{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:I4QUDRMXYZBDPHZYDDHW3PRVCC","short_pith_number":"pith:I4QUDRMX","canonical_record":{"source":{"id":"2102.03582","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2021-02-06T13:18:13Z","cross_cats_sorted":[],"title_canon_sha256":"b853aa8c3013dbc4aec659604badcd48f2b721117fb8769da013bd1880a62312","abstract_canon_sha256":"81323b7c10f9f2677fc37d8e28754cbc93dc34cbcc1da58a643827435aed36e1"},"schema_version":"1.0"},"canonical_sha256":"472141c597c642379f3818cf6dbe3510ab88a646c7a70b168bf8215c1a1cd922","source":{"kind":"arxiv","id":"2102.03582","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.03582","created_at":"2026-07-05T02:13:25Z"},{"alias_kind":"arxiv_version","alias_value":"2102.03582v1","created_at":"2026-07-05T02:13:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.03582","created_at":"2026-07-05T02:13:25Z"},{"alias_kind":"pith_short_12","alias_value":"I4QUDRMXYZBD","created_at":"2026-07-05T02:13:25Z"},{"alias_kind":"pith_short_16","alias_value":"I4QUDRMXYZBDPHZY","created_at":"2026-07-05T02:13:25Z"},{"alias_kind":"pith_short_8","alias_value":"I4QUDRMX","created_at":"2026-07-05T02:13:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:I4QUDRMXYZBDPHZYDDHW3PRVCC","target":"record","payload":{"canonical_record":{"source":{"id":"2102.03582","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2021-02-06T13:18:13Z","cross_cats_sorted":[],"title_canon_sha256":"b853aa8c3013dbc4aec659604badcd48f2b721117fb8769da013bd1880a62312","abstract_canon_sha256":"81323b7c10f9f2677fc37d8e28754cbc93dc34cbcc1da58a643827435aed36e1"},"schema_version":"1.0"},"canonical_sha256":"472141c597c642379f3818cf6dbe3510ab88a646c7a70b168bf8215c1a1cd922","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:13:25.240215Z","signature_b64":"7GthvK5fhdInLXZhgeQH00LFm+YT+iJQjeBM+Kg4TiVIzl9q45fsK2YblNlfr/em2opMUMF5p/1Chkx3PoTRDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"472141c597c642379f3818cf6dbe3510ab88a646c7a70b168bf8215c1a1cd922","last_reissued_at":"2026-07-05T02:13:25.239823Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:13:25.239823Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2102.03582","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:13:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0ba9DsooMm3Io6C8XpJXgBmqoHS3S0R+Ifn1yQGSTKu1jAapbjduOuCUeBEBBrvb6inqPHfl3uXI9/4fAJ+kBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T05:24:37.253232Z"},"content_sha256":"08a64373e670ba45e1d67001431a904d13bb9e14207cbfd5fd04126d20cbf7f8","schema_version":"1.0","event_id":"sha256:08a64373e670ba45e1d67001431a904d13bb9e14207cbfd5fd04126d20cbf7f8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:I4QUDRMXYZBDPHZYDDHW3PRVCC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A LP relaxation based matheuristic for multi-objective integer programming","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Duleabom An, Fabien Tricoire, Markus Sinnl, Sophie N. Parragh","submitted_at":"2021-02-06T13:18:13Z","abstract_excerpt":"Motivated by their success in the single-objective domain, we propose a very simple linear programming-based matheuristic for tri-objective binary integer programming. To tackle the problem, we obtain lower bound sets by means of the vector linear programming solver Bensolve. Then, simple heuristic approaches, such as rounding and path relinking, are applied to this lower bound set to obtain high-quality approximations of the optimal set of trade-off solutions. The proposed algorithm is compared to a recently suggested algorithm which is, to the best of our knowledge, the only existing matheur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.03582","kind":"arxiv","version":1},"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/2102.03582/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":"2026-07-05T02:13:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TYFrtxfFoQbPR/uk0BR4e/HvxWDQSnCT00q839xS7WSYlrDj9prESTA+JFeq6WhOE5ylfF0J5BFDvpd7qzCwCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T05:24:37.253737Z"},"content_sha256":"e01d4d37fa24bcdf11ac33a6eed3996ad1d41c159e7eedece3dab2e4fc13a927","schema_version":"1.0","event_id":"sha256:e01d4d37fa24bcdf11ac33a6eed3996ad1d41c159e7eedece3dab2e4fc13a927"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I4QUDRMXYZBDPHZYDDHW3PRVCC/bundle.json","state_url":"https://pith.science/pith