SPEA2's density estimation method is theoretically insufficient for maintaining solution diversity on complex problems; switching to all-pairwise distance calculations fixes this while keeping the algorithm practical.
This paper analyzes the theoretical performance of SPEA2, a popular multi-objective optimization algorithm, and identifies a weakness in how it maintains diversity among non-optimal solutions. The authors propose SPEA2+, an improved version that uses all pairwise distances instead of just nearest-neighbor distances, proving it can efficiently cover Pareto fronts like competing algorithms.