Adaptive variance scaling in continuous multi-objective estimation-of-distribution algorithms

Recent research into single-objective continuous Estimation-of-Distribution Algorithms (EDAs)has shown that when maximum-likelihood estimationsare used for parametric distributions such as thenormal distribution, the EDA can easily suffer frompremature convergence. In this paper we argue thatthe same holds for multi-objective optimization.Our aim in this paper is to transfer a solutioncalled Adaptive Variance Scaling (AVS) from thesingle-objective case to the multi-objectivecase. To this end, we zoom in on an existing EDAfor continuous multi-objective optimization, theMIDEA, which employs mixturedistributions. We propose a means to combine AVSwith the normal mixture distribution, as opposedto the single normal distribution for which AVS wasintroduced. In addition, we improve the AVS schemeusing the Standard-Deviation Ratio(SDR) trigger. Intuitively put, variance scalingis triggered by the SDR trigger only ifimprovements are found to be far awayfrom the mean. For the multi-objective case,this addition is important to keep the variancefrom being scaled to excessively large values.From experiments performed on five well-knownbenchmark problems, the addition of SDR andAVS is found to enlarge the class of problems thatcontinuous multi-objective EDAs can solve reliably.

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