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A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II

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... They are known as non-dominated solutions and they compose the so-called Pareto front. The preferred optimization engines to obtain it are NSGA-II [18] and SPEA-2 [19]. There is an extensive literature comparing the performance of both methods when solving a set of known or particular problems. ...
... The NSGA-II method has been used. A complete explanation is given in [18], of which the main ideas will be presented in subSection 2.4. It considers two objectives: ...
... A flow chart of the NSGA-II is shown in Fig. 10, and a description of the algorithm is given below. A more detailed explanation of this method can be found in [18]. ...
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The investment profitability is the strongest economic driver when deciding the location, and optimizing the orientation and layout of a wind power plant. However, and despite of their usual good social acceptance, wind farms must overcome the displeasure of some neighbouring residents, mainly due to the natural landscape alteration. Optimization algorithms must consider the techno-economic aspect, but also the expected visual impact. Unfortunately, there is a lack of objective indicators to quantify it. Three are the main contributions of this paper. First, it introduces an innovative method of assessing the visual impact of an offshore wind farm, integrated in a optimization algorithm. Secondly, it explains a method to speed up the annual energy production, allowing the algorithm to optimize the wind farm site and layout within an unlimited space, with unlimited number of turbines, and considering seabed characteristics, depth and cable prices. Finally, it presents a multi-objective optimization algorithm based on Pareto fronts. With this, a set of optimal solutions has been obtained taking into account the conflicting relationship between profitability and visual impact. The analysis of the optimal solutions also provides the designer with valuable guidelines on the characteristics that the projected wind farm should have.
... They are still used to this day; however, it would appear that their ability to handle problems with more than three objectives (many-objective problems) is somewhat limited. Some examples among many of this type of category are NSGA-II [39] and MOPSO [123] (Reference that contains a review on the many variations of MOPSO) ...
... Genetic algorithm seeks the solution of a problem in the form of a string of numbers and always uses recombination in addition to selection and mutation operations. The best example for genetic algorithms in multi-objective optimization is the non dominated sorting version (NSGA-II) [39] represented in algorithm 7. ...
Thesis
Most mechanical engineering design problems are optimization problems. These optimization problems hold three characteristics that make them difficult to solve. These characteristics are the mixed nature of the variables (continuous and discrete), the existence of non linear constraints and the presence of multiple non linear criteria or objectives that needs to be minimized to guide the decision making. To tackle such problems, our approach consisted on defining a benchmark of representative test problems that capture the essence of these difficulties, for which we can calculate the theoretical Pareto front. The performance of five ''traditional'' metaheuristics algorithms that integrates specific enhancement to handle particularities of the benchmark problems was tested. Then, in light of the shortcomings of these ''traditional'' modified metaheuristics to meet certain evaluation metrics, a new hybrid algorithm that couples metaheuristics and branch & bound was introduced. The hybrid algorithm combines the advantages of metaheuristics like its efficiency for non-linear multi-objective problems alongside with systematic exploration of mixed variables that branch & bound algorithms have. This new hybrid algorithm including specific branching techniques is well suited for solving nonlinear multi-objective mixed problems. It gives better results than "traditional" metaheuristics on the test problems and opens up many prospects for improvement.
... We also propose applying the multi-objective genetic algorithm method named NSGA-II, developed by Deb et al.(DEB et al., 2000), to solve it. Hence, portfolio managers can apply our method to define a theoretical optimum credit portfolio based on historical data and use it as a reference benchmark to better support the following year's budget definition. ...
... The main advantages of using GA algorithm, more specifically, the multi-objective genetic NSGA-II (DEB et al., 2000), compared to other optimization techniques to solve this problem were: ...
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This research proposes a methodology to improve credit products' selection process to compose a reference portfolio modeling it according to the framework established by the combinatorial optimization problem known as the Knapsack problem. We also propose applying the genetic algorithm multi-objective method named NSGA-II to solve it. The performed experiments' outcome provided evidence that portfolio managers can apply our method to generate a theoretical optimum credit portfolio based on historical data and use it as a reference benchmark for the following year's budget definition.
