Abstract
In the field of population-based multi-objective optimization, a non-dominated sorting approach amounts to sort a set of candidate solutions with multiple objective function values, based on their dominance relations, and to find out solutions distributed into the first front set, second front set, and so on. A fast non-dominated sorting approach used within the framework of Non-dominated Sorting Genetic Algorithm (NSGA-II) reaches a \(\mathcal {O}(MN^2)\) time complexity (N is the population size, M is the number of the objectives). In this paper, we show an approach based on the Location Gradient (LG) number (LG sorting). Our LG sorting method is especially efficient in dealing with duplicate solutions, which only costs \(\mathcal {O}(N)\) in front assignment process when all the solutions are duplicate. Except that, in many cases, the LG sorting method can reach \(\mathcal {O}(N\log N)\) time complexity. But in the worst case, it still costs \(\mathcal {O}(MN^2)\). We demonstrate the efficacy of the LG-based sorting method comparison against several existing non-dominated sorting procedures.
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Acknowledgements
This work was supported by the ESF in “Science without borders” project, reg.nr.CZ.02.2.69/0.0/0.0/16_027/0008463 within the Operational Programme Research, Development and Education, and by the Ministry of Education, Youth and Sports of the Czech Republic in project “Metaheuristics Framework for Multi-objective Combinatorial Optimization Problems (META MO-COP)”, reg.no.LTAIN19176.
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Kong, L., Snášel, V., Das, S., Pan, JS. (2022). A Location Gradient Induced Sorting Approach for Multi-objective Optimization. In: Zhang, JF., Chen, CM., Chu, SC., Kountchev, R. (eds) Advances in Intelligent Systems and Computing. Smart Innovation, Systems and Technologies, vol 268. Springer, Singapore. https://doi.org/10.1007/978-981-16-8048-9_15
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DOI: https://doi.org/10.1007/978-981-16-8048-9_15
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