On Timing the Nadir-Point Estimation and/or Termination of Reference-Based Multi- and Many-objective Evolutionary Algorithms

摘要

There is considerable evidence that the Multi- and Many-objective Evolutionary Algorithms (jointly referred as MaOEAs, here) are mostly run for arbitrarily fixed number of generations. The absence of any justification for the same raises more questions than answers, and it is plausible to infer that the choices made for different problems coincide with the best-observed results. Reference-based MaOEAs (RMaOEAs) are a prominently emerging class of MaOEAs, where the diversity maintenance is assisted by externally provided reference vectors or points. However, the performance of most existing RMaOEAs is impacted by the efficacy with which the population is normalized along the search. This paper presents a novel and computationally efficient Termination Algorithm which under different parameter settings (strong and mild) not only determines the appropriate timing for RMaOEAs' termination but also the intermittent timings at which the population ought to be normalized. The proposed Algorithm can be tuned to integrate with different RMaOEAs. An instance of it is demonstrated here, with respect to NSGA-Ⅲ. Experimental Results on the call for final termination of NSGA-III have been validated through Hypervolume measures. The results also establish that the performance of NSGA-Ⅲ could be improved just by changing the frequency of Nadir-point estimates (used for population normalization). While several efforts have been made on how to estimate the Nadir-point, this to the best of the authors' knowledge is one of the rarest studies that explores when to estimate the Nadir-point.