... This section presents the results of extensive evaluations that were performed to demonstrate the effectiveness of the contributions. In the experiments, the results of the proposed method were compared with the results of several similar algorithms comprising Non-dominated Sorting Genetic Algorithm-II (NSGA-II) [113], Multi-Objective Particle Swarm Algorithm (MOPSO) [114], Multi-Objective Multi-Verse Optimization (MOMVO) [115], and Multi-Objective Grasshopper Optimization Algorithm (MOGOA) [116]. The parameter values of the algorithm are listed in Table 2. ...
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... La méthode MOTS proposée part de ce principe en distribuant l'espace de recherche parmi les différents agents Critère_TS dont chacun optimise son propre critère avec un algorithme de recherche tabou en respectant les contraintes du problème de régulation. Au cours de cette recherche, les différents agents Critère_TS s'échangent des connaissances afin d'améliorer la qualité des solutions explorées et l'agent MOTS évalue la qualité des solutions trouvées par les agents Critère_TS en appliquant deux techniques qui sont la relation de dominance et la distance crowding [Deb et al. 2000]. La distance crowdind fournit une estimation de la densité des solutions entourant une solution, elle est calculée en triant d'abord l'ensemble des solutions selon l'ordre croissant de leur valeur par rapport à la fonction objectif. ...
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Ce manuscrit présente une synthèse des travaux de recherche que j’ai effectués de 2007 à 2018 en tant que Maître Assistante, et chercheur depuis 1999 au sein de l’unité de recherche URIASIS qui était ensuite promue Laboratoire SOIE (et actuellement SMART) à l’ISG de Tunis et à partir de 2016-2018 au sein du Laboratoire COSMOS (Complex Outstanding Systems Modeling Optimization and Supervision) à l’ENSI, Université de la Manouba.
... The predicted fan performance parameters are obtained by training the DD network. Finally, DD is coupled with the non-dominated sorting genetic algorithm-II (NSGA-II) [25]. The optimization process was finished once the prediction results reach the termination conditions of the genetic algorithm. ...
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... The fitness function is formed by two functions (functional formulation and a function for the standard deviation of this functional or square root of the functional variance function). The result obtained from multiobjective GA (considering a variant of NSGA-II algorithm developed by (Deb et al., 2000) in MATLAB®) is a set of Pareto front points (non-dominated solutions) and the best tradeoff solution is found by a decision-making method based on fuzzy set theory. ...
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This chapter presents a compilation of the research work being done by the authors and collaborators on the topics of optimization and identification techniques for inverse methods in damage detection and localization.
... After this, many other derivations with attempts at improvement came. The main ones are: i) VEGA, ii) Lexigraphic Ordering GA (LOGA-a priori preference) (Fourman, 1985), iii) Vector Optimized Evolution Strategy (VOES) (KURSAWE, 1991), vi) Weight-Based GA (WBGA) (Hajela and Lin, 1992), v) Multiple Objective GA (MOGA) (FONSECA & FLEMING, 1993), vi) Niched Pareto GA (NPGA, NPGA 2) (Horn and Nafpliotis, 1993;Horn, Nafpliotis, & Goldberg, 1994), vii) Non-dominated Sorting GA (NSGA, NSGA II) (Srinivas and Deb, 1994;DEB et al., 2000), viii) Strength Pareto Evolutionary Algorithm (SPEA, SPEA II) (Zitzler & Thiele, 1999;ZITZLER et al., 2001) ...
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... The optimisation algorithm is an elitist non-dominated sorting genetic algorithm (NSGA-II) implementation, originally developed by Deb et al. [34]. This widely used optimisation algorithm has been proven to be particularly suitable for multi-objective problems for a wide range of applications. ...
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... It has been found that about 97.68% of variability can be explained by the first three components. Hence, the first three components are close enough to the total variance explanation Swarm Optimization (CPSO) [47], and NSGA-II [30]. A Brief description of these three algorithms is given below. ...
