In order to meet new environmental standards, sewage treatment plants may need to be redesigned or extended. Instead of reconstructing large parts of a sewage treatment plant, which can be very costly, it is in many cases sufficient to install relatively inexpensive equipment, which controls parts of the plant in a new way. Fuzzy controllers are often used for this task. Use of these controller...

Evolutionary multiobjective optimization has become a very popular topic in the last few years. Since the 1980s, various evolutionary approaches that are capable of searching for multiple solutions simultaneously in a single run have been developed to solve multiobjective optimization problems (MOPs). However, to find a uniformly distributed, near-complete, and near-optimal Pareto front in a sm...

Classical evolutionary multi-objective optimization algorithms aim at finding an approximation of the entire set of Pareto optimal solutions. By considering the preferences of a decision maker within evolutionary multi-objective optimization algorithms, it is possible to focus the search only on those parts of the Pareto front that satisfy his/her preferences. In this paper, an extended prefere...

Decomposition-based algorithms for multi-objective optimization problems have increased in popularity in the past decade. Although their convergence to the Pareto optimal front (PF) is in several instances superior to that of Pareto-based algorithms, the problem of selecting a way to distribute or guide these solutions in a high-dimensional space has not been explored. In this work, we introduc...

While noise is a phenomenon present in many real-world optimization problems, the understanding of its potential e ects on the performance of evolutionary algorithms is still incomplete. This paper investigates the e ects of noise for the in nite-dimensional quadratic sphere and a (1+1)-ES with isotropic normal mutations. It is shown that overvaluation as a result of failure to reevaluate paren...

In this article, a procedure to estimate a nonlinear models set (Θp) in a robust identification context, is presented. The estimated models are Pareto optimal when several identification error norms are considered simultaneously. A new multiobjective evolutionary algorithm ↗−MOEA has been designed to converge towards Θ P , a reduced but well distributed representation of ΘP since the algorithm ...

This paper introduces a deterministic method for capturing the Pareto front in multi-objective real parameter optimization problems. It is an effort to deal with multi-objective optimization problems that were until now confronted only by stochastic algorithms, specifically evolutionary algorithms. The method is based on a theoretical result that proves the equivalence of non-dominated points t...

Based on evolutionary computation techniques, we present a parallel, globally convergent, multiobjective optimization algorithm which extends the Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES). This approach enables identifying multiple global optima and multiple discontinuous Pareto set solutions of the optimization problem in a compact search space. After evaluating the algorithm...

In fuzzy optimization it is desirable that all fuzzy solutions under consideration be attainable, so that the decision maker will be able to make ‘‘a posteriori’’ decisions according to current decision environments. No additional optimization runs will be needed when the decision environment changes or when the decision maker needs to evaluate several decisions to establish the most appropriat...