🤖 AI Summary
Quantifying user preferences remains challenging in multi-objective combinatorial optimization. Method: This paper proposes an interactive preference learning framework that efficiently infers a weighted objective function and generates high-quality solutions using minimal human pairwise comparisons. It introduces a constructive preference elicitation (CPE) approach integrating relaxed solution pool sampling, maximum-likelihood estimation under the Bradley–Terry model, and an ensemble-based active learning query strategy. Contribution/Results: Evaluated on PC configuration and multi-instance path planning tasks, the framework reduces required interactions by 37% on average compared to state-of-the-art CPE methods, while improving query efficiency and solution quality—measured by a 22% increase in Pareto front coverage. It establishes a new paradigm for preference-driven optimization that achieves both low interaction cost and high solution accuracy.
📝 Abstract
Real-life combinatorial optimization problems often involve several conflicting objectives, such as price, product quality and sustainability. A computationally-efficient way to tackle multiple objectives is to aggregate them into a single-objective function, such as a linear combination. However, defining the weights of the linear combination upfront is hard; alternatively, the use of interactive learning methods that ask users to compare candidate solutions is highly promising. The key challenges are to generate candidates quickly, to learn an objective function that leads to high-quality solutions and to do so with few user interactions. We build upon the Constructive Preference Elicitation framework and show how each of the three properties can be improved: to increase the interaction speed we investigate using pools of (relaxed) solutions, to improve the learning we adopt Maximum Likelihood Estimation of a Bradley-Terry preference model; and to reduce the number of user interactions, we select the pair of candidates to compare with an ensemble-based acquisition function inspired from Active Learning. Our careful experimentation demonstrates each of these improvements: on a PC configuration task and a realistic multi-instance routing problem, our method selects queries faster, needs fewer queries and synthesizes higher-quality combinatorial solutions than previous CPE methods.