Identifying the redundant, and ranking the critical, constraints in practical optimization problems

Abstract

This article presents a procedure for identification of the redundant constraints and ranking of the critical constraints by order of their importance, in single- and multi-objective optimization problems. The revelation of the redundant constraints throws light on the physics of the problem which may otherwise not be obvious to the engineers. Furthermore, the ranking of critical constraints allows for an exploration of the potential gain in objective value(s) through a logical elimination of certain constraints. Given a constrained optimization problem, the proposed procedure transforms the constraints into additional objectives (constraint objectives) and obtains a set of non-dominated solutions for the transformed problem by using a multi-objective evolutionary algorithm. Then, operating on the objective vectors of the obtained solutions, the procedure identifies the redundant, and ranks the critical constraints, based on the range of the constraint objectives and their correlations. The utility of the proposed procedure is demonstrated on four practical optimization problems.

Keywords:

• constrained multi-objective optimization
• redundant constraint
• critical constraint
• correlation matrix
• optimal system design