Dominance Based Crossover Operator for Evolutionary Multi-objective Algorithms

TL;DR

The paper addresses restricted mating in Evolutionary Multi-objective Algorithms by introducing Dominance-Based Crossover (DBX), which restricts matings to pairs where a non-dominated individual is paired with a dominated partner and then applies BLX-$\alpha$ crossover. Two DBX variants, Symmetric DBX and Biased DBX, differ in the sampling of the BLX parameter $\phi_i$, biasing offspring toward the dominant parent. Evaluations on ZDT bi-objective benchmarks and an industrial constrained problem (EAmultipla) show that DBX yields a small but consistent acceleration toward the Pareto set and can improve extreme front sampling in constrained problems, with biased DBX performing particularly well in the presence of feasibility constraints. The work suggests that dominance-guided mating is a lightweight, transferable enhancement for EMAs and motivates further validation with other EMAs, crossover operators, and many-objective scenarios.

Abstract

In spite of the recent quick growth of the Evolutionary Multi-objective Optimization (EMO) research field, there has been few trials to adapt the general variation operators to the particular context of the quest for the Pareto-optimal set. The only exceptions are some mating restrictions that take in account the distance between the potential mates - but contradictory conclusions have been reported. This paper introduces a particular mating restriction for Evolutionary Multi-objective Algorithms, based on the Pareto dominance relation: the partner of a non-dominated individual will be preferably chosen among the individuals of the population that it dominates. Coupled with the BLX crossover operator, two different ways of generating offspring are proposed. This recombination scheme is validated within the well-known NSGA-II framework on three bi-objective benchmark problems and one real-world bi-objective constrained optimization problem. An acceleration of the progress of the population toward the Pareto set is observed on all problems.

Figures (6)

• Figure 1:
• Figure 2: ZDT1: the black bullets (for the biased DBX) and the gray crosses (for the standard BLX-0.5) represent the non-dominated individuals over 31 runs at generations 10, 20, 30 and 40.
• Figure 3: ZDT2: the black bullets (for the biased DBX) and the gray crosses (for the standard BLX-0.5) represent the non-dominated individuals over 31 runs at generations 20, 30, 40 and 50.
• Figure 4: ZDT3: the black bullets (for the biased DBX) and the gray crosses (for the standard BLX-0.5) represent the non-dominated individuals over 31 runs at generations 10, 20, 30 and 40.
• Figure 5: Effect of the dominance-based mating restriction in the presence of constraints: biased DBX (rings) VS standard BLX-0.5 (crosses)