Pareto frontier enhancement via uncertainty-region interpolation of multiple approximate frontiers

Multi-objective evolutionary algorithms produce diverse approximate Pareto frontiers, each capturing a different region of the optimal front depending on the decomposition strategy used. Rather than selecting a single best frontier and discarding the rest, this paper proposes an uncertainty-region interpolation algorithm that combines the complementary strengths of multiple approximate frontiers to produce an enhanced frontier 𝑃𝐹_𝑏∗ with provably non-degrading quality. The algorithm operates in two phases: it first ranks 𝐾 input frontiers using the Gaussian integration measure and selects the best as 𝑃𝐹_𝑏; it then identifies under-covered regions of 𝑃𝐹_𝑏 via a crowding-distance threshold 𝜀 and fills them by incorporating non-dominated solutions from the remaining frontiers or by polynomial interpolation within geometrically defined uncertainty regions. A formal monotonicity guarantee (Corollary ۱) establishes that 𝑄(𝑃𝐹_𝑏∗) ≥ 𝑄(𝑃𝐹_𝑏) for any input satisfying the convexity assumption, independently of the number of input methods 𝐾. The algorithm is validated on five ZDT benchmark problems (𝑚 = ۲ objectives) and three DTLZ problems (𝑚 = ۳ objectives) using the MOEA/D framework with four decomposition approaches (𝐷𝐺_𝑎, 𝐷𝑇_𝑒, 𝐷𝐵𝐼, 𝐷𝑃𝐵𝐼). Consistent IGD improvements are observed on all problems with connected Pareto fronts, with the number of frontier points increasing by up to ۱۷۲% on selected benchmarks. The algorithm’s behaviour on disconnected fronts is fully characterised through a diagnostic root-cause analysis, and concrete extensions based on DBSCAN clustering and surrogate-assisted interpolation are identified as theoretically motivated directions for future work.

کلیدواژه ها:

Multi-Objective Optimization ، Evolutionary Algorithm ، Pareto frontier approximation ، Uncertainty region ، Decomposition ، Interpolation