Advances in Multi-Objective Optimization and Verification

The field of multi-objective optimization and verification is moving towards more efficient and effective methods for handling complex problems. Researchers are exploring new approaches to decompose complex problems into smaller subproblems, such as assume-guarantee reasoning, and developing new quality measures for evaluating solutions. There is also a growing interest in stochastic multi-objective optimization, with a focus on developing principled and tractable methods for ranking multivariate distributions. Additionally, statistical model checking is being extended to handle multi-objective Pareto queries, enabling the evaluation of multiple optimization objectives simultaneously. Notable papers in this area include: Picking a Representative Set of Solutions in Multiobjective Optimization, which introduces a new measure called directed coverage and analyzes the computational complexity of optimizing various quality measures. Center-Outward q-Dominance, which proposes a new relation for strong stochastic dominance in multi-objective optimization and develops an empirical test procedure based on q-dominance.

Sources

Towards Assume-Guarantee Verification of Abilities in Stochastic Multi-Agent Systems

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

Evaluation of Multi- and Single-objective Learning Algorithms for Imbalanced Data

Center-Outward q-Dominance: A Sample-Computable Proxy for Strong Stochastic Dominance in Multi-Objective Optimisation

Multi-Objective Statistical Model Checking using Lightweight Strategy Sampling (extended version)

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