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Runtime Analysis of Evolutionary Diversity Optimization on the Multi-objective (LeadingOnes, TrailingZeros) Problem

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The central aim is to analyze evolutionary diversity optimization on the multi-objective LeadingOnes and TrailingZeros problem.
Analyzed GSEMO and GSEMOD algorithms on the LOTZk function.
Proved runtime bounds for finding Pareto-optimal solutions and optimizing diversity measures.
Conducted an empirical study to confirm theoretical bounds.
GSEMO computes all Pareto-optimal solutions in O(kn3) expected iterations.
GSEMOD optimizes total imbalance in O(kn2log(n)), faster than the upper bound for Pareto-optimal populations.
Experimental results align closely with theoretical predictions for the total imbalance measure.

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Analysis reveals runtime efficiency for diversity optimization on multi-objective problems, suggesting improvements in algorithms.

Antipov et al. (2025) studied this question.

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