A New Dominance Relation-Based Evolutionary Algorithm for Many-Objective Optimization

Abstract

Many-objective optimization has posed a great challenge to the classical Pareto-dominance based multi-objective evolutionary algorithms. In this paper, an evolutionary algorithm based on a new dominance relation is proposed for manyobjective optimization. The proposed evolutionary algorithm aims to enhance the convergence of the recently suggested nondominated sorting genetic algorithm III by exploiting the fitness evaluation scheme in multi-objective evolutionary algorithm based on decomposition, but still inherit the strength of the former in diversity maintenance. In the proposed algorithm, the non-dominated sorting scheme based on the introduced new dominance relation is employed to rank solutions in the environmental selection phase, ensuring both convergence and diversity. The proposed algorithm is applied to a number of well-known benchmark problems having 3 to 15 objectives and compared against eight state-of-the-art algorithms. The extensive experimental results show that the proposed algorithm can work well on almost all the test instances considered in this study, and it is compared favourably with the other many-objective optimizers. Additionally, a parametric study is provided to investigate the influence of a key parameter in the proposed algorithm.

Effectiveness and efficiency of non-dominated sorting for evolutionary multi- and many-objective optimization

“…The fourth idea enhances the effectiveness of the Pareto dominance by means of a set of uniformly distributed reference vectors as suggested in decomposition-based MOEAs [47,48]. θ -Dominance [48] is a dominance relation belonging to this category, where each solution is associated with its nearest reference vector, and a solution is said to dominate another one if and only if the two solutions are associated with the same reference vector and the former has better convergence and diversity than the latter.…”

“…θ -Dominance [48] is a dominance relation belonging to this category, where each solution is associated with its nearest reference vector, and a solution is said to dominate another one if and only if the two solutions are associated with the same reference vector and the former has better convergence and diversity than the latter. θ -dominance relation aims to make each solution converge to the same direction of one reference vector, which can enable the population to hold a good convergence and diversity.…”

On the effect of normalization in MOEA/D for multi-objective and many-objective optimization

“…In this paper, we use the PBI function, since it has been frequently used in the literature. The idea of the PBI function has also been used in recently proposed many-objective algorithms such as I-DBEA [1] and θ -DEA [26]. The PBI function is defined as…”

“…For many-objective problems, it has been demonstrated in the literature [10,12] that MOEA/D [27] works well in comparison with Pareto dominance-based and hypervolume-based algorithms in terms of their search ability and computation time. As a result, a number of EMO algorithms have been proposed for many-objective problems based on the same or similar framework as MOEA/D (e.g., NSGA-III [5], MOEA/DD [16], I-DBEA [1], and θ -DEA [26]). …”

Improving the multiobjective evolutionary algorithm based on decomposition with new penalty schemes

“…This way, MOEA/D can quickly approximate the Pareto front and provide a set of diverse solutions. Recently, various versions of MOEA/D have been proposed in the literature (Zhang and Li, 2007;Li and Zhang, 2009;Asafuddoula et al, 2015;Li et al, 2015a;Jiang and Yang, 2015), and the idea of decomposition has been exploited in a number of studies Li et al, 2014bLi et al, ,c, 2015aLiu et al, 2014;Yuan et al, 2015).…”