The Rolling Tide Evolutionary Algorithm: A Multiobjective Optimizer for Noisy Optimization Problems

Abstract

Abstract-As methods for evolutionary multi-objective optimisation (EMO) mature and are applied to a greater number of real world problems, there has been gathering interest in the effect of uncertainty and noise on multi-objective optimisation. Specifically, how algorithms are affected by it, how to mitigate its effects, and whether some optimisers are better suited to dealing with it than others. Here we address the problem of uncertain evaluation, where the uncertainty can be modelled as additive noise in objective space. We develop a novel algorithm, the rolling tide evolutionary algorithm (RTEA), which progressively improves the accuracy of its estimated Pareto set, whilst simultaneously driving the front towards the true Pareto front. It can cope with noise whose characteristics change as a function of location (both design and objective), or which alter during the course of an optimisation. Four state-of-the-art noisetolerant EMO algorithms, as well as four widely used standard EMO algorithms, are compared to RTEA on 70 instances of ten continuous space test problems from the CEC'09 multiobjective optimisation test suite. Different instances of these problems are generated by modifying them to exhibit different types and intensities of noise. RTEA is seen to provide competitive performance across both the range of test problems used, and noise types.

Efficiently identifying pareto solutions when objective values change

“…We have exploited the time-cost improvements it provides in a state-of-the-art noisy optimiser [6], and example Matlab code is available from https://github.com/fieldsend.…”

“…This mimics the refinement of objectives in noisy optimisation (see e.g. [9,6]). We model the iterative generating process of Y t in four distinct ways, based on two solution generation models, and two selection models.…”

“…The problems were optimised with a (|E t | + 1)-Evolution Strategy (ES), in which at each iteration (time step) a member of E t was selected at random. This member was either mutated on a single design parameter (using Gaussian mutation with σ = 0.1), creating y t+1 new , or reevaluated to update its mean objective vector estimate, resulting in y t+1 chg , using an accumulative resampling approach to improve the objective estimate [9,6]. Figure 4 shows the empirical results of using the different methods to identify E t for this optimiser.…”

On the exploitation of search history and accumulative sampling in robust optimisation

“…We combine elite accumulative sampling (EAS), used in noisy optimisation problems [4,5,7], with updating the robust tness approximations across the entire search history (Algorithm 1). e e ective tness of a design is estimated by weighting previously evaluated points in its disturbance neighbourhood.…”

A Toolkit for Generating Scalable Stochastic Multiobjective Test Problems

“…Typically, in these studies, symmetric random noise is added to the decision variables [3,7,14,15,16] or the objective functions [5,9,12,18] in a bespoke way that meets the requirements for the specific uncertainties and definitions of robustness being considered. The problem that is used to benchmark every suggested algorithm is tailored to the type of uncertainty and definition of robustness considered in the study.…”