MB3 - Multi-Objective Optimization 1

Effectively representing and reasoning about user preferences is essential in applications such as recommender systems, product configuration, resource allocation, and scheduling. While quantitative models such as utility functions and Valued CSPs have been widely adopted, they often fail to reflect how users naturally express qualitative preferences. Conditional Preference Networks (CP-nets) address this limitation through Conditional Preference Tables (CPTs), and Constrained CP-nets (CCP-nets) further extend this framework by incorporating hard constraints that restrict feasible outcomes. Identifying Pareto-optimal solutions that satisfy both preferences and constraints is an NP-hard problem, making exact methods such as backtracking with constraint propagation computationally expensive for large-scale instances. To tackle this challenge, we propose a hybrid framework that combines the exploration capability of Genetic Algorithms with the exploitation strength of Simulated Annealing to approximate the set of Pareto optimal solutions of a given CCP-net and construct a solution relations landscape. The proposed approach utilizes a preference–feasibility fitness function to evaluate solution quality and applies threshold-based dominance testing along with inference-driven transitive trees to extract the Pareto-optimal solution set. Experimental results conducted on randomly generated CCP-nets instances show notable improvements in runtime, solution diversity, and solution quality compared to exact approaches.

We present a preference- and constraint-aware multi-objective framework for real-time continuous path planning in dynamic environments. The problem is formulated as a constrained multi-objective optimization task, where feasible trajectories are generated through an evolutionary search process designed to efficiently explore complex solution spaces while respecting safety constraints. Candidate paths are evaluated based on multiple conflicting criteria, including path length, motion quality (smoothness), and safety (collision risk), with strict feasibility enforcement to ensure reliable operation. To address real-world uncertainty, the framework incorporates a reactive execution mechanism that enables continuous adaptation during navigation. The approach dynamically responds to newly perceived environmental changes through online sensing and incremental replanning, ensuring robustness in the presence of incomplete or evolving information. A memory-guided adaptation strategy further enhances responsiveness by leveraging previously explored feasible solutions to improve convergence and reduce computational overhead during online updates. A key feature of the proposed approach is the incorporation of preference- and constraint-driven decision-making, enabling qualitative reasoning over the set of feasible alternatives. This allows the method to select context-appropriate solutions based on user preferences and operational conditions. By combining multi- objective optimization with preference-guided reasoning, the framework provides a flexible and interpretable mechanism for selecting solutions from the Pareto-optimal set.
The proposed method demonstrates strong adaptability and robustness in dynamic scenarios while maintaining high-quality feasible solutions. Its ability to balance multiple objectives, respond to environmental changes, and incorporate operational preferences and constraints makes it well-suited for complex real-world robotic navigation applications. This work highlights the potential of integrating evolutionary optimization, adaptive execution, and preference-based reasoning within a unified framework for intelligent autonomous systems.

In this work, we study the fair sparse principal component analysis (PCA) problem through the lens of nonsmooth multiobjective Riemannian optimization. In particular, we formulate fair sparse PCA as a nonsmooth multiobjective optimization problem constrained on the Stiefel manifold, where one objective is the sparse PCA reconstruction term, and the other objective is a fairness measure that captures disparity between the reconstruction errors of different classes. This formulation enables a direct trade-off analysis between sparsity and reconstruction quality on one side, and fairness on the other side, without relying on scalarization. To solve this problem, we develop a retraction-based nonsmooth multiobjective Riemannian trust-region method. The proposed algorithm uses local models built from generalized directional derivatives and subdifferential information, which makes it suitable for locally Lipschitz objective functions defined on Riemannian manifolds. We establish convergence analysis of the method and derive a worst-case iteration-complexity bound. Numerical experiments on fair sparse PCA instances, including real data sets, illustrate that the proposed method effectively captures the Pareto front and produces fair and sparse principal components, thereby demonstrating its proficiency in analyzing the trade-off between fairness and data representation quality.

MOCVXPY is a library built on top of CVXPY for convex vector optimization. It enables practitioners to describe their convex vector optimization problems using an intuitive algebraic language that closely follows the mathematical formulation. This talk presents the main features of MOCVXPY and the algorithms employed by the library. We also illustrate its functionality with examples and an application in energy.