{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:INU5NGDEVGRWJDUK7R5ZBPC3ZW","short_pith_number":"pith:INU5NGDE","canonical_record":{"source":{"id":"1908.04452","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-08-13T01:18:05Z","cross_cats_sorted":[],"title_canon_sha256":"dd14f358903c776104959f657f454536519e64b881740ffa862397bd1ecc5eb9","abstract_canon_sha256":"432abd088c8120564aba23c58a37c491433c078513eab77a478f9f2a913645df"},"schema_version":"1.0"},"canonical_sha256":"4369d69864a9a3648e8afc7b90bc5bcda2fe9c068e195f276bda7b4f8b30f7af","source":{"kind":"arxiv","id":"1908.04452","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.04452","created_at":"2026-07-05T02:04:03Z"},{"alias_kind":"arxiv_version","alias_value":"1908.04452v2","created_at":"2026-07-05T02:04:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.04452","created_at":"2026-07-05T02:04:03Z"},{"alias_kind":"pith_short_12","alias_value":"INU5NGDEVGRW","created_at":"2026-07-05T02:04:03Z"},{"alias_kind":"pith_short_16","alias_value":"INU5NGDEVGRWJDUK","created_at":"2026-07-05T02:04:03Z"},{"alias_kind":"pith_short_8","alias_value":"INU5NGDE","created_at":"2026-07-05T02:04:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:INU5NGDEVGRWJDUK7R5ZBPC3ZW","target":"record","payload":{"canonical_record":{"source":{"id":"1908.04452","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-08-13T01:18:05Z","cross_cats_sorted":[],"title_canon_sha256":"dd14f358903c776104959f657f454536519e64b881740ffa862397bd1ecc5eb9","abstract_canon_sha256":"432abd088c8120564aba23c58a37c491433c078513eab77a478f9f2a913645df"},"schema_version":"1.0"},"canonical_sha256":"4369d69864a9a3648e8afc7b90bc5bcda2fe9c068e195f276bda7b4f8b30f7af","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:04:03.934303Z","signature_b64":"HBqbFkV0zqmu/a8deV8Kv+umjgwarf7FMnVFWwMetQSK0rC+sQIMdZ+e5RahxKghM5afMOkOgq3aIr3i/TZ1AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4369d69864a9a3648e8afc7b90bc5bcda2fe9c068e195f276bda7b4f8b30f7af","last_reissued_at":"2026-07-05T02:04:03.933882Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:04:03.933882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.04452","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:04:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W2Xv9YVK7Z2b/bYUYGAW3P+WbYdKBdKqIzd/Rrl/EikhrnILobr9i7Auh5SztkYJyziunoo4DVCBpO0uqxAvDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T17:41:56.365348Z"},"content_sha256":"80e10aa1d4a748ea48a0ddd44a4002900aaadc33849bd6d13f2875fdbde975d4","schema_version":"1.0","event_id":"sha256:80e10aa1d4a748ea48a0ddd44a4002900aaadc33849bd6d13f2875fdbde975d4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:INU5NGDEVGRWJDUK7R5ZBPC3ZW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multi-objective scheduling on two dedicated processors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Abdelaziz Dammak, Adel Kacem","submitted_at":"2019-08-13T01:18:05Z","abstract_excerpt":"We study a multi-objective scheduling problem on two dedicated processors. The aim is to minimize simultaneously the makespan, the total tardiness and the total completion time. This NP-hard problem requires the use of well-adapted methods. For this, we adapted genetic algorithms to multi-objective case. Three methods are presented to solve this problem. The first is aggregative, the second is Pareto and the third is non-dominated sorting genetic algorithm II (NSGA-II). We proposed some adapted lower bounds for each criterion to evaluate the quality of the found results on a large set of insta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.04452","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.04452/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:04:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uFVbqmbP2SkDSJhP7BJFxsG6Dmsjjv6m81OZAFnED7Iv82TtJnssP3M5JF43Q3V/pIWIVCmr6nPI6heoXIBvBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T17:41:56.365874Z"},"content_sha256":"4c6cdae0f8cbdab8c44cb2260cd0e8a28a1d60b1630a80b44458206b5ea805c2","schema_version":"1.0","event_id":"sha256:4c6cdae0f8cbdab8c44cb2260cd0e8a28a1d60b1630a80b44458206b5ea805c2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/INU5NGDEVGRWJDUK7R5ZBPC3ZW/bundle.json","state_url":"https://pith