Parallel Best Order Sort for Non-dominated Sorting: A Theoretical Study Considering the PRAM-CREW Model

In the current paper we focus on parallelization of non-dominated sorting which is an essential step in Pareto-based multi-objective evolutionary algorithms. The parallel approaches can help to reduce the overall execution time of multi-objective evolutionary algorithms. Although there have been some proposals to parallelize non-dominated sorting algorithms, most of them have focused on the fast non-dominated sort algorithm proposed by Deb et al. This paper explores the scope of parallelism in a recently proposed approach known as Best Order Sort, which was proposed by Roy et al. We focus on two different ways of achieving parallelism in Best Order Sort. The time and space complexity of these two parallel schemes is also analyzed theoretically considering the PRAM CREW model.

[1]  Marc Parizeau,et al.  Generalizing the improved run-time complexity algorithm for non-dominated sorting , 2013, GECCO '13.

[2]  Erik D. Goodman,et al.  A novel non-dominated sorting algorithm for evolutionary multi-objective optimization , 2017, J. Comput. Sci..

[3]  Samarth Gupta,et al.  A scalable parallel implementation of evolutionary algorithms for multi-objective optimization on GPUs , 2015, 2015 IEEE Congress on Evolutionary Computation (CEC).

[4]  Mikkel T. Jensen,et al.  Reducing the run-time complexity of multiobjective EAs: The NSGA-II and other algorithms , 2003, IEEE Trans. Evol. Comput..

[5]  Kent McClymont,et al.  Deductive Sort and Climbing Sort: New Methods for Non-Dominated Sorting , 2012, Evolutionary Computation.

[6]  Kalyanmoy Deb,et al.  An Efficient Nondominated Sorting Algorithm for Large Number of Fronts , 2019, IEEE Transactions on Cybernetics.

[7]  Leocadio G. Casado,et al.  Non-dominated sorting procedure for Pareto dominance ranking on multicore CPU and/or GPU , 2017, J. Glob. Optim..

[8]  Kalyanmoy Deb,et al.  Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms , 1994, Evolutionary Computation.

[9]  Ye Tian,et al.  An Efficient Approach to Nondominated Sorting for Evolutionary Multiobjective Optimization , 2015, IEEE Transactions on Evolutionary Computation.

[10]  Xin Yao,et al.  Corner Sort for Pareto-Based Many-Objective Optimization , 2014, IEEE Transactions on Cybernetics.

[11]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[12]  Kalyanmoy Deb,et al.  Best Order Sort: A New Algorithm to Non-dominated Sorting for Evolutionary Multi-objective Optimization , 2016, GECCO.

[13]  Dominik Zelazny,et al.  Very Fast Non-dominated Sorting , 2014 .

[14]  Carlos A. Coello Coello,et al.  GBOS: Generalized Best Order Sort algorithm for non-dominated sorting , 2018, Swarm Evol. Comput..

[15]  Carlos A. Coello Coello,et al.  A divide-and-conquer based efficient non-dominated sorting approach , 2019, Swarm Evol. Comput..

[16]  Ye Tian,et al.  A Decision Variable Clustering-Based Evolutionary Algorithm for Large-Scale Many-Objective Optimization , 2018, IEEE Transactions on Evolutionary Computation.

[17]  Sriparna Saha,et al.  Divide and conquer based non-dominated sorting for parallel environment , 2016, 2016 IEEE Congress on Evolutionary Computation (CEC).

[18]  Anna Syberfeldt,et al.  A New Algorithm Using the Non-Dominated Tree to Improve Non-Dominated Sorting , 2017, Evolutionary Computation.

[19]  José A. Martínez,et al.  Improving the performance and energy of Non-Dominated Sorting for evolutionary multiobjective optimization on GPU/CPU platforms , 2018, Journal of Global Optimization.

[20]  Sriparna Saha,et al.  MBOS: Modified Best Order Sort Algorithm for Performing Non-Dominated Sorting , 2018, 2018 IEEE Congress on Evolutionary Computation (CEC).