A Review of the Application of Multiobjective Evolutionary Fuzzy Systems: Current Status and Further Directions
TL;DR: An overview of multiobjective evolutionary fuzzy systems is presented, describing the main contributions on this field and providing a two-level taxonomy of the existing proposals, in order to outline a well-established framework that could help researchers who work on significant further developments.
Abstract: Over the past few decades, fuzzy systems have been widely used in several application fields, thanks to their ability to model complex systems. The design of fuzzy systems has been successfully performed by applying evolutionary and, in particular, genetic algorithms, and recently, this approach has been extended by using multiobjective evolutionary algorithms, which can consider multiple conflicting objectives, instead of a single one. The hybridization between multiobjective evolutionary algorithms and fuzzy systems is currently known as multiobjective evolutionary fuzzy systems. This paper presents an overview of multiobjective evolutionary fuzzy systems, describing the main contributions on this field and providing a two-level taxonomy of the existing proposals, in order to outline a well-established framework that could help researchers who work on significant further developments. Finally, some considerations of recent trends and potential research directions are presented.
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TL;DR: An approach based on the mixed-integer linear programming paradigm, which is able to provide an optimal solution in terms of tasks power consumption and management of renewable resources, is developed and yields an optimal task scheduling under dynamic electrical constraints.
Abstract: The optimization of energy consumption, with consequent costs reduction, is one of the main challenges in present and future smart grids. Of course, this has to occur keeping the living comfort for the end-user unchanged. In this work, an approach based on the mixed-integer linear programming paradigm, which is able to provide an optimal solution in terms of tasks power consumption and management of renewable resources, is developed. The proposed algorithm yields an optimal task scheduling under dynamic electrical constraints, while simultaneously ensuring the thermal comfort according to the user needs. On purpose, a suitable thermal model based on heat-pump usage has been considered in the framework. Some computer simulations using real data have been performed, and obtained results confirm the efficiency and robustness of the algorithm, also in terms of achievable cost savings.
256 citations
TL;DR: This paper proposes a new model-based method for representing and searching nondominated solutions that is able to alleviate the requirement on solution diversity and in principle, as many solutions as needed can be generated.
Abstract: To approximate the Pareto front, most existing multiobjective evolutionary algorithms store the nondominated solutions found so far in the population or in an external archive during the search. Such algorithms often require a high degree of diversity of the stored solutions and only a limited number of solutions can be achieved. By contrast, model-based algorithms can alleviate the requirement on solution diversity and in principle, as many solutions as needed can be generated. This paper proposes a new model-based method for representing and searching nondominated solutions. The main idea is to construct Gaussian process-based inverse models that map all found nondominated solutions from the objective space to the decision space. These inverse models are then used to create offspring by sampling the objective space. To facilitate inverse modeling, the multivariate inverse function is decomposed into a group of univariate functions, where the number of inverse models is reduced using a random grouping technique. Extensive empirical simulations demonstrate that the proposed algorithm exhibits robust search performance on a variety of medium to high dimensional multiobjective optimization test problems. Additional nondominated solutions are generated a posteriori using the constructed models to increase the density of solutions in the preferred regions at a low computational cost.
248 citations
Cites background from "A Review of the Application of Mult..."
...4) NSGA-II is probably the most popular dominance based MOEAs [73]–[76]....
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TL;DR: The empirical results indicate that although the compared algorithms exhibit slightly different capabilities in dealing with the challenges in the test problems, none of them are able to efficiently solve these optimization problems, calling for the need for developing new EAs dedicated to large-scale multiobjective and many-objective optimization.
Abstract: The interests in multiobjective and many-objective optimization have been rapidly increasing in the evolutionary computation community. However, most studies on multiobjective and many-objective optimization are limited to small-scale problems, despite the fact that many real-world multiobjective and many-objective optimization problems may involve a large number of decision variables. As has been evident in the history of evolutionary optimization, the development of evolutionary algorithms (EAs) for solving a particular type of optimization problems has undergone a co-evolution with the development of test problems. To promote the research on large-scale multiobjective and many-objective optimization, we propose a set of generic test problems based on design principles widely used in the literature of multiobjective and many-objective optimization. In order for the test problems to be able to reflect challenges in real-world applications, we consider mixed separability between decision variables and nonuniform correlation between decision variables and objective functions. To assess the proposed test problems, six representative evolutionary multiobjective and many-objective EAs are tested on the proposed test problems. Our empirical results indicate that although the compared algorithms exhibit slightly different capabilities in dealing with the challenges in the test problems, none of them are able to efficiently solve these optimization problems, calling for the need for developing new EAs dedicated to large-scale multiobjective and many-objective optimization.
208 citations
Cites background from "A Review of the Application of Mult..."
...3) NSGA-II is one of the most popular dominance based MOEAs [60]–[63]....
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TL;DR: It will be pointed out why evolutionary fuzzy systems are important from an explainable point of view, when they began, what they are used for, and where the attention of researchers should be directed to in the near future in this area.
