In this lecture, we review the concept of Pareto optimality (Pareto improvements, Pareto efficiency, Pareto-efficient sets of non-dominated solutions, and the Pareto frontier/front) and then start laying the foundations of building multi-objective evolutionary algorithms to find the Pareto front. This starts with introducing historical MOEA's – like WBGA-MO, RWGA, and VEGA – which are all based on a linear scalarization of multi-objective problems. We then show that these methods not only have trouble promoting diversity along the discovered samples of the Pareto frontier, but they completely miss non-convex portions of the Pareto frontier. To address these issues, we introduce Pareto ranking (from SPGA, MOGA, and NSGA) and the general concept of the community ecology of multi-objective optimization (where fitness is inversely proportional to distance to the Pareto frontier, and diversity is maintained in coexisting "niches" along the community of similar-fitness individuals). We will pick up with this idea and transition to multi-modal optimization (and the various diversity-preserving "niching" methods taht enable it) next time.
Whiteboard notes for this lecture can be found at:
https://www.dropbox.com/scl/fi/5umaoz9i6bt1w0fkeuw37/IEE598-Lecture3C-2026-02-26-Multi_Objective_EA-s_from_Linearization_to_Pareto_Ranking_and_Beyond-Notes.pdf?rlkey=2cixolbjafhd61r88055rxr3r&dl=0
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