Picking a Representative Set of Solutions in Multiobjective Optimization: Axioms, Algorithms, and Experiments

• URL: http://arxiv.org/abs/2511.10716v1
• Date: Thu, 13 Nov 2025 15:53:23 GMT
• Title: Picking a Representative Set of Solutions in Multiobjective Optimization: Axioms, Algorithms, and Experiments
• Authors: Niclas Boehmer, Maximilian T. Wittmann,
• Abstract summary: We propose a measure to compute a fixed-size subset of optimal solutions that best represent the full set.<n>We show that the choice of quality measure has a decisive impact on the characteristics of the selected set of solutions.
• Score: 12.396743022905925
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Many real-world decision-making problems involve optimizing multiple objectives simultaneously, rendering the selection of the most preferred solution a non-trivial problem: All Pareto optimal solutions are viable candidates, and it is typically up to a decision maker to select one for implementation based on their subjective preferences. To reduce the cognitive load on the decision maker, previous work has introduced the Pareto pruning problem, where the goal is to compute a fixed-size subset of Pareto optimal solutions that best represent the full set, as evaluated by a given quality measure. Reframing Pareto pruning as a multiwinner voting problem, we conduct an axiomatic analysis of existing quality measures, uncovering several unintuitive behaviors. Motivated by these findings, we introduce a new measure, directed coverage. We also analyze the computational complexity of optimizing various quality measures, identifying previously unknown boundaries between tractable and intractable cases depending on the number and structure of the objectives. Finally, we present an experimental evaluation, demonstrating that the choice of quality measure has a decisive impact on the characteristics of the selected set of solutions and that our proposed measure performs competitively or even favorably across a range of settings.

Related papers

• A Principled Approach to Randomized Selection under Uncertainty: Applications to Peer Review and Grant Funding [61.86327960322782]
  We propose a principled framework for randomized decision-making based on interval estimates of the quality of each item.<n>We introduce MERIT, an optimization-based method that maximizes the worst-case expected number of top candidates selected.<n>We prove that MERIT satisfies desirable axiomatic properties not guaranteed by existing approaches.
  arXiv  Detail & Related papers  (2025-06-23T19:59:30Z)
• Bounded Rationality for LLMs: Satisficing Alignment at Inference-Time [52.230936493691985]
  We propose SITAlign, an inference framework that addresses the multifaceted nature of alignment by maximizing a primary objective while satisfying threshold-based constraints on secondary criteria.<n>We provide theoretical insights by deriving sub-optimality bounds of our satisficing based inference alignment approach.
  arXiv  Detail & Related papers  (2025-05-29T17:56:05Z)
• Balancing Optimality and Diversity: Human-Centered Decision Making through Generative Curation [6.980546503227467]
  Operational decisions in healthcare, logistics, and public policy increasingly involve algorithms that recommend candidate solutions, while leaving the final choice to human decision-makers.<n>We propose generative curation, a framework that optimally generates recommendation sets when desirability depends on both observable objectives and unobserved qualitative considerations.<n>Our framework provides decision-makers with a principled way to design algorithms that complement, rather than replace, human judgment.
  arXiv  Detail & Related papers  (2024-09-17T20:13:32Z)
• An incremental preference elicitation-based approach to learning potentially non-monotonic preferences in multi-criteria sorting [53.36437745983783]
  We first construct a max-margin optimization-based model to model potentially non-monotonic preferences. We devise information amount measurement methods and question selection strategies to pinpoint the most informative alternative in each iteration. Two incremental preference elicitation-based algorithms are developed to learn potentially non-monotonic preferences.
  arXiv  Detail & Related papers  (2024-09-04T14:36:20Z)
• Illuminating the Diversity-Fitness Trade-Off in Black-Box Optimization [9.838618121102053]
  In real-world applications, users often favor structurally diverse design choices over one high-quality solution.<n>This paper considers the problem of identifying a fixed number of solutions with a pairwise distance above a specified threshold.<n>We analyze how this trade-off depends on the properties of the underlying optimization problem.
  arXiv  Detail & Related papers  (2024-08-29T09:55:55Z)
• Differentiation of Multi-objective Data-driven Decision Pipeline [34.577809430781144]
  Real-world scenarios frequently involve multi-objective data-driven optimization problems. Traditional two-stage methods apply a machine learning model to estimate problem coefficients, followed by invoking a solver to tackle the predicted optimization problem. Recent efforts have focused on end-to-end training of predictive models that use decision loss derived from the downstream optimization problem.
  arXiv  Detail & Related papers  (2024-06-02T15:42:03Z)
• Best-Effort Adaptation [62.00856290846247]
  We present a new theoretical analysis of sample reweighting methods, including bounds holding uniformly over the weights. We show how these bounds can guide the design of learning algorithms that we discuss in detail. We report the results of a series of experiments demonstrating the effectiveness of our best-effort adaptation and domain adaptation algorithms.
  arXiv  Detail & Related papers  (2023-05-10T00:09:07Z)
• Bi-objective Ranking and Selection Using Stochastic Kriging [0.0]
  We consider bi-objective ranking and selection problems in which the two objective outcomes have been observed with uncertainty. We propose a novel Bayesian bi-objective ranking and selection method that sequentially allocates extra samples to competitive solutions. Experimental results show that the proposed method outperforms the standard allocation method, as well as a well-known state-of-the-art algorithm.
  arXiv  Detail & Related papers  (2022-09-05T23:51:07Z)
• Learning Proximal Operators to Discover Multiple Optima [66.98045013486794]
  We present an end-to-end method to learn the proximal operator across non-family problems. We show that for weakly-ized objectives and under mild conditions, the method converges globally.
  arXiv  Detail & Related papers  (2022-01-28T05:53:28Z)
• Learning MDPs from Features: Predict-Then-Optimize for Sequential Decision Problems by Reinforcement Learning [52.74071439183113]
  We study the predict-then-optimize framework in the context of sequential decision problems (formulated as MDPs) solved via reinforcement learning. Two significant computational challenges arise in applying decision-focused learning to MDPs.
  arXiv  Detail & Related papers  (2021-06-06T23:53:31Z)
• Solution Subset Selection for Final Decision Making in Evolutionary Multi-Objective Optimization [7.745468825770201]
  We discuss subset selection from a viewpoint of the final decision making. We show that the formulated function is the same as the IGD plus indicator.
  arXiv  Detail & Related papers  (2020-06-15T06:26:58Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.