Abstract: Evolutionary fuzzy systems are one of the greatest advances within the area of computational intelligence. They consist of evolutionary algorithms applied to the design of fuzzy systems. Thanks to this hybridization, superb abilities are provided to fuzzy modeling in many different data science scenarios. This contribution is intended to comprise a position paper developing a comprehensive analysis of the evolutionary fuzzy systems research field. To this end, the "4 W" questions are posed and addressed with the aim of understanding the current context of this topic and its significance. Specifically, it will be pointed out why evolutionary fuzzy systems are important from an explainable point of view, when they began, what they are used for, and where the attention of researchers should be directed to in the near future in this area. They must play an important role for the emerging area of eXplainable Artificial Intelligence (XAI) learning from data.
163 citations
Cites background from "A Review of the Application of Mult..."
...However, this goal is not easy to achieve, as these criteria are usually in Evolutionary Fuzzy Systems Evolutionary Learning/ Tuning of FRBS Components (via SingleObjective or MOEFS) Objectives Tradeoff (via MOEFS) New Representations Evolutionary KB Learning Evolutionary Learning of KB Components and Inference Engine Parameters Evolutionary Tuning Performance Versus Interpretability Performance Versus Performance (Control Problems) Interval-Valued Fuzzy Sets Type-2 Fuzzy Sets Evolutionary Rule Selection (a Priori Rule Extraction) Simultaneous Evolutionary Learning of KB Components Evolutionary Rule Learning (a Priori DB) Evolutionary DB Learning Evolutionary Tuning of KB Parameters Evolutionary Adaptive Inference Engine Evolutionary Learning of Linguistic Models Evolutionary Learning of Approximative/ TSK-Rules Embedded Evolutionary DB Learning A Priori Evolutionary DB Learning Evolutionary Adaptive Inference System Evolutionary Adaptive Defuzzification Methods FIgurE 2 Evolutionary Fuzzy Systems Taxonomy....
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...In case of using MOEFSs for learning or tuning FRBS components, the reader should refer to those models introduced in the previous section....
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...In 2013, Fazzolari, Alcalá, Nojima, Ishibuchi, and Herrera published an overview focused on the MOEFSs topic, which was intended to summarize the main contributions in this particular field [23]....
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...This solution is known as MOEFS [23], which can consider any metric of performance to carry out the optimization of the FRBSs, namely the cost, or the simplicity or comprehensibility, among others....
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...In this context, the use of MOEFSs has shown that obtained rules allow the descriptions of the emerging phenomena to be simpler than those in the state of the art [54]....
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TL;DR: This paper will review the progression of Evolutionary Fuzzy Systems by analyzing their taxon- omy and components, and present a discussion on the most recent and difficult Data Mining tasks to be addressed, and which are the latest trends in the development.
Abstract: Evolutionary Fuzzy Systems are a successful hybridization between fuzzy systems and Evolutionary Algo- rithms. They integrate both the management of imprecision/uncertainty and inherent interpretability of Fuzzy Rule Based Systems, with the learning and adaptation capabilities of evolutionary optimization. Over the years, many different approaches in Evolutionary Fuzzy Systems have been developed for improving the behavior of fuzzy systems, either acting on the Fuzzy Rule Base Systems' elements, or by defining new approaches for the evolutionary components. All these efforts have enabled Evolutionary Fuzzy Systems to be successfully applied in several areas of Data Mining and engineering. In accordance with the former, a wide number of applications have been also taken advantage of these types of systems. However, with the new advances in computation, novel problems and challenges are raised every day. All these issues motivate researchers to make an effort in releasing new ways of addressing them with Evolutionary Fuzzy Systems. In this paper, we will review the progression of Evolutionary Fuzzy Systems by analyzing their taxon- omy and components. We will also stress those problems and applications already tackled by this type of approach. We will present a discussion on the most recent and difficult Data Mining tasks to be addressed, and which are the latest trends in the development of Evolutionary Fuzzy Systems.
130 citations
Cites background or methods from "A Review of the Application of Mult..."
...For more detailed descriptions or an exhaustive list of contributions see [53] or its associated Webpage (http:// sci2s....
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...These hybrid approaches are known as MOEFSs [53] that, in addition to the two aforementioned goals, may include any other kind of objective, such as the complexity of the system, the cost, the computational time, and additional performance metrics....
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...These specific types of approaches are known as Multi-Objective Evolutionary Fuzzy Systems (MOEFSs), and they have become an important part of the more general EFSs [53]....
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...In previous reviews on the topic [38,53,75] we may find them widely mentioned....
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...We acknowledge that there has been an explosion of related works, which have already been partially covered in four previous reviews [36,38,53,75] and a book [39]....
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References
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Book•
01 Sep 1988
TL;DR: In this article, the authors present the computer techniques, mathematical tools, and research results that will enable both students and practitioners to apply genetic algorithms to problems in many fields, including computer programming and mathematics.
