In this lecture, we introduce multi-objective optimization as a subset of multi-criteria decision making, and we use a game-theoretic example to motivate the discussion (as game theory is a subset of multi-objective optimization). We define the Nash equilibrium concept and draw connections to multi-agent reinforcement learning. That then lets us pivot to other solution concepts for more general multi-objective problems, such as the knapsack problem. We discuss weighting/scalarization approaches (both convex combinations and Chebyshev scalarization), satisficing approaches (common in dynamic programming examples), and target approaches, and we highlight that each of these still has a subjective degree of freedom remaining. We then motivate Pareto-efficient sets and the Pareto frontier, which is an approach that minimizes all subjectivity by producing a set of possible outcomes (instead of a single "optimal" solution). We then close by introducing multi-objective evolutionary algorithms, whose population structure is naturally suited to solving for (samples of) set-based optima.
Whiteboard notes for this lecture can be found at:
https://www.dropbox.com/scl/fi/lpb8i4mp93iegdjyccly2/IEE598-Lecture3A-2025-02-18-Multi_Criteria_Decision_Making_Pareto_Optimality_and_Intro_to_Multi_Objective_Evolutionary_Algorithms-Notes.pdf?rlkey=hef5n0e77k3k7i0zqwg8cn0cs&dl=0
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