Yaochu Jin

Evolutionary optimization in uncertain environments-a survey

Evolutionary algorithms often have to solve optimization problems in the presence of a wide range of uncertainties. Generally, uncertainties in evolutionary computation can be divided into the following four categories. First, the fitness function is noisy. Second, the design variables and/or the environmental parameters may change after optimization, and the quality of the obtained optimal solution should be robust against environmental changes or deviations from the optimal point. Third, the fitness function is approximated, which means that the fitness function suffers from approximation errors. Fourth, the optimum of the problem to be solved changes over time and, thus, the optimizer should be able to track the optimum continuously. In all these cases, additional measures must be taken so that evolutionary algorithms are still able to work satisfactorily. This paper attempts to provide a comprehensive overview of the related work within a unified framework, which has been scattered in a variety of research areas. Existing approaches to addressing different uncertainties are presented and discussed, and the relationship between the different categories of uncertainties are investigated. Finally, topics for future research are suggested.

A comprehensive survey of fitness approximation in evolutionary computation

Evolutionary algorithms (EAs) have received increasing interests both in the academy and industry. One main difficulty in applying EAs to real-world applications is that EAs usually need a large number of fitness evaluations before a satisfying result can be obtained. However, fitness evaluations are not always straightforward in many real-world applications. Either an explicit fitness function does not exist, or the evaluation of the fitness is computationally very expensive. In both cases, it is necessary to estimate the fitness function by constructing an approximate model. In this paper, a comprehensive survey of the research on fitness approximation in evolutionary computation is presented. Main issues like approximation levels, approximate model management schemes, model construction techniques are reviewed. To conclude, open questions and interesting issues in the field are discussed.

A framework for evolutionary optimization with approximate fitness functions

It is not unusual that an approximate model is needed for fitness evaluation in evolutionary computation. In this case, the convergence properties of the evolutionary algorithm are unclear due to the approximation error of the model. In this paper, extensive empirical studies are carried out to investigate the convergence properties of an evolution strategy using an approximate fitness function on two benchmark problems. It is found that incorrect convergence will occur if the approximate model has false optima. To address this problem, individual- and generation-based evolution control are introduced and the resulting effects on the convergence properties are presented. A framework for managing approximate models in generation-based evolution control is proposed. This framework is well suited for parallel evolutionary optimization, which is able to guarantee the correct convergence of the evolutionary algorithm, as well as to reduce the computation cost as much as possible. Control of the evolution and updating of the approximate models are based on the estimated fidelity of the approximate model. Numerical results are presented for three test problems and for an aerodynamic design example.

Surrogate-assisted evolutionary computation: Recent advances and future challenges

Surrogate-assisted, or meta-model based evolutionary computation uses efficient computational models, often known as surrogates or meta-models, for approximating the fitness function in evolutionary algorithms. Research on surrogate-assisted evolutionary computation began over a decade ago and has received considerably increasing interest in recent years. Very interestingly, surrogate-assisted evolutionary computation has found successful applications not only in solving computationally expensive single- or multi-objective optimization problems, but also in addressing dynamic optimization problems, constrained optimization problems and multi-modal optimization problems. This paper provides a concise overview of the history and recent developments in surrogate-assisted evolutionary computation and suggests a few future trends in this research area.

RM-MEDA: A Regularity Model-Based Multiobjective Estimation of Distribution Algorithm

Under mild conditions, it can be induced from the Karush-Kuhn-Tucker condition that the Pareto set, in the decision space, of a continuous multiobjective optimization problem is a piecewise continuous (m - 1)-D manifold, where m is the number of objectives. Based on this regularity property, we propose a regularity model-based multiobjective estimation of distribution algorithm (RM-MEDA) for continuous multiobjective optimization problems with variable linkages. At each generation, the proposed algorithm models a promising area in the decision space by a probability distribution whose centroid is a (m - 1)-D piecewise continuous manifold. The local principal component analysis algorithm is used for building such a model. New trial solutions are sampled from the model thus built. A nondominated sorting-based selection is used for choosing solutions for the next generation. Systematic experiments have shown that, overall, RM-MEDA outperforms three other state-of-the-art algorithms, namely, GDE3, PCX-NSGA-II, and MIDEA, on a set of test instances with variable linkages. We have demonstrated that, compared with GDE3, RM-MEDA is not sensitive to algorithmic parameters, and has good scalability to the number of decision variables in the case of nonlinear variable linkages. A few shortcomings of RM-MEDA have also been identified and discussed in this paper.