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Gene expression studies can explore various information about different diseases more specifically the working mechanism of diseases. Fortunately, HIV (Human Immunodeficiency Virus)-1 has a well-known pattern of progression. There are three stages through which HIV-1 progresses namely acute, chronic, and non-progressor. The detection of different stages is very important because late detection can lead to AIDS. Automated frameworks can be helpful in the precise detection of different progression stages. In this work, an automated framework has been proposed to detect several stages of HIV-1 progression. This work is based on the analysis of transcriptional profiles of CD4+ and CD8+ T cells. The microarray array data has been processed and reduced before classification. The detection process is based on the Artificial Neural Network which is trained with the help of meta-heuristic algorithms for better convergence. Three different metaheuristic algorithms namely GA, CPSO, and NSGA-II have been compared. The experimental results show that the artificial neural network trained with the Genetic Algorithm achieves 72.22% accuracy, 69.05% precision, 70.73% recall, and 69.88% F-Measure whereas the artificial neural network trained with the Constrained Particle Swarm Optimization achieves 86.67% accuracy, 78.79% precision, 83.87% recall, and 81.25% F-Measure. In contrast, the proposed approach i.e., the artificial neural network trained with the NSGA-II approach achieves 88.24% accuracy, 82.56% precision, 88.87% recall, and 85.6% F-Measure values and outperforms other approaches including decision tree, SVM, and KNN. The results have been verified using the cross-validation procedure that ensures and reflects the usefulness of the method.
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... A modified Nelder-Mead algorithm [35] has also been proposed for solving a general nonlinear constrained optimization problem that handles linear and nonlinear (in)equality constraints. Several benchmark problems have been examined and compared with various methods (the α constrained method with mutation [53]; the genetic algorithm [54]; and the bees algorithm [55]-to mention a few) to evaluate the performance of their algorithm. Regarding the effectiveness and efficiency, the authors discovered that it is competitive to such algorithms. ...
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... As already mentioned, electromagnetic optimal design problems vary widely in their characteristics. Plenty of algorithms exist for dealing with the simplest: a standard genetic algorithm can deal with single-objective problems with inexpensive objective functions; whilst a standard Multi-Objective Evolutionary Algorithm (MOEA), such as Multi-Objective Genetic Algorithm (MOGA) [25], the Non-dominated Sorting Genetic Algorithm (NSGA, NSGA-II) [26,27], the Niched-Pareto Genetic Algorithm (NPGA) [28], the Pareto-Archived Evolutionary Strategy (PAES) [29] or the Strength Pareto Evolutionary Algorithm (SPEA, SPEA-II) [30,31] can deal with multi-objective problems with inexpensive objective problems. This thesis concentrates exclusively on algorithms dealing with the most complex type of problem: those with objective functions so computationally expensive that the use of a cost-effective technique is essential. ...
Thesis
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... The result of the calculations will be S , having received which one can try to evaluate its dependence on each of the parameters. If such dependence can be represented by polynomials of low degrees, then the simplified problem can be solved numerically by using various methods, from simple enumeration to the use of genetic algorithms [20]. ...
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... The distribution of the discrete aiming points on the cavity aperture and the allocation of the aiming points for each heliostat were optimized simultaneously. The solar flux was calculated through MCRT, and the fast elitist nondominated sorting genetic algorithm (NSGA-II) (Deb et al., 2000) was applied to optimize the aiming strategy. In addition to the successful homogenization of the solar flux on the receiver surface, the proposed method provided a trade-off between the non-uniformity of the flux distribution and the optical losses in the form of Pareto optimal front curves. ...
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... The first adopted GA-based meta-heuristic is NSGA-II that was first introduced by Deb et al. [51] and has been proved to be suitable for many real-world multi-objective optimization problems (Coello,[52]). NSGA-II utilizes a non-dominated sorting method for convergence. ...
