Utopia constrained multi objective optimisation evolutionary algorithm

A new multiobjective evolutionary optimisation algorithm (MOEA) to solve multimodal, multidimensional, nonconvex, nonlinear, dynamic multiobjective optimisation problems (MOPs) is the need of the hour. The quality of an MOEA lies in a good balance between the exploration and exploitation stages of the MOEA. Utopia constrained MOEA (U-MOEA) is proposed in this paper that improves the exploitation in the replacement step to achieve a perfect balance between exploration and exploitation. The proposed U-MOEA is tested on benchmark MOPs and a multivariable controller design problem. The performance of the proposed algorithm is also compared with other MOEAs such as NSGA-II and ICMDRA concerning hyper volume, nondomination count, combined Pareto set metric, and C-metric. The performance metrics show better hyper volume and spread metric values for the proposed algorithm, indicating the ability in attaining trade-off region closeness along with diversified Pareto front for U-MOEA when compared to the other two algorithms. Results clearly show that the proposed U-MOEA produces good convergence, diversity characteristics with many numbers of trade-off solutions in a Pareto front.