Pareto-Based Multiobjective Machine Learning: An Overview and Case Studies

Machine learning is inherently a multiobjective task. Traditionally, however, either only one of the objectives is adopted as the cost function or multiple objectives are aggregated to a scalar cost function. This can be mainly attributed to the fact that most conventional learning algorithms can only deal with a scalar cost function. Over the last decade, efforts on solving machine learning problems using the Pareto-based multiobjective optimization methodology have gained increasing impetus, particularly due to the great success of multiobjective optimization using evolutionary algorithms and other population-based stochastic search methods. It has been shown that Pareto-based multiobjective learning approaches are more powerful compared to learning algorithms with a scalar cost function in addressing various topics of machine learning, such as clustering, feature selection, improvement of generalization ability, knowledge extraction, and ensemble generation. One common benefit of the different multiobjective learning approaches is that a deeper insight into the learning problem can be gained by analyzing the Pareto front composed of multiple Pareto-optimal solutions. This paper provides an overview of the existing research on multiobjective machine learning, focusing on supervised learning. In addition, a number of case studies are provided to illustrate the major benefits of the Pareto-based approach to machine learning, e.g., how to identify interpretable models and models that can generalize on unseen data from the obtained Pareto-optimal solutions. Three approaches to Pareto-based multiobjective ensemble generation are compared and discussed in detail. Finally, potentially interesting topics in multiobjective machine learning are suggested.

On generating FC/sup 3/ fuzzy rule systems from data using evolution strategies

Sophisticated fuzzy rule systems are supposed to be flexible, complete, consistent and compact (FC(3)). Flexibility, and consistency are essential for fuzzy systems to exhibit an excellent performance and to have a clear physical meaning, while compactness is crucial when the number of the input variables increases. However, the completeness and consistency conditions are often violated if a fuzzy system is generated from data collected from real world applications. A systematic design paradigm is proposed using evolution strategies. The structure of the fuzzy rules, which determines the compactness of the fuzzy systems, is evolved along with the parameters of the fuzzy systems. Special attention has been paid to the completeness and consistency of the rule base. The completeness is guaranteed by checking the completeness of the fuzzy partitioning of input variables and the completeness of the rule structure. An index of inconsistency is suggested with the help of a fuzzy similarity which can prevent the algorithm from generating rules that seriously contradict with each other or with the heuristic knowledge. In addition, soft T-norm and BADD defuzzification are introduced and optimized to increase the flexibility of the fuzzy system. The proposed approach is applied to the design of a distance controller for cars. It is verified that a FC(3) fuzzy system works very well both, for training and test driving situations, especially when the training data are insufficient.

Efficient Hierarchical Parallel Genetic Algorithms using Grid computing

In this paper, we present an efficient Hierarchical Parallel Genetic Algorithm framework using Grid computing (GE-HPGA). The framework is developed using standard Grid technologies, and has two distinctive features: (1) an extended GridRPC API to conceal the high complexity of the Grid environment, and (2) a metascheduler for seamless resource discovery and selection. To assess the practicality of the framework, a theoretical analysis of the possible speed-up offered is presented. An empirical study on GE-HPGA using a benchmark problem and a realistic aerodynamic airfoil shape optimization problem for diverse Grid environments having different communication protocols, cluster sizes, processing nodes, at geographically disparate locations also indicates that the proposed GE-HPGA using Grid computing offers a credible framework for providing a significant speed-up to evolutionary design optimization in science and engineering.

Multi-objective hierarchical genetic algorithm for interpretable fuzzy rule-based knowledge extraction

A new scheme based on multi-objective hierarchical genetic algorithm (MOHGA) is proposed to extract interpretable rule-based knowledge from data. The approach is derived from the use of multiple objective genetic algorithm (MOGA), where the genes of the chromosome are arranged into control genes and parameter genes. These genes are in a hierarchical form so that the control genes can manipulate the parameter genes in a more effective manner. The effectiveness of this chromosome formulation enables the fuzzy sets and rules to be optimally reduced. Some important concepts about the interpretability are introduced and the fitness function in the MOGA will consider both the accuracy and interpretability of the fuzzy model. In order to remove the redundancy of the rule base proactively, we further apply an interpretability-driven simplification method to newborn individuals. In our approach, we first apply the fuzzy clustering to generate an initial rule-based model. Then the multi-objective hierarchical genetic algorithm and the recursive least square method are used to obtain the optimized fuzzy models. The accuracy and the interpretability of fuzzy models derived by this approach are studied and presented in this paper. We compare our work with other methods reported in the literature on four examples: a synthetic nonlinear dynamic system, a nonlinear static system, the Lorenz system and the Mackey-Glass system. Simulation results show that the proposed approach is effective and practical in knowledge extraction.

A critical survey of performance indices for multi-objective optimisation

A large number of methods for solving multiobjective optimisation (MOO) problems have been developed. To compare these methods rigorously, or to measure the performance of a particular MOO algorithm quantitatively, a variety of performance indices (PIs) have been proposed. We provide an overview of the various PIs and attempts to categorise them into a certain number of classes according to their properties. Comparative studies have been conducted using a group of artificial solution sets and a group of solution sets obtained by various MOO solvers to show the advantages and disadvantages of the PIs. The comparative studies show that many PIs may be misleading in that they fail to truly reflect the quality of solution sets. Thus, it may not be a good practice to evaluate the performance of MOO solvers based on PIs only.