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Research progress uplifts human living bring easiness and rich living experience. Today large amount of research scholars and individual at various levels are dedicated to research domain. Evaluating this efforts which require to be true in scientific society progress is major challenge faced today. In current state many scholars in order to achiever higher payscale present falsifying efforts. identification of this act would require a complete Research effort evaluation framework. this research project highlights the need of such research effort evaluation framework which could be deployed at universities to compute student effort. This article gives big picture of what is required to be done and focusing on common evaluation techniques like plagiarism analysis. Plagiarism analysis sis commonly used techniques to detect any falsifying effort of scholar. current limitation of this techniques are they are singular either text plagiarism , code plagiarism , image plagiarism detection ,which require a integrated module to developed at academic level. This research effort evaluation framework is an idea proposed and would require years of development, as currently only content based analysis is done , future an idea based system would be areal step towards complete research effort evaluation framework.
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Many, if not most, optimization problems have multiple objectives. Historically, multiple objectives have been combined ad hoc to form a scalar objective function, usually through a linear combination (weighted sum) of the multiple attributes, or by turning objectives into constraints. The genetic algorithm (GA), however, is readily modified to deal with multiple objectives by incorporating the concept of Pareto domination in its selection operator, and applying a niching pressure to spread its population out along the Pareto optimal tradeoff surface. We introduce the Niched Pareto GA as an algorithm for finding the Pareto optimal set. We demonstrate its ability to find and maintain a diverse “Pareto optimal population” on two artificial problems and an open problem in hydrosystems
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The paper describes a rank-based fitness assignment method for Multiple Objective Genetic Algorithms (MOGAs). Conventional niche formation methods are extended to this class of multimodal problems and theory for setting the niche size is presented. The fitness assignment method is then modified to allow direct intervention of an external decision maker (DM). Finally, the MOGA is generalised further: the genetic algorithm is seen as the optimizing element of a multiobjective optimization loop, which also comprises the DM. It is the interaction between the two that leads to the determination of a satisfactory solution to the problem. Illustrative results of how the DM can interact with the genetic algorithm are presented. They also show the ability of the MOGA to uniformly sample regions of the trade-off surface.
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In this paper, we study the problem features that may cause a multi-objective genetic algorithm (GA) difficulty in converging to the true Pareto-optimal front. Identification of such features helps us develop difficult test problems for multi-objective optimization. Multi-objective test problems are constructed from single-objective optimization problems, thereby allowing known difficult features of single-objective problems (such as multi-modality, isolation, or deception) to be directly transferred to the corresponding multi-objective problem. In addition, test problems having features specific to multi-objective optimization are also constructed. More importantly, these difficult test problems will enable researchers to test their algorithms for specific aspects of multi-objective optimization.
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In this paper, we provide a systematic comparison of various evolutionary approaches to multiobjective optimization using six carefully chosen test functions. Each test function involves a particular feature that is known to cause difficulty in the evolutionary optimization process, mainly in converging to the Pareto-optimal front (e.g., multimodality and deception). By investigating these different problem features separately, it is possible to predict the kind of problems to which a certain technique is or is not well suited. However, in contrast to what was suspected beforehand, the experimental results indicate a hierarchy of the algorithms under consideration. Furthermore, the emerging effects are evidence that the suggested test functions provide sufficient complexity to compare multiobjective optimizers. Finally, elitism is shown to be an important factor for improving evolutionary multiobjective search.
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The success of binary-coded genetic algorithms (GAs) in problems having discrete search space largely depends on the coding used to represent the problem variables and on the crossover operator that propagates building-blocks from parent strings to children strings. In solving optimization problems having continuous search space, binary-coded GAs discretize the search space by using a coding of the problem variables in binary strings. However, the coding of real-valued variables in finite-length strings causes a number of difficulties---inability to achieve arbitrary precision in the obtained solution, fixed mapping of problem variables, inherent Hamming cliff problem associated with the binary coding, and processing of Holland's schemata in continuous search space. Although, a number of real-coded GAs are developed to solve optimization problems having a continuous search space, the search powers of these crossover operators are not adequate. In this paper, the search power...