Abstract
Non-dominated sorting, used to find pareto solutions or assign solutions to different fronts, is a key but time-consuming process in multi-objective evolutionary algorithms (MOEAs). The best-case and worst-case time complexity of non-dominated sorting algorithms currently known are O(MNlogN) and O(MN2); M and N represent the number of objectives and the population size, respectively. In this paper, a more efficient SET-based non-dominated sorting algorithm, shorted to SETNDS, is proposed. The proposed algorithm can greatly reduce the number of comparisons on the promise of ensuring a shorter running time. In SETNDS, the rank of a solution to be sorted is determined by only comparing with the one with the highest rank degree in its dominant set. This algorithm is compared with six generally existing non-dominated sorting algorithms—fast non-dominated sorting, the arena’s principle sort, the deductive sort, the corner sort, the efficient non-dominated sort and the best order sort on several kinds of datasets. The compared results show that the proposed algorithm is feasible and effective and its computational efficiency outperforms other existing algorithms.
Highlights
In many practical living and production activities, we often need to make decisions through weighing the pros and cons of multiple objectives, but they always conflict with each other.Manufacturers need to select the optimal production program to make a tradeoff between the cost of production, time and quality and so on, which can be formalized as a multi-objective optimization problem (MOP) [1]
It is important to note that throughout the whole paper we focus on minimal optimization problems and vice versa
Unlike other non-dominated sorting algorithms, this paper adopts the positional information of solutions and combines them with set theory to find the dominant set that dominates the solution that needs to be sorted first
Summary
In many practical living and production activities, we often need to make decisions through weighing the pros and cons of multiple objectives, but they always conflict with each other. As described in [2], non-dominated sorting, used to find pareto solutions or assign solutions to different fronts, is a key but time-consuming process in multi-objective evolutionary algorithms (MOEAs). Sci. 2020, 10, 6858 method, solutions which are not dominated by others are recognized as non-dominated solutions or a pareto set and they will be assigned to the first rank and deleted from the population These solutions correspond to p6, p7 and p8 in Figure 1 (an example of a bi-objective minimization problem with eight solutions). The process will be repeated until the population is empty Another typical representative of the second method to assign solutions to the related rank is given in [6,7].
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