Multi Objective Optimization Concepts Questions

Study of problems that require optimizing multiple competing objectives simultaneously, focusing on both theory and practical product trade offs. Core concepts include Pareto optimality, Pareto frontier and dominance relations; scalarization approaches such as weighted sums and Lagrangian methods; constrained formulations; and algorithmic families including multi objective evolutionary algorithms and multi objective gradient methods. Candidates should be able to reason about normalization and weighting of heterogeneous metrics, how to construct utility functions and select operating points on the Pareto frontier, and how to evaluate trade offs through offline simulation and online experimentation. Practical issues covered include sensitivity analysis, fairness and safety constraints, design of multi objective experiments, and computational trade offs when optimizing at scale.