{"id":"W2583058118","doi":"","title":"On the Impact of Symmetry-Breaking Constraints on Spatial Branch-and-Bound for Circle Packing in a Square","year":2011,"lang":"en","type":"article","venue":"Les Cahiers du GERAD","topic":"Optimization and Packing Problems","field":"Engineering","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"Group for Research in Decision Analysis","funders":"","keywords":"Homogeneous space; Square (algebra); Symmetry (geometry); Point (geometry); Branch and bound; Node (physics); Task (project management); Relaxation (psychology); Mathematics; Regular polygon; Packing problems; Symmetry breaking; Square root; Linear programming relaxation; Upper and lower bounds; Branch and cut; Mathematical optimization; Computer science; Linear programming; Geometry; Mathematical analysis; Physics; Engineering","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.004156228,0.001018031,0.001207078,0.0009339987,0.001133084,0.002356166,0.001254302,0.001242693,0.007174793],"category_scores_gemma":[0.02655513,0.0006607711,0.0007417384,0.002265754,0.002271946,0.004115317,0.001796282,0.002060475,0.0006699347],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001554029,"about_ca_system_score_gemma":0.001500211,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.005019046,"about_ca_topic_score_gemma":0.004290968,"domain_scores_codex":[0.9975504,0.001459842,0.00006653328,0.0001783344,0.0004755267,0.0002693385],"domain_scores_gemma":[0.9849216,0.01309057,0.0006257124,0.0006110173,0.0005456684,0.0002054803],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.0002159012,0.00008002153,0.0005629324,0.0001494243,0.0000263168,0.0001053672,0.0001274373,0.837876,0.001604369,0.1144193,0.0026927,0.04214031],"study_design_scores_gemma":[0.00003054893,0.00006370648,0.0001358007,0.00002047585,0.000009844931,0.00002846884,0.0000574833,0.9503082,0.001051292,0.04730352,0.000978986,0.0000115517],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.09815353,0.001077942,0.8692973,0.001742764,0.000125201,0.0001364151,0.0001076914,0.0001990245,0.02916027],"genre_scores_gemma":[0.6363088,0.001605271,0.3562104,0.0005010049,0.0001573555,0.000242479,0.0001454039,0.0004029999,0.00442624],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.007174793,"threshold_uncertainty_score":0.02400208,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0186887099980384,"score_gpt":0.2275861404880182,"score_spread":0.2088974304899798,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}