The anticipated mean shift and cluster registration in mixture-based EDAs for multi-objective optimization

Abstract

It is known that in real-valued Single-Objective (SO) optimization with Gaussian Estimation-of-Distribution Algorithms (EDAs), it is important to take into account how distribution parameters change in subsequent generations to prevent inefficient convergence as a result of overfitting, especially if dependencies are modelled. We illustrate that in Multi-Objective (MO) optimization the risk of overfitting is even larger and only further increased if clustered variation is used, a technique often employed in Multi-Objective EDAs (MOEDAs) in the form of mixture modelling via clustering selected solutions in objective space. We point out that a technique previously used in EDAs to remove the risk of overfitting for SO optimization, the anticipated mean shift (AMS), can also be used in MO optimization if clusters in subsequent generations are registered. We propose to compute this registration explicitly. Although computationally more intensive than existing approaches, the effectiveness of AMS is thereby increased. We further propose a new clustering technique to improve mixture modelling in EDAs by 1) allowing clusters to overlap substantially and 2) assigning each cluster the same number of solutions. This allows any existing EDA to be transformed into a mixture-based version straightforwardly. Finally, we point out the benefit of injecting solutions obtained from running equal-capacity SO optimizers in synchronous parallel and investigate experimentally, using 9 well-known benchmark problems, the advantages of each of the techniques.

Pareto Fronts in Clinical Practice for Pinnacle

“…We are working on implementing a technique by Bosman (12). In this approach, the search space of the planning objectives is iteratively aligned with the Pareto front of the evaluation objectives.…”

A Clustering-Based Model-Building EA for Optimization Problems with Binary and Real-Valued Variables

“…Once the centers are determined, n/k solutions closest to the chosen centers are added to the clusters in accordance with the chosen distance metric. This cluster selection process is based on a similar approach used for Multi-Objective optimization in [2].…”

MONEDA: scalable multi-objective optimization with a neural network-based estimation of distribution algorithm

“…Another important milestone has been the introduction of the anticipated mean shift (AMS) that takes into account the previous values of the means of the distribution to "push" solutions towards the Pareto-optimal front. AMS has been conjointly used with AVS in the multi-objective adapted maximum-likelihood Gaussian mixture model (MAMaLGaM-X) [21].…”

“…Therefore, an analysis of the experimental results is indispensable for gaining a better understanding of the issue. For this reason, we now focus on solving a set of well-known problems with a selected set of the previously discussed evolutionary multi-objective optimizers, namely, naïve MIDEA [24], MrBOA [1], RM-MEDA [135], the parameter-free version of MAMaLGaM-X + [21,25], MOPED [40], NSGA-II [47], SPEA2 [140] and, of course, MONEDA/NS and MONEDA/Hyp.…”

“…(21) Although this procedure circumvents the problems of performing a direct sampling of the Pareto-optimal front shape function, special precautions should be taken when interpreting the results. Note that algorithm performance will be measured with regard to the set of best overall solutions; not against the actual Pareto-optimal front.…”