A quantitative pairwise comparison-based constraint handling technique for constrained optimization

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.