Delta_p-MOEA: A New Multi-Objective Evolutionary Algorithm Based on the Delta_p Indicator


In this paper, we propose a new selection scheme for Multi-Objective Evolutionary Algorithms (MOEAs) based on the Delta_p indicator. Our new selection scheme is incorporated into a MOEA giving rise to the "Delta_p-MOEA." Perhaps, one of the most important disadvantages of MOEAs based on Delta_p is the definition of the reference set. In this work, we propose to create a reference set at each generation using epsilon-dominance and the set of nondominated solutions found so far. Our new selection scheme uses two different techniques to select solutions according to the modified generational distance indicator or the modified inverted generational distance indicator. Our proposed Delta_p-MOEA is validated using standard test functions taken from the specialized literature, having three to six objective functions and it is compared with respect to two well-known MOEAs: MOEA/D using Penalty Boundary Intersection (PBI), which is based on decomposition, and SMS-EMOA-HYPE (a version of SMS-EMOA that uses a fitness assignment scheme based on the use of an approximation of the hypervolume indicator). Our preliminary results indicate that our Delta_p-MOEA is a good alternative to solve MOPs with low and high dimensionality (in objective function space) since it outperforms MOEAs such as MOEA/D and SMS-EMOA-HYPE in several problems and its computational cost is reasonably low (it is slower than MOEA/D but is faster than SMS-EMOA-HYPE).