A Metric-Based Preference-Guided Evolutionary Algorithm for Multi-Objective Optimization

Many real-world decision-making problems involve multiple conflicting objectives that cannot be reduced to a single scalar criterion without loss of essential trade-off information. While multi-objective evolutionary algorithms are capable of approximating entire Pareto fronts, their scalability in many-objective settings and their emphasis on approximating the entire Pareto front may be unnecessary when the decision maker is interested in a specific trade-off region. Conversely, scalarization-based approaches require precise a priori specification of weights, which may not accurately capture the decision maker’s intent. This thesis proposes a physics-inspired preference-driven multi-objective evolutionary algorithm designed to approximate the Pareto front locally around a prescribed fairness direction. The method models candidate solutions as interacting particles governed by Coulomb-like repulsive forces, while an anisotropic metric deformation aligned with a prescribed fairness direction induces ellipsoidal isocurves that guide and concentrate the search dynamics. This formulation enables controlled concentration around a preference direction while preserving solution dispersion. To ensure consistent evaluation, conical regions of interest are introduced, allowing performance to be assessed progressively over increasing angular semi-openings. The approach is experimentally validated on a representative subset of the DTLZ benchmark suite and compared against established state-of-the-art algorithms under uniform experimental conditions. Results demonstrate that the proposed method achieves a competitive - and often superior - trade-off between convergence and directional coverage across diverse Pareto front geometries. An adaptive repulsion mechanism is further investigated to mitigate hyperparameter sensitivity and improve exploration-exploitation balance. Overall, the proposed framework provides a principled and interpretable contribution to preference-driven multi-objective optimization.