Constrained multi-objective optimization using constrained non-dominated sorting combined with an improved hybrid multi-objective evolutionary algorithm

ABSTRACT

Constrained multi-objective optimization problems (cMOPs) are complex because the optimizer should balance not only between exploration and exploitation, but also between feasibility and optimality. This article suggests a parameter-free constraint handling approach called constrained non-dominated sorting (CNS). In CNS, each solution in a population is assigned a constrained non-dominated rank based on its constraint violation degree and Pareto rank. An improved hybrid multi-objective optimization algorithm called cMOEA/H for solving cMOPs is proposed. Additionally, a dynamic resource allocation mechanism is adopted by cMOEA/H to spare more computational efforts for those relatively hard sub-problems. cMOEA/H is first compared with the baseline algorithm using an existing constraint handling mechanism, verifying the advantages of the proposed constraint handling mechanism. Then cMOEA/H is compared with some classic constrained multi-objective optimizers, experimental results indicating that cMOEA/H could be a competitive alternative for solving cMOPs. Finally, the characteristics of cMOEA/H are studied.

KEYWORDS:

• Multi-objective optimization
• constraint handling
• hybrid algorithm
• dynamic resource allocation

Disclosure statement

The authors declare that they have no conflict of interest. This article does not contain any studies with human participants or animals performed by any of the authors.

Notes

1. The jMetal framework (Durillo and Nebro 2011) is used to implement cMOEA/H, NSGA-II and the four cMOEA/Ds.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [Grant Nos. 61305041 and 61571346].