In addition to satisfying several competing objectives, many real-world applications are also characterized by a certain degree of noise, manifesting itself in the form of signal distortion or uncertain information. In this paper, extensive studies are carried out to examine the impact of noisy environments in evolutionary multiobjective optimization. Three noise-handling features are then proposed based upon the analysis of empirical results, including an experiential learning directed perturbation operator that adapts the magnitude and direction of variation according to past experiences for fast convergence, a gene adaptation selection strategy that helps the evolutionary search in escaping from local optima or premature convergence, and a possibilistic archiving model based on the concept of possibility and necessity measures to deal with problem of uncertainties. In addition, the performances of various multiobjective evolutionary algorithms in noisy environments, as well as the robustness and effectiveness of the proposed features are examined based upon five benchmark problems characterized by different difficulties in local optimality, nonuniformity, discontinuity, and nonconvexity

An Investigation on Noisy Environments in Evolutionary Multiobjective Optimization

Foreword. Acknowledgments. 1. Introduction. 2. Preliminaries. 3. The (1+1)-ES: Overvaluation. 4. The (mu, lambda)-ES: Distributed Populations. 5. The (mu/mu, lambda-ES: Genetic Repair. 6. Comparing Approaches to Noisy Optimization. 7. Conclusions. Appendices. A. Some Statistical Basics. B. Some Useful Identities. C. Computing the Overvaluation. D. Determining the Effects of Sampling and Selection. References. Index.

Noisy Optimization With Evolution Strategies

A threshold-varying artificial neural network approach for classification and its application to bankruptcy prediction problem

Noisy optimization is currently receiving increasing popularity for its widespread applications in engineering optimization problems, where the objective functions are often found to be contaminated with noisy sensory measurements. In absence of knowledge of the noise-statistics, discriminating better trial solutions from the rest becomes difficult in the “selection” step of an evolutionary optimization algorithm with noisy objective/s. This paper provides a thorough survey of the present state-of-the-art research on noisy evolutionary algorithms for both single and multi-objective optimization problems. This is undertaken by incorporating one or more of the five strategies in traditional evolutionary algorithms. The strategies include (i) fitness sampling of individual trial solution, (ii) fitness estimation of noisy samples, (iii) dynamic population sizing over the generations, (iv) adaptation of the evolutionary search strategy, and (v) modification in the selection strategy.

Noisy evolutionary optimization algorithms – A comprehensive survey

Evolution strategies are general, nature-inspired heuristics for search and optimization. Due to their use of populations of candidate solutions and their advanced adaptation schemes, there is a common belief that evolution strategies are especially useful for optimization in the presence of noise. Empirical evidence as well as a number of theoretical findings with respect to the performance of evolution strategies on a class of spherical objective functions disturbed by Gaussian noise support that belief. However, little is known with respect to the capabilities in the presence of noise of evolution strategies relative to those of other direct optimization strategies.

In the present paper, theoretical results with respect to the performance of evolution strategies in the presence of Gaussian noise are summarized and discussed. Then, the performance of evolution strategies is compared empirically with that of several other direct optimization strategies in the noisy, spherical environment that the theoretical results have been obtained in. Due to the simplicity of that environment, the results are easily interpretable and can serve to reveal the respective strengths and weaknesses of the algorithms. It is seen that for low levels of noise, most of the strategies exhibit similar degrees of efficiency. For higher levels of noise, their step length adaptation scheme affords evolution strategies a greater degree of robustness than the other algorithms tested.

A Comparison of Evolution Strategies with Other Direct Search Methods in the Presence of Noise

Practical optimization problems often require the evaluation of solutions through experimentation, stochastic simulation, sampling, or even interaction with the user. Thus, most practical problems involve noise. We address the robustness of population-based versus point-based optimization on a range of parameter optimization problems when noise is added to the deterministic objective function values. Population-based optimization is realized by a genetic algorithm and an evolution strategy. Point-based optimization is implemented as the classical Hooke-Jeeves pattern search strategy and threshold accepting as a modern local search technique. We investigate the performance of these optimization methods for varying levels of additive normally distributed fitness-independent noise and different sample sizes for evaluating individual solutions. Our results strongly favour population-based optimization, and the evolution strategy in particular.

J. Propach

Papers

On the robustness of population-based versus point-based optimization in the presence of noise