The widespread use and applicability of evolutionary algorithms is due in part to the ability to adapt them to a particular problem-solving context by tuning their parameters. This is one of the problems that a user f...
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The widespread use and applicability of evolutionary algorithms is due in part to the ability to adapt them to a particular problem-solving context by tuning their parameters. This is one of the problems that a user faces when applying an evolutionary Algorithm to solve a given problem. Before running the algorithm, the user typically has to specify values for a number of parameters, such as population size, selection rate, and probability operators. This paper empirically assesses the performance of an automatic parameter tuning system in order to avoid the problems of time requirements and the interaction of parameters. The system, based on Bayesian Networks and Case-Based Reasoning methodology, estimates the best parameter setting for maximizing the performance of evolutionary algorithms. The algorithms are applied to solve a basic problem in constraint-based, geometric parametric modeling, as an instance of general constraint-satisfaction problems. The experimental results demonstrate the validity of the proposed system and its potential effectiveness for configuring algorithms. (C) 2014 Elsevier B.V. All rights reserved.
This paper proposes a novel adaptive nesting evolutionary Algorithm to jointly optimize two important aspects of the configuration and planning of a Microgrid (MG): the structure's design and the way it is operate...
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This paper proposes a novel adaptive nesting evolutionary Algorithm to jointly optimize two important aspects of the configuration and planning of a Microgrid (MG): the structure's design and the way it is operated in time (specifically, the charging and discharging scheduling of the Energy Storage System, ESS, elements). For this purpose, a real MG scenario consisting of a wind and a photovoltaic generator, an ESS made up of one electrochemical battery, and residential and industrial loads is considered. Optimization is addressed by nesting a two-steps procedure [the first step optimizes the structure using an evolutionary Algorithm (EA), and the second step optimizes the scheduling using another EA] following different adaptive approaches that determine the number of fitness function evaluations to perform in each EA. Finally, results obtained are compared to non-nesting 2-steps algorithm evolving following a classical scheme. Results obtained show a 3.5 % improvement with respect to the baseline scenario (the non-nesting 2-steps algorithm), or a 21 % improvement when the initial solution obtained with the Baseline Charge and Discharge Procedure is used as reference.
In this paper, a novel general class of optimality criteria is defined and proposed to solve multi-objective optimization problems by using evolutionary algorithms. These criteria, named p-optimality criteria, allow u...
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In this paper, a novel general class of optimality criteria is defined and proposed to solve multi-objective optimization problems by using evolutionary algorithms. These criteria, named p-optimality criteria, allow us to value (assess) the relative importance of those solutions with outstanding performance in very few objectives and poor performance in all others, regarding those solutions with an equilibrium (balance) among all the objectives. The optimality criteria avoid interrelating the relative values of the different objectives, respecting the integrity of each one in a rational way. As an example, a simple multi-objective approach based on the p-optimality criteria and genetic algorithms is designed, where solutions used to generate new solutions are selected according to the proposed optimality criteria. It is implemented and applied on several benchmark test problems, and its performance is compared to that of the nondominated sort genetic algorithm-II method, in order to analyze the contribution and potential of these new optimality criteria.
The profitability of the livestock industry largely depends on cost-effective feed ration formulation as feed accounts for between 60 and 80% of production costs. Therefore, feed formulation is a recurring problem for...
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The profitability of the livestock industry largely depends on cost-effective feed ration formulation as feed accounts for between 60 and 80% of production costs. Therefore, feed formulation is a recurring problem for breeders. In addition, the presence of linear and non-linear constraints, and multiple possible combinations that are subject to upsurge makes the formulation of feed a Non-deterministic Polynomial-time hard (NP-hard) problem. Generally, feed formulation is done by specifying the nutritional requirements as rigid constraints and an algorithm attempts to find a feasible cost-effective formulation. However, relaxing the constraints can sometimes provide a huge reduction in the cost of feed while not seriously affecting the economic performance of the livestock. This entails the development of a feed formulation software that has an inbuilt mechanism to enable relaxation to the constraints based on the users' necessities. Accordingly, the problem formulation and the optimization algorithm should facilitate this. We modified the conventional problem formulation with a tolerance parameter (as a percentage of the actual value) to accommodate the relaxation of constraints. We solved this problem with differential evolution, a variant of evolutionary algorithms, which are good for handling NP-hard problems. In addition, the relaxation of the constraints was done in an interactive way using the proposed method without penalties. In other words, the proposed method is flexible and possesses the ability to search for a feasible and least-cost solution if available or otherwise, the best solution and finds the suitable feed components to be used in ration formulation at an optimal cost depending on the nutrient requirements and growth stage of the animal.
This paper presents a simple but effective tuning strategy for robust static output feedback (SOF) controllers with minimal quadratic cost in the context of multiple parametric uncertainties. Finding this type of cont...
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This paper presents a simple but effective tuning strategy for robust static output feedback (SOF) controllers with minimal quadratic cost in the context of multiple parametric uncertainties. Finding this type of controller is known to be computationally intractable using conventional techniques. This is mainly due to the non-convexity of the resulting control problem, which has a fixed structure. To solve this kind of control problem easily and directly, without using any complicated mathematical manipulations, we utilize Kharitonov's theorem and an evolutionary algorithm (EA) for the resolution of the underlying constrained optimization problem. Using Kharitonov's theorem, a family of bounded, robustly stable static output feedback controllers can be defined and EA is used to select the controller that ensures a minimal quadratic cost within this family. The resulting tuning strategy is applicable to both stable and unstable systems, without any limitations on the order of the process to be controlled. A numerical study was conducted to demonstrate the validity of the proposed tuning procedure. (C) 2010 Elsevier Inc. All rights reserved.
