  This study proposes a new constraint handling technique for assisting
metaheuristic optimization algorithms to solve constrained optimization
problems more effectively and efficiently. Given any two solutions of any
constrained optimization problems, they are first mapped into a two-dimensional
Cartesian coordinate system with their objective function value differences and
constraint violation differences as the two axes. To the best of our knowledge,
we are the first to deal with constraints by building such a Cartesian
coordinate system. Then, the Cartesian coordinate system is divided into a
series of grids by assigning ranks to different intervals of differences. In
this way, a pairwise comparison criterion is derived with the use of the fused
ranks, which achieves non-hierarchical comparison neither preferring objective
function values nor constraint violations, resulting in more accurate
evaluation compared with existing techniques. Moreover, an evaluation function
that is equivalent to the pairwise comparison criterion is proposed, which
further improves computational efficiency. The effectiveness and efficiency of
the proposed constraint handling technique are verified on two well-known
public datasets, that is, CEC 2006 and CEC 2017. The results demonstrate that
metaheuristic optimization algorithms with using the proposed constraint
handling technique can converge to a feasible optimal solution faster and more
reliably. Experimental analysis on the parameters involved reveal guidance for
their optimal settings.
