Near-Tight Runtime Guarantees for Many-Objective Evolutionary Algorithms
arxiv(2024)
摘要
Despite significant progress in the field of mathematical runtime analysis of
multi-objective evolutionary algorithms (MOEAs), the performance of MOEAs on
discrete many-objective problems is little understood. In particular, the few
existing bounds for the SEMO, global SEMO, and SMS-EMOA algorithms on classic
benchmarks are all roughly quadratic in the size of the Pareto front. In this
work, we prove near-tight runtime guarantees for these three algorithms on the
four most common benchmark problems OneMinMax, CountingOnesCountingZeros,
LeadingOnesTrailingZeros, and OneJumpZeroJump, and this for arbitrary numbers
of objectives. Our bounds depend only linearly on the Pareto front size,
showing that these MOEAs on these benchmarks cope much better with many
objectives than what previous works suggested. Our bounds are tight apart from
small polynomial factors in the number of objectives and length of bitstrings.
This is the first time that such tight bounds are proven for many-objective
uses of these MOEAs. While it is known that such results cannot hold for the
NSGA-II, we do show that our bounds, via a recent structural result, transfer
to the NSGA-III algorithm.
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