A Decision-Support Framework for Structuring and Reducing Large Multi-Objective Solution Sets: An Application to Proton Therapy

Large multi-objective optimization problems often produce extensive sets of non-dominated or preference-sensitive solutions. Although such alternatives contain valuable trade-off information, their interpretation and selection remain difficult in practice. This work proposes a four-phase decision-support framework for structuring and reducing large solution sets into compact and interpretable collections of representative alternatives. The methodology integrates: (i) systematic solution generation via Extended Goal Programming and structured preference exploration; (ii) robustness-aware evaluation; (iii) acceptability filtering and dominance pruning; and (iv) clustering-based extraction of representative solutions. The framework is instantiated in intensity-modulated
proton therapy treatment planning, a demanding real-world application involving highly conflicting clinical objectives. Computational experiments with head-and-neck cases from the TROTS benchmark dataset show that large candidate ensembles can be consistently compressed into a small number of clinically meaningful strategies without loss of relevant trade-off information.