.science/pith/INU5NGDEVGRWJDUK7R5ZBPC3ZW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/INU5NGDEVGRWJDUK7R5ZBPC3ZW/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-16T17:41:56Z","links":{"resolver":"https://pith.science/pith/INU5NGDEVGRWJDUK7R5ZBPC3ZW","bundle":"https://pith.science/pith/INU5NGDEVGRWJDUK7R5ZBPC3ZW/bundle.json","state":"https://pith.science/pith/INU5NGDEVGRWJDUK7R5ZBPC3ZW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/INU5NGDEVGRWJDUK7R5ZBPC3ZW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:INU5NGDEVGRWJDUK7R5ZBPC3ZW","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"432abd088c8120564aba23c58a37c491433c078513eab77a478f9f2a913645df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-08-13T01:18:05Z","title_canon_sha256":"dd14f358903c776104959f657f454536519e64b881740ffa862397bd1ecc5eb9"},"schema_version":"1.0","source":{"id":"1908.04452","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.04452","created_at":"2026-07-05T02:04:03Z"},{"alias_kind":"arxiv_version","alias_value":"1908.04452v2","created_at":"2026-07-05T02:04:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.04452","created_at":"2026-07-05T02:04:03Z"},{"alias_kind":"pith_short_12","alias_value":"INU5NGDEVGRW","created_at":"2026-07-05T02:04:03Z"},{"alias_kind":"pith_short_16","alias_value":"INU5NGDEVGRWJDUK","created_at":"2026-07-05T02:04:03Z"},{"alias_kind":"pith_short_8","alias_value":"INU5NGDE","created_at":"2026-07-05T02:04:03Z"}],"graph_snapshots":[{"event_id":"sha256:4c6cdae0f8cbdab8c44cb2260cd0e8a28a1d60b1630a80b44458206b5ea805c2","target":"graph","created_at":"2026-07-05T02:04:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.04452/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study a multi-objective scheduling problem on two dedicated processors. The aim is to minimize simultaneously the makespan, the total tardiness and the total completion time. This NP-hard problem requires the use of well-adapted methods. For this, we adapted genetic algorithms to multi-objective case. Three methods are presented to solve this problem. The first is aggregative, the second is Pareto and the third is non-dominated sorting genetic algorithm II (NSGA-II). We proposed some adapted lower bounds for each criterion to evaluate the quality of the found results on a large set of insta","authors_text":"Abdelaziz Dammak, Adel Kacem","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-08-13T01:18:05Z","title":"Multi-objective scheduling on two dedicated processors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.04452","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:80e10aa1d4a748ea48a0ddd44a4002900aaadc33849bd6d13f2875fdbde975d4","target":"record","created_at":"2026-07-05T02:04:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"432abd088c8120564aba23c58a37c491433c078513eab77a478f9f2a913645df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-08-13T01:18:05Z","title_canon_sha256":"dd14f358903c776104959f657f454536519e64b881740ffa862397bd1ecc5eb9"},"schema_version":"1.0","source":{"id":"1908.04452","kind":"arxiv","version":2}},"canonical_sha256":"4369d69864a9a3648e8afc7b90bc5bcda2fe9c068e195f276bda7b4f8b30f7af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4369d69864a9a3648e8afc7b90bc5bcda2fe9c068e195f276bda7b4f8b30f7af","first_computed_at":"2026-07-05T02:04:03.933882Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:04:03.933882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HBqbFkV0zqmu/a8deV8Kv+umjgwarf7FMnVFWwMetQSK0rC+sQIMdZ+e5RahxKghM5afMOkOgq3aIr3i/TZ1AQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:04:03.934303Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.04452","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:80e10aa1d4a748ea48a0ddd44a4002900aaadc33849bd6d13f2875fdbde975d4","sha256:4c6cdae0f8cbdab8c44cb2260cd0e8a28a1d60b1630a80b44458206b5ea805c2"],"state_sha256":"2476b79d62dbb2c0b1a5d86847d76cf4f1621b221fa12c1924d71d6e13179835"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"psa2NAI+AHUpRPVioT6uEEke8W9jWgNG6BXkWs2+gTUNNRmpoHfkHr/Go9iqtJ8AAT9JD3Ri864NF2P1CmADBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T17:41:56.372551Z","bundle_sha256":"ea799e09514565f02ebed94bd7c68c1845a8a6f728f6f2b165c6b7eecd3bde1a"}}