Fast Nondominated Sorting Genetic Algorithm II with Lévy Distribution for Network Topology Optimization

Abstract

Fast nondominated sorting genetic algorithm II (NSGA-II) is a classical method for multiobjective optimization problems and has exhibited outstanding performance in many practical engineering problems. However, the tournament selection strategy used for the reproduction in NSGA-II may generate a large amount of repetitive individuals, resulting in the decrease of population diversity. To alleviate this issue, Lévy distribution, which is famous for excellent search ability in the cuckoo search algorithm, is incorporated into NSGA-II. To verify the proposed algorithm, this paper employs three different test sets, including ZDT, DTLZ, and MaF test suits. Experimental results demonstrate that the proposed algorithm is more promising compared with the state-of-the-art algorithms. Parameter sensitivity analysis further confirms the robustness of the proposed algorithm. In addition, a two-objective network topology optimization model is then used to further verify the proposed algorithm. The practical comparison results demonstrate that the proposed algorithm is more effective in dealing with practical engineering optimization problems.

Adaptive Weighted Strategy Based Integrated Surrogate Models for Multiobjective Evolutionary Algorithm

“…The performance evaluation indicators of the solution set of multiobjective optimization algorithm is mainly divided into convergence, uniformity, and spread. Convergence [ 46 ] reflects the difference between the solution set obtained by the optimization algorithm and the real Pareto-front. It is generally hoped that the solution set obtained is as close to the real Pareto front as possible.…”

Nondominated sorting genetic algorithm II with merged strategies for industrial network topology optimization

“…Zhang et al [37] alleviated this issue by introducing a local perturbation strategy to crossover individuals. Furthermore, Zhang et al [32,38] replaced the local perturbation strategy with Levy distribution. Su et al [39] proposed a nonrevisiting genetic algorithm with a novel binary space partition (BSP) tree.…”

“…This article employs NSGA-II [23], SPEA2 [24], MOPSO [25], and LDNSGA-II [32] for comparison, where LDNSGA-II is a recently improved version of NSGA-II. The parameter related to the comparison algorithms are presented in Table 1.…”

“…To optimize industry network topology structure, Li et al [31] proposed an asexual crossover operator, and then applied it to NSGA-II. After that, Zhang et al [32] further incorporated Levy distribution to NSGA-II to decrease the amount of repetitive individuals, and then incorporate it to the industry network topology optimization problem. To find the optimal threshold to separate the image into the optimal number of regions, Abd and Lu [33] constructed a seven-objective optimization model and tackled it with a competitive knee point strategy.…”