A parallel naive approach for non-dominated sorting: a theoretical study considering PRAM CREW model

Abstract

Pareto-based multi-objective evolutionary algorithms use non-dominated sorting as an intermediate step. These algorithms are easy to parallelize as various steps of these algorithms are independent of each other. Researchers have focused on the parallelization of non-dominated sorting in order to reduce the execution time of these algorithms. In this paper, we focus on one of the initial approaches for non-dominated sorting also known as naive approach, proposed by Srinivas et al. and explore the scope of parallelism in this approach. Parallelism is explored in the considered approach in three different ways considering Parallel Random Access Machine, Concurrent Read Exclusive Write model. The time and space complexities of three different parallel versions are also analyzed. Analysis of parallel algorithms is usually carried out under the assumption that an unbounded number of processors are available. Thus, the same assumption has been considered in our analysis too and we have obtained the maximum number of processors required for three parallel versions.