A new multi-objective model for constrained optimisation

Abstract

Multi-objective optimization evolutionary algorithms have becoming a promising approach for solving constrained optimization problems in the last decade. Standard two-objective schemes aim at minimising the objective function and the degrees of violating constraints (the degrees of violating each constraint or their sum) simultaneously. This paper proposes a new multi-objective model for constrained optimization. The model keeps the standard objectives: the original objective function and the sum of the degrees of constraint violation. Besides them, other helper objectives are constructed, which are inspired from MOEA/D or Tchebycheff method for multi-objective optimization. The new helper objectives are weighted sums of the normalized original objective function and normalized degrees of constraint violation. The normalization is a major improvement. Unlike our previous model without the normalization, experimental results demonstrate that the new model is completely superior to the standard model with two objectives. This confirms our expectation that adding more help objectives may improve the solution quality significantly.