/I4QUDRMXYZBDPHZYDDHW3PRVCC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I4QUDRMXYZBDPHZYDDHW3PRVCC/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":"2026-08-21T05:24:37Z","links":{"resolver":"https://pith.science/pith/I4QUDRMXYZBDPHZYDDHW3PRVCC","bundle":"https://pith.science/pith/I4QUDRMXYZBDPHZYDDHW3PRVCC/bundle.json","state":"https://pith.science/pith/I4QUDRMXYZBDPHZYDDHW3PRVCC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I4QUDRMXYZBDPHZYDDHW3PRVCC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:I4QUDRMXYZBDPHZYDDHW3PRVCC","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":"81323b7c10f9f2677fc37d8e28754cbc93dc34cbcc1da58a643827435aed36e1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2021-02-06T13:18:13Z","title_canon_sha256":"b853aa8c3013dbc4aec659604badcd48f2b721117fb8769da013bd1880a62312"},"schema_version":"1.0","source":{"id":"2102.03582","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.03582","created_at":"2026-07-05T02:13:25Z"},{"alias_kind":"arxiv_version","alias_value":"2102.03582v1","created_at":"2026-07-05T02:13:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.03582","created_at":"2026-07-05T02:13:25Z"},{"alias_kind":"pith_short_12","alias_value":"I4QUDRMXYZBD","created_at":"2026-07-05T02:13:25Z"},{"alias_kind":"pith_short_16","alias_value":"I4QUDRMXYZBDPHZY","created_at":"2026-07-05T02:13:25Z"},{"alias_kind":"pith_short_8","alias_value":"I4QUDRMX","created_at":"2026-07-05T02:13:25Z"}],"graph_snapshots":[{"event_id":"sha256:e01d4d37fa24bcdf11ac33a6eed3996ad1d41c159e7eedece3dab2e4fc13a927","target":"graph","created_at":"2026-07-05T02:13:25Z","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/2102.03582/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Motivated by their success in the single-objective domain, we propose a very simple linear programming-based matheuristic for tri-objective binary integer programming. To tackle the problem, we obtain lower bound sets by means of the vector linear programming solver Bensolve. Then, simple heuristic approaches, such as rounding and path relinking, are applied to this lower bound set to obtain high-quality approximations of the optimal set of trade-off solutions. The proposed algorithm is compared to a recently suggested algorithm which is, to the best of our knowledge, the only existing matheur","authors_text":"Duleabom An, Fabien Tricoire, Markus Sinnl, Sophie N. Parragh","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2021-02-06T13:18:13Z","title":"A LP relaxation based matheuristic for multi-objective integer programming"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.03582","kind":"arxiv","version":1},"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":"sha256:08a64373e670ba45e1d67001431a904d13bb9e14207cbfd5fd04126d20cbf7f8","target":"record","created_at":"2026-07-05T02:13:25Z","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":"81323b7c10f9f2677fc37d8e28754cbc93dc34cbcc1da58a643827435aed36e1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2021-02-06T13:18:13Z","title_canon_sha256":"b853aa8c3013dbc4aec659604badcd48f2b721117fb8769da013bd1880a62312"},"schema_version":"1.0","source":{"id":"2102.03582","kind":"arxiv","version":1}},"canonical_sha256":"472141c597c642379f3818cf6dbe3510ab88a646c7a70b168bf8215c1a1cd922","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"472141c597c642379f3818cf6dbe3510ab88a646c7a70b168bf8215c1a1cd922","first_computed_at":"2026-07-05T02:13:25.239823Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:13:25.239823Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7GthvK5fhdInLXZhgeQH00LFm+YT+iJQjeBM+Kg4TiVIzl9q45fsK2YblNlfr/em2opMUMF5p/1Chkx3PoTRDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:13:25.240215Z","signed_message":"canonical_sha256_bytes"},"source_id":"2102.03582","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08a64373e670ba45e1d67001431a904d13bb9e14207cbfd5fd04126d20cbf7f8","sha256:e01d4d37fa24bcdf11ac33a6eed3996ad1d41c159e7eedece3dab2e4fc13a927"],"state_sha256":"79433cdc20ececa6863f5e3aa836a0ed5c1271f994c89e9689f924b205e36771"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LrYve5PU2csW0pY9w38eIkoVHZP8waM1ofNbDea0aJzM9mshUDaxnkM+ZTHvlZmJKxGgPD2NbJUxCvlxYeQ5Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T05:24:37.257553Z","bundle_sha256":"9017859faebae671eb223da056e0346ceed8ad64cd4813da7fb77a1e62a2d2ed"}}