# A multi-tier adaptive grid algorithm for the evolutionary multi-objective optimisation of complex problems

ROSTAMI, Shahin and SHENFIELD, Alex (2016). A multi-tier adaptive grid algorithm for the evolutionary multi-objective optimisation of complex problems. Soft Computing - A Fusion of Foundations, Methodologies and Applications. (In Press)

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## Abstract

The multi-tier Covariance Matrix Adaptation Pareto Archived Evolution Strategy (m-CMA-PAES) is an evolutionary multi-objective optimisation (EMO) algorithm for real-valued optimisation problems. It combines a non-elitist adaptive grid based selection scheme with the efficient strategy parameter adaptation of the elitist Covariance Matrix Adaptation Evolution Strategy (CMA-ES). In the original CMA-PAES, a solution is selected as a parent for the next population using an elitist adaptive grid archiving (AGA) scheme derived from the Pareto Archived Evolution Strategy (PAES). In contrast, a multi-tiered AGA scheme to populate the archive using an adaptive grid for each level of non-dominated solutions in the considered candidate population is proposed. The new selection scheme improves the performance of the CMA-PAES as shown using benchmark functions from the ZDT, CEC09, and DTLZ test suite in a comparison against the $(\mu + \lambda)$ Multi-Objective Covariance Matrix Adaptation Evolution Strategy (MO-CMA-ES). In comparison to MO-CMA-ES, the experimental results show that the proposed algorithm offers up to a 69\% performance increase according to the Inverse Generational Distance (IGD) metric.

Item Type: Article Cultural Communication and Computing Research Institute > Communication and Computing Research Centre 10.1007/s00500-016-2227-6 Alex Shenfield 29 Jul 2016 10:18 20 Aug 2017 20:40 http://shura.shu.ac.uk/id/eprint/12686