Abstract: From the Publisher:
This book brings together - in an informal and tutorial fashion - the computer techniques, mathematical tools, and research results that will enable both students and practitioners to apply genetic algorithms to problems in many fields
Major concepts are illustrated with running examples, and major algorithms are illustrated by Pascal computer programs No prior knowledge of GAs or genetics is assumed, and only a minimum of computer programming and mathematics background is required
52,797 citations
TL;DR: This paper suggests a non-dominated sorting-based MOEA, called NSGA-II (Non-dominated Sorting Genetic Algorithm II), which alleviates all of the above three difficulties, and modify the definition of dominance in order to solve constrained multi-objective problems efficiently.
Abstract: Multi-objective evolutionary algorithms (MOEAs) that use non-dominated sorting and sharing have been criticized mainly for: (1) their O(MN/sup 3/) computational complexity (where M is the number of objectives and N is the population size); (2) their non-elitism approach; and (3) the need to specify a sharing parameter. In this paper, we suggest a non-dominated sorting-based MOEA, called NSGA-II (Non-dominated Sorting Genetic Algorithm II), which alleviates all of the above three difficulties. Specifically, a fast non-dominated sorting approach with O(MN/sup 2/) computational complexity is presented. Also, a selection operator is presented that creates a mating pool by combining the parent and offspring populations and selecting the best N solutions (with respect to fitness and spread). Simulation results on difficult test problems show that NSGA-II is able, for most problems, to find a much better spread of solutions and better convergence near the true Pareto-optimal front compared to the Pareto-archived evolution strategy and the strength-Pareto evolutionary algorithm - two other elitist MOEAs that pay special attention to creating a diverse Pareto-optimal front. Moreover, we modify the definition of dominance in order to solve constrained multi-objective problems efficiently. Simulation results of the constrained NSGA-II on a number of test problems, including a five-objective, seven-constraint nonlinear problem, are compared with another constrained multi-objective optimizer, and the much better performance of NSGA-II is observed.
37,111 citations
"A Review of the Application of Mult..." refers methods in this paper
...The method that is used in this model is usually unsupervised learning, which differs from supervised learning in that there is no a priori output to train the model....
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01 Jan 1985
TL;DR: A mathematical tool to build a fuzzy model of a system where fuzzy implications and reasoning are used is presented and two applications of the method to industrial processes are discussed: a water cleaning process and a converter in a steel-making process.
Abstract: A mathematical tool to build a fuzzy model of a system where fuzzy implications and reasoning are used is presented. The premise of an implication is the description of fuzzy subspace of inputs and its consequence is a linear input-output relation. The method of identification of a system using its input-output data is then shown. Two applications of the method to industrial processes are also discussed: a water cleaning process and a converter in a steel-making process.
18,803 citations
"A Review of the Application of Mult..." refers background in this paper
...Digital Object Identifier 10.1109/TFUZZ.2012.2201338 (FRBSs)....
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...The number and type of the objectives are reported together with the name of the MOEA, its generation type, and the kind of proposal (novel, general use or based on a previous MOEA)....
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01 May 1992
TL;DR: Initially applying his concepts to simply defined artificial systems with limited numbers of parameters, Holland goes on to explore their use in the study of a wide range of complex, naturally occuring processes, concentrating on systems having multiple factors that interact in nonlinear ways.
Abstract: From the Publisher:
Genetic algorithms are playing an increasingly important role in studies of complex adaptive systems, ranging from adaptive agents in economic theory to the use of machine learning techniques in the design of complex devices such as aircraft turbines and integrated circuits. Adaptation in Natural and Artificial Systems is the book that initiated this field of study, presenting the theoretical foundations and exploring applications.
In its most familiar form, adaptation is a biological process, whereby organisms evolve by rearranging genetic material to survive in environments confronting them. In this now classic work, Holland presents a mathematical model that allows for the nonlinearity of such complex interactions. He demonstrates the model's universality by applying it to economics, physiological psychology, game theory, and artificial intelligence and then outlines the way in which this approach modifies the traditional views of mathematical genetics.
Initially applying his concepts to simply defined artificial systems with limited numbers of parameters, Holland goes on to explore their use in the study of a wide range of complex, naturally occuring processes, concentrating on systems having multiple factors that interact in nonlinear ways. Along the way he accounts for major effects of coadaptation and coevolution: the emergence of building blocks, or schemata, that are recombined and passed on to succeeding generations to provide, innovations and improvements.
John H. Holland is Professor of Psychology and Professor of Electrical Engineering and Computer Science at the University of Michigan. He is also Maxwell Professor at the Santa Fe Institute and isDirector of the University of Michigan/Santa Fe Institute Advanced Research Program.
12,584 citations
"A Review of the Application of Mult..." refers background in this paper
...Another category of fuzzy models is represented by scatter partition-based FRBSs [12], which differ from linguistic FRBSs as their rules are semantic-free....
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