An Interactive Evolutionary Multiobjective Optimization Algorithm Based on Interpretable Active Preference Learning

High-stakes decision-making involves navigating multiple competing objectives with expensive evaluations. For instance, in brachytherapy, clinicians must balance maximizing tumor coverage (e.g., an aspirational target or soft bound of >95% coverage) against strict organ dose limits (e.g., a non-negotiable hard bound of <601cGy to the bladder). Selecting Pareto-optimal solutions that match implicit preferences is challenging, as exhaustive Pareto frontier exploration is computationally and cognitively prohibitive, necessitating interactive frameworks to guide users. While decision-makers (DMs) often possess domain knowledge to narrow the search via such soft-hard bounds, current methods often lack systematic approaches to iteratively refine these multi-faceted preference structures. Furthermore, DMs often require confidence that they have not overlooked superior alternatives, a paramount necessity in high-stakes scenarios. We present Active-MoSH, an interactive local-global framework designed for this process. Its local component integrates probabilistic preference learning with an active sampling strategy to adaptively refine Pareto subsets while minimizing cognitive burden. To bolster decision confidence, Active-MoSH's global component, C-MoSH, leverages multi-objective sensitivity analysis to identify potentially overlooked, high-value points beyond immediate feedback. We demonstrate Active-MoSH's performance benefits through diverse synthetic and real-world applications. A high-stakes case study with real cervical cancer brachytherapy treatment plans and an image selection user study further validate our hypotheses regarding the framework's ability to improve convergence, enhance DM confidence, and provide expressive preference articulation.

Interactive multi-objective optimization systems face a budget allocation dilemma: one can spend resources on expensive objective evaluations or on eliciting decision-maker preferences that identify the relevant region of the Pareto set. Moreover, preference elicitation itself spans modalities with different information content and cognitive burden, ranging from cheap, noisy pairwise preference statements (PS) to richer but costlier indifference adjustments (IA). We study cost-aware optimization under an unknown scalarization and introduce QUIVER (Query-Informed Value Estimation for Regret), a surrogate-assisted evolutionary multi-objective optimizer that adaptively chooses between objective evaluations and heterogeneous preference queries. At each step, QUIVER selects the next action by maximizing the expected decision-quality improvement per unit total cost. Across DTLZ and WFG benchmarks under synthetic decision-maker models, QUIVER achieves the lowest final utility regret on challenging WFG problems (utility regret of 2.14 on WFG4, 2.82 on WFG9: a 25% improvement over baselines), outperforming all single-modality baselines. We analyze how the optimal mix of PS and IA adapts to problem difficulty: on easy problems (DTLZ2), QUIVER selects 80% PS queries; on hard problems (WFG9), it shifts to 35% IA queries. This adaptive modality selection demonstrates cost-aware preference learning in action.

Multi-objective optimization models are often deployed in settings where decision makers (DMs) must balance some conflicting criteria. In practice, however, stakeholders must translate their qualitative preferences between different criteria into numerical weights, priorities, or reference points required by optimization methods, which can be difficult to specify and interpret. This paper proposes ParetoChat, an LLM (large language model)-based expert-agent interface for interactive multi-objective optimization. The agent translates natural-language user input into structured scalarization parameters, invokes an optimization system, presents candidate solutions, and iteratively elicits feedback. We describe a multi-agent architecture that separates input processing, multi-criteria decision-making (MCDM) expertise, solution presentation, and feedback processing. We then present a simulation study using an LLM-based DM agent and benchmark ParetoChat against interactive methods implemented in DESDEO, including reference-point and NIMBUS methods. The computational experiments on multi-objective binary knapsack and set-partitioning instances show that ParetoChat can guide the search efficiently toward solutions that match the DM's preferences. An application to historical courier-order assignment instances illustrates how users can explore objective extremes and intermediate trade-offs through natural-language requests. The results indicate that LLM agents may provide a practical interaction layer between business stakeholders and optimization tools.