On Improving the Constraint-Handling Performance with Modified Multiple Constraint Ranking (MCR-mod) for Engineering Design Optimization Problems Solved by Evolutionary Algorithms

This work presents a new rank-based constraint handling technique (CHT) by implementing a modification on Multiple Constraint Ranking (MCR), a recently proposed rank-based constraint handling technique (CHT) for real-world engineering design optimization problems solved by evolutionary algorithms. The new technique, namely MCR-mod, not only maintains MCR's superior feature, i.e. balanced assessment of constraints with different orders of magnitude and/or different units, but also adds some more good features, such as more proper rank definition that the best feasible solution in the population always has better rank than the best infeasible solution, involvement of good infeasible solution, and easier way of implementation. Numerical experiments on benchmark problems from IEEE-CEC 2006 competition and engineering design are conducted to assess the accuracy and robustness of MCR-mod. From 25 independent runs on each problem, MCR-mod has proven its robustness compared to MCR, by its ability to produce better feasible optimal solution in most problems. Based on nonparametric statistical tests, there are indications that MCR-mod yields significant superiority in terms of accuracy compared with MCR on problems whose most constraints are inequality and active constraints, indicating that all added features of MCR-mod produce some improvements on the constraint-handling performance.