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Nondominated sorting is a discrete process that sorts points in Euclidean space according to the coordinatewise partial order and is used to rank feasible solutions to multiobjective optimization problems. It was previously shown that nondominated sorting ...

Nondominated sorting (NS) is commonly needed in multi-objective optimization to distinguish the fitness of solutions. Since it was suggested, several NS algorithms have been proposed to reduce its time complexity. In our study, we found that their ...

Nondominated sorting, also called Pareto depth analysis (PDA), is widely used in multiobjective optimization and has recently found important applications in multicriteria anomaly detection. Recently, a partial differential equation (PDE) continuum limit ...

Many multiobjective evolutionary algorithms rely on the nondominated sorting procedure to determine the relative quality of individuals with respect to the population. In this paper, we propose a new method to decrease the cost of this procedure. Our ...

Evolutionary algorithms have been shown to be powerful for solving multiobjective optimization problems, in which nondominated sorting is a widely adopted technique in selection. This technique, however, can be computationally expensive, especially when ...

In this paper, a new multiobjective optimization framework based on nondominated sorting and local search (NSLS) is introduced. The NSLS is based on iterations. At each iteration, given a population P, a simple local search method is used to get a better ...

Nondominated sorting is a fundamental combinatorial problem in multiobjective optimization and is equivalent to the longest chain problem in combinatorics and random growth models for crystals in materials science. In a previous work [SIAM J. Math. Anal.,...

We show that nondominated sorting of a sequence $X_1,\dots,X_n$ of independent and identically distributed random variables in $\mathbb{R}^d$ has a continuum limit that corresponds to solving a Hamilton--Jacobi equation involving the probability density ...

Nondominated sorting and diversity estimation procedures are an essential part of many multiobjective optimization algorithms. In many cases these procedures are the computational bottleneck of the entire algorithm. We present the methods to decrease ...

Biogeography-based optimization (BBO) is a new evolutionary optimization method inspired by biogeography. In this paper, BBO is extended to a multi-objective optimization, and a biogeography-based multi-objective optimization (BBMO) is introduced, which ...

This paper proposes a multi-objective genetic programming (MOGP) for automatic construction of feature extraction programs (FEPs). The proposed method is modified from a well known non-dominated sorting evolutionary algorithm, i.e., NSGA-II. The key ...

This paper proposes a hybrid quantum-inspired genetic algorithm (HQGA) for the multiobjective flow shop scheduling problem (FSSP), which is a typical NP-hard combinatorial optimization problem with strong engineering backgrounds. On the one hand, a ...

The scalability of EMO algorithms is an issue of significant concern for both algorithm developers and users. A key aspect of the issue is scalability to objective space dimension, other things being equal. Here, we make some observations about the ...

This paper describes a scalable algorithm for solving multiobjective decomposable problems by combining the hierarchical Bayesian optimization algorithm (hBOA) with the nondominated sorting genetic algorithm (NSGA-II) and clustering in the objective ...

In trying to solve multiobjective optimization problems, many traditional methods scalarize the objective vector into a single objective. In those cases, the obtained solution is highly sensitive to the weight vector used in the scalarization process ...