The biological control of plagues in agriculture, a practice that has been growing around the world, is performed by leaving a suitable quantity of natural enemies of the plague in the farm during the finite time horizon of the farming cycle. This work proposes a multi-objective mathematical solution for the problem of optimal biological plague control for soy farmings, considering the control cost and the cost of farming damage due to plague. The system model is non-linear with impulsive control dynamics, in order to cope with the real-problem feature of control action, that should be performed in a finite number of discrete time instants. The dynamic optimization problem is solved using the NSGA-II, a fast and elitist multiobjective genetic algorithm. The results suggest a dual plague control policy, in which the relative price of control action versus the associated additional harvesting determine the usage of either a low control action or a higher well-defined one.

This paper presents a new operator for genetic algorithms that enhances convergence in the case of multiple nonlinear equality constraints. The proposed operator, named CQA-MEC (Constraint Quadratic Approximation for Multiple Equality Constraints), performs the steps: (i) the approximation of the non-linear constraints via quadratic functions; (ii) the determination of exact equality-constrained projections of some points onto the approximated constraint surface, via an iterative projection algorithm; and (iii) the re-insertion of the constraint- satisfying points in the genetic algorithm population. This operator can be interpreted both as a local search engine (that employs local approximations of constraint functions for correcting the feasibility) and a kind of elitism operator for equality constrained problems that plays the role of "fixing" the best estimates of the feasible set. The proposed operator has the advantage of not requiring any additional function evaluation per algorithm iteration, solely making usage of the information that is 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.

A large number of evolutionary algorithms for solving multiobjective optimization problems has been already developed. Several merit factors for comparing the outcomes of these algorithms have also been proposed. However, evaluating Pareto-surface sample sets is still considered an open problem, since the result of a multiobjective evolutionary algorithm is a collection of vectors forming a nondominated set, that can be viewed under rather different merit criteria. In this paper, we present a new performance metric: the Integrated Sphere Counting. This metric is motivated on two reasoning principles: (i) the Pareto-surface is an object that is to be described via sample sets, in a sense that is similar to the sampled function description in signal processing; and (ii) the resolution that is to be employed in the Pareto-surface sample set depends on the decision-making procedure resolution, instead of the surface structure itself. We test this metric with two benchmark problems: the 0/1 Knapsack Problem and ZDT number 6 test suite.

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.

This paper presents a comparative study of six encodings which have been used to represent trees in evolutionary algorithms. The study has been divided into two steps: 1) The encoding methods have been evaluated taking into account the time necessary to perform operations such as decoding, crossover and mutation, the feasibility of solutions after those operations, and the corresponding heritability and locality; 2) The encoding methods have been employed in a genetic algorithm to solve three different instances (with 10, 25 and 50 nodes) of the optimal communication spanning tree problem. Finally, the results obtained with each of the encodings are statistically compared using Kruskal-Wallis non-parametric tests and multiple comparisons. The results of this study provide insight into the properties of current encoding schemes for network design 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 article presents a simple efficient algorithm for the subdivision of a d -dimensional simplex in k d simplices, where k is any positive integer number. The algorithm is an extension of Freudenthal's subdivision method. The proposed algorithm deals with the more general case of k d subdivision, and is considerably simpler than the RedRefinementND algorithm for implementation of Freudenthal's strategy. The proposed simplex subdivision algorithm is motivated by a problem in the field of robust control theory: the computation of a tight upper bound of a dynamical system performance index by means of a branch-and-bound algorithm.

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.

This paper presents a new scheme for training MLPs which employs a relaxation method for multi-objective optimization. The algorithm works by obtaining a reduced set of solutions, from which the one with the best generalization is selected. This approach allows balancing between the training error and norm of network weight vectors, which are the two objective functions of the multi-objective optimization problem. The method is applied to classification and regression problems and compared with Weight Decay (WD), Support Vector Machines (SVMs) and standard Backpropagation (BP). It is shown that the systematic procedure for training proposed results on good generalization neural models, and outperforms traditional methods.