Evolutionary Archived Evolution Strategy (PAES) [17] and Strength Pareto

Evolutionary algorithms have been exploited to cope with multi-objective optimization problem in 13, 14. Although they have proved their abilities in finding multiple nondominated solutions on many test problems, it is necessary to introduce evolutionary algorithms that have better convergence speed. Elitism is a process that copies the fittest individuals to the next generation. By doing that, the solution quality will not degrade in the next generation and it helps in achieving better convergence 15. The most well-known elitist multiobjective evolutionary algorithm (MOEAs) is Non-dominated Sorting Genetic Algorithm II (NSGA-II) 16 which outperforms other elitist MOEAs (Pareto Archived Evolution Strategy (PAES) 17 and Strength Pareto Evolutionary Algorithm (SPEA) 18). However, when it comes to high number of objectives (more than 3 objectives), a number of MOEAs is unable to find well-converged and diversified non-dominated solutions because of the loss of selection pressure in fitness evaluation 19. Non-dominated Sorting Genetic Algorithm III (NSGA III) 20 was introduced to address this challenge. Except selection mechanism, other fundamental components of NSGAIII are similar to NSGA-II. The new population in NSGA-II is selected by a combination of non-dominated sorting and crowding-distance sorting, while NSGA-III selects the new population based on supplied reference points. These reference points can be identified by using the proposed procedure in 21. NSGA-III have been demonstrated to work well from three to 15-objective DTLZ 20. A variant of NSGA-III, named unified-NSGA-III, has been introduced in 22 in order to provide an evolutionary algorithm that is able to cope with mono-, multi- and many objective optimization problem. Another variant of NSGA-III, EliteNSGA-III 23, stores elite population and modifies the parent selection mechanism to enhance diversity. However, the authors in 24 showed that NSGA-III does not always outperform NSGA-II. It depends on the problem. Due to the diversity of MOEAs, it is necessary to design a scheme that can be adopted by any MOEA. The proposed mechanism is able to work with any MOEA.