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...
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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.
A new procedure for the building and selection of supersaturated design matrices is presented. The procedure is useful in generating screening experimental designs in the range 8-22 runs. An evolutionary algorithm is ...
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A new procedure for the building and selection of supersaturated design matrices is presented. The procedure is useful in generating screening experimental designs in the range 8-22 runs. An evolutionary algorithm is used to select between all possible candidate columns, which in turn, are a Function of the selected run number, those producing the optimal matrix. Optimality, as defined by three sequentially applied common criteria (Es-2. n0, m0), is used as fitness functions in the evolution algorithm. The problem in the construction of an optimal design matrix as a particular subset of a much larger universal set of potential solutions needs specially problem-adapted genetic operators. Several have been tested and applied. To make the procedure practical, a toolkit has bern developed which allows, in a reasonable computation time, to build and select well characterised experimental supersaturated designs for a given run and factor numbers. (C) 2000 Elsevier Science B.V. All rights reserved.
An important issue in multiobjective optimization is the study of the convergence speed of algorithms. An optimization problem must be defined as simple as possible to minimize the computational cost required to solve...
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An important issue in multiobjective optimization is the study of the convergence speed of algorithms. An optimization problem must be defined as simple as possible to minimize the computational cost required to solve it. In this work, we study the convergence speed of seven multiobjective evolutionary algorithms: DEPT, MO-VNS, MOABC, MO-GSA, MO-FA, NSGA-II, and SPEA2;when solving an important biological problem: the motif discovery problem. We have used twelve instances of four different organisms as benchmark, analyzing the number of fitness function evaluations required by each algorithm to achieve reasonable quality solutions. We have used the hypervolume indicator to evaluate the solutions discovered by each algorithm, measuring its quality every 100 evaluations. This methodology also allows us to study the hit rates of the algorithms over 30 independent runs. Moreover, we have made a deeper study in the more complex instance of each organism. In this study, we observe the increase of the archive (number of non-dominated solutions) and the spread of the Pareto fronts obtained by the algorithm in the median execution. As we will see, our study reveals that DEPT, MOABC, and MO-FA provide the best convergence speeds and the highest hit rates.
Chaotic maps play an important role in improving evolutionary algorithms (EAs) for avoiding the local optima and speeding up the convergence. However, different chaotic maps in different phases have different effects ...
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Chaotic maps play an important role in improving evolutionary algorithms (EAs) for avoiding the local optima and speeding up the convergence. However, different chaotic maps in different phases have different effects on EAs. This paper focuses on exploring the effects of chaotic maps and giving comprehensive guidance for improving multiobjective evolutionary algorithms (MOEAs) by series of experiments. NSGA-II algorithm, a representative of MOEAs using the nondominated sorting and elitist strategy, is taken as the framework to study the effect of chaotic maps. Ten chaotic maps are applied in MOEAs in three phases, that is, initial population, crossover, and mutation operator. Multiobjective problems (MOPs) adopted are ZDT series problems to show the generality. Since the scale of some sequences generated by chaotic maps is changed to fit for MOPs, the correctness of scaling transformation of chaotic sequences is proved by measuring the largest Lyapunov exponent. The convergence metric.. and diversity metric. are chosen to evaluate the performance of new algorithms with chaos. The results of experiments demonstrate that chaotic maps can improve the performance of MOEAs, especially in solving problems with convex and piecewise Pareto front. In addition, cat map has the best performance in solving problems with local optima.
In current decades, various evolutionary algorithms(EAs) raise as well as many kinds of benchmarks are popular in evaluations of EAs' performances. Since there exists randomness in EAs' performances, the evalu...
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In current decades, various evolutionary algorithms(EAs) raise as well as many kinds of benchmarks are popular in evaluations of EAs' performances. Since there exists randomness in EAs' performances, the evaluations are made by a large number of runs in simulations or experiments in order to present a relatively fair comparison. However, there still exit several problems that have not been well explained. Does it make sense to deem two algorithms have equal ability if they have same final results? Is it convinced to decide winners or losers in comparisons just by tiny difference in performances? Besides the final results, how to compare algorithms' performances during the optimization iterations? In this paper, a neural network classifier based on extreme learning machine (ELM) is proposed to solve these problems. A novel role of classifier is first proposed to convince the differences between algorithms. If the classifier succeeds to classify algorithms based on their performances recorded in all generations, we deem the two algorithms have so convinced difference that comparisons of two algorithms can reflect algorithms' disparity. Therefore, the conclusions to judge the two algorithms are feasible and acceptable. Otherwise, if classifiers cannot distinguish two algorithms, we deem the two have similar performances so that it is meaningless to differ two algorithms just by tiny differences. By employing a set of classical benchmarks and six EAs, the simulations and computations are conducted. According to the analysis results, the proposed classifier can provide more information to reflect true abilities of algorithms, which is a novel view to compare EAs. (C) 2015 Elsevier B.V. All rights reserved.
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