Evolutionary multiobjective optimization in noisy problem environments

Abstract

This paper presents a multiobjective evolutionary algorithm (MOEA) capable of handling stochastic objective functions. We extend a previously developed approach to solve multiple objective optimization problems in deterministic environments by incorporating a stochastic nondomination-based solution ranking procedure. In this study, concepts of stochastic dominance and significant dominance are introduced in order to better discriminate among competing solutions. The MOEA is applied to a number of published test problems to assess its robustness and to evaluate its performance relative to NSGA-II. Moreover, a new stopping criterion is proposed, which is based on the convergence velocity of any MOEA to the true Pareto optimal front, even if the exact location of the true front is unknown. This stopping criterion is especially useful in real-world problems, where finding an appropriate point to terminate the search is crucial.

Optimized allocation of power quality monitors in transmission systems: A multiobjective approach

“…However, this solution presents several drawbacks, such as: the necessity and difficulty to establish a vector of ideal weights; the lack of other relevant solutions of the Pareto-optimal set; and the difficulty to homogenize different quantities (e.g. : quality, cost, and time) to a common metric unity in a single objective [20].…”

Interval-based ranking in noisy evolutionary multi-objective optimization

“…Eskandari and Geiger [31] considered the expected values of the objective functions and proposed the stochastic dominance relation for ranking the solutions. In the selection process, the solutions are divided into two sets depending on whether they are stochastically dominated.…”

An Moea-Based Method to Tune Ea Parameters on Multiple Objective Functions

“…In tuning terms, this means that the utility of a parameter vectorx can only be estimated. The usual way of improving these estimates is to repeat the measurements (Hughes, 2001;University and Fieldsend, 2005;Eskandari and Geiger, 2009;Deb and Gupta, 2005), that is, to do more EA runs usingx, but this is clearly an expensive way of gaining more confidence. The main idea behind our technique is to do just one run with each parameter vectorx and to improve the confidence by looking at the utilities of similar parameter vectors in our archive, assessed before.…”