This paper proposes a four-stage decision-support framework for structuring and reducing large multi-objective solution sets into compact and interpretable collections of representative alternatives.
The methodology combines:
(Phase 1) systematic solution generation through extended goal programming and structured preference exploration;
(Phase 2) robustness-aware enrichment and profiling under weight sensitivity analysis;
(Phase 3) filtering and dominance-based reduction to remove infeasible or redundant alternatives; and
(Phase 4) unsupervised clustering and representative selection to extract a small number of archetypal solutions.
Rather than returning a single optimum, the framework constructs and analyzes ensembles of solutions and organizes them into meaningful trade-off profiles. The output is a concise decision subset that preserves the diversity of the original Pareto set while substantially reducing its size, thereby facilitating transparent and actionable decision-making.
The approach is demonstrated on intensity-modulated proton therapy treatment planning for head-and-neck cancer, a naturally multi-objective and highly constrained problem that provides a demanding real-world testbed. Computational results show that large candidate ensembles can be consistently compressed into a small number of representative plans without loss of relevant trade-off information.
The proposed methodology is shown to be scalable and, while demonstrated here on proton therapy, is designed to be applicable across a range of multi-objective optimization problems.