Pith Number

pith:SYAGVP25

pith:2024:SYAGVP256565ZAA5JKC2NZPSBS

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Proven Advantage of Multiobjective Evolutionary Algorithms for Problems with Different Degrees of Conflict

Weijie Zheng

MOEAs achieve expected runtime O(max{k,1}n ln n) on OneMaxMin_k for any conflict degree k, while scalarization fails to cover the Pareto front for k>2

arxiv:2408.04207 v3 · 2024-08-08 · cs.NE

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We prove the same expected runtime of O(max{k,1}n ln n) for the (G)SEMO, MOEA/D, NSGA-II, and SMS-EMOA on OneMaxMin_k.

C2weakest assumption

The analysis assumes that the specific definition of OneMaxMin_k (with its per-bit conflict structure for each k) accurately captures the intended degrees of conflict and that the standard selection and variation operators of the listed MOEAs behave as modeled in the runtime proofs (Section 3 and 4).

C3one line summary

MOEAs achieve O(max{k,1}n ln n) expected runtime on OneMaxMin_k for all k while scalarization fails full coverage for k>2 and epsilon-constraint requires tuned parameters.

Formal links

3 machine-checked theorem links

Receipt and verification

First computed	2026-06-09T02:07:00.046711Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

96006abf5df77ddc801d4a85a6e5f20cb769f9d73c37e03778af5fd0b3cb2000

Aliases

arxiv: 2408.04207 · arxiv_version: 2408.04207v3 · doi: 10.48550/arxiv.2408.04207 · pith_short_12: SYAGVP256565 · pith_short_16: SYAGVP256565ZAA5 · pith_short_8: SYAGVP25

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/SYAGVP256565ZAA5JKC2NZPSBS \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 96006abf5df77ddc801d4a85a6e5f20cb769f9d73c37e03778af5fd0b3cb2000

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ccc3ca89030db7ddb96155fb99247bb4fa2eaa1429ebe17a159d7866ac6e6ed0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.NE",
    "submitted_at": "2024-08-08T04:09:52Z",
    "title_canon_sha256": "6f09a03b38baaa519dfbce7ce9fc2e281d0f72fc6647b96a54d20b9ad197b0e0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2408.04207",
    "kind": "arxiv",
    "version": 3
  }
}