A stopping criterion for decomposition-based multi-objective evolutionary algorithms.

This paper proposes a new stopping criterion for decomposition-based multi-objective evolutionary algorithms (MOEA/Ds) to reduce the unnecessary usage of computational resource. In MOEA/D, a multi-objective problem is decomposed into a number of single-objective subproblems using a Tchebycheff decomposition approach. Then, optimal Pareto front (PF) is obtained by optimizing the Tchebycheff objective of all the subproblems. The proposed stopping criterion monitors the variations of Tchebycheff objective at every generation using maximum Tchebycheff objective error (MTOE) of all the subproblems and stops the algorithm, when there is no significant improvement in MTOE. $$\chi ^{2}$$ test is used for statistically verifying the significant changes of MTOE for every $$\gamma $$ generations. The proposed stopping criterion is implemented in a recently constrained MOEA/D variant, namely CMOEA/D-CDP, and a simulation study is conducted with the constrained test instances for choosing a suitable tolerance value for the MTOE stopping criterion. A comparison with the recent stopping methods demonstrates that the proposed MTOE stopping criterion is simple and has minimum computational complexity. Moreover, the MTOE stopping criterion is tested on real-world application, namely multi-objective $$\hbox {H}_{\infty }$$ loop shaping PID controller design. Simulation results revealed that the MTOE stopping criterion reduces the unnecessary usage of computational resource significantly when solving the constrained test instances and multi-objective $$\hbox {H}_{\infty }$$ loop shaping PID controller design problems. [ABSTRACT FROM AUTHOR]