# Quadratic Multiple Knapsack Problem on QMKP 10k Source: [Quadratic Multiple Knapsack Problem on QMKP 10k]() Collection index: [llms.txt]() Data updated: 2026-03-23T11:07:11.319Z Evaluation of algorithms solving the Quadratic Multiple Knapsack Problem using the QMKP 10k instance set, measured by optimality gap percentage (gap%). A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. | Scope | Recorded value | | --- | --- | | Task | Quadratic Multiple Knapsack Problem | | Dataset (including any stated split) | QMKP 10k | | Metric | Optimality Gap (%) | | Unit | PERCENT | | Direction | Lower is better | | Results loaded | 26 of 26 | | Coverage | All results currently returned for this benchmark | Evaluation settings may differ between results. The original papers and recorded configurations are needed to establish comparability. A shared metric name alone does not establish an identical protocol. ## Metrics - [Optimality Gap (%)](): Lower is better; unit: PERCENT. ## Recorded results | Method | Optimality Gap (%) | Result date | Report paper | | --- | --- | --- | --- | | Neural QP | 0.03 | Not recorded | 69c0c9030636e5bf4afc3b6f | | GNNQP | 0.03 | Not recorded | 69c0c9030636e5bf4afc3b6f | | HNN | 0.03 | Not recorded | 69c0c9030636e5bf4afc3b6f | | HNN | 0.03 | Not recorded | 69c0c9030636e5bf4afc3b6f | | Neural QP | 0.04 | Not recorded | 69c0c9030636e5bf4afc3b6f | | Neural QP | 0.04 | Not recorded | 69c0c9030636e5bf4afc3b6f | | TriGNN | 0.04 | Not recorded | 69c0c9030636e5bf4afc3b6f | | TriGNN | 0.04 | Not recorded | 69c0c9030636e5bf4afc3b6f | | TriGNN | 0.04 | Not recorded | 69c0c9030636e5bf4afc3b6f | | HNN | 0.04 | Not recorded | 69c0c9030636e5bf4afc3b6f | | HNN | 16.79 | Not recorded | 69c0c9030636e5bf4afc3b6f | | TriGNN | 17.25 | Not recorded | 69c0c9030636e5bf4afc3b6f | | Neural QP | 17.41 | Not recorded | 69c0c9030636e5bf4afc3b6f | | HNN | 17.45 | Not recorded | 69c0c9030636e5bf4afc3b6f | | Neural QP | 17.9 | Not recorded | 69c0c9030636e5bf4afc3b6f | | GNNQP | 17.9 | Not recorded | 69c0c9030636e5bf4afc3b6f | | HNN | 17.93 | Not recorded | 69c0c9030636e5bf4afc3b6f | | TriGNN | 18.26 | Not recorded | 69c0c9030636e5bf4afc3b6f | | TriGNN | 18.77 | Not recorded | 69c0c9030636e5bf4afc3b6f | | Neural QP | 19.44 | Not recorded | 69c0c9030636e5bf4afc3b6f | | Exact solver | 26.69 | Not recorded | 69c0c9030636e5bf4afc3b6f | | Exact solver | 27.61 | Not recorded | 69c0c9030636e5bf4afc3b6f | | GNNQP | 31.12 | Not recorded | 69c0c9030636e5bf4afc3b6f | | GNNQP | 38.09 | Not recorded | 69c0c9030636e5bf4afc3b6f | | GNNQP | 38.95 | Not recorded | 69c0c9030636e5bf4afc3b6f | | GNNQP | 39.05 | Not recorded | 69c0c9030636e5bf4afc3b6f | ### Neural QP Optimality Gap (%): 0.03. Result ID: 69c11eda47f34ce924a975a8. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"Mini","Base solver":"Gurobi"}. This record does not assert independent reproduction. ### GNNQP Optimality Gap (%): 0.03. Result ID: 69c11eda47f34ce924a975ae. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"Mini","Base solver":"Gurobi"}. This record does not assert independent reproduction. ### HNN Optimality Gap (%): 0.03. Result ID: 69c11eda47f34ce924a975ba. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"Mini","Base solver":"Gurobi"}. This record does not assert independent reproduction. ### HNN Optimality Gap (%): 0.03. Result ID: 69c11eda47f34ce924a975be. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"2k","Base solver":"Gurobi"}. This record does not assert independent reproduction. ### Neural QP Optimality Gap (%): 0.04. Result ID: 69c11eda47f34ce924a975aa. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"1k","Base solver":"Gurobi"}. This record does not assert independent reproduction. ### Neural QP Optimality Gap (%): 0.04. Result ID: 69c11eda47f34ce924a975ac. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"2k","Base solver":"Gurobi"}. This record does not assert independent reproduction. ### TriGNN Optimality Gap (%): 0.04. Result ID: 69c11eda47f34ce924a975b4. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"Mini","Base solver":"Gurobi"}. This record does not assert independent reproduction. ### TriGNN Optimality Gap (%): 0.04. Result ID: 69c11eda47f34ce924a975b6. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"1k","Base solver":"Gurobi"}. This record does not assert independent reproduction. ### TriGNN Optimality Gap (%): 0.04. Result ID: 69c11eda47f34ce924a975b8. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"2k","Base solver":"Gurobi"}. This record does not assert independent reproduction. ### HNN Optimality Gap (%): 0.04. Result ID: 69c11eda47f34ce924a975bc. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"1k","Base solver":"Gurobi"}. This record does not assert independent reproduction. ### HNN Optimality Gap (%): 16.79. Result ID: 69c11eda47f34ce924a975bd. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"1k","Base solver":"SCIP"}. This record does not assert independent reproduction. ### TriGNN Optimality Gap (%): 17.25. Result ID: 69c11eda47f34ce924a975b5. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"Mini","Base solver":"SCIP"}. This record does not assert independent reproduction. ### Neural QP Optimality Gap (%): 17.41. Result ID: 69c11eda47f34ce924a975ad. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"2k","Base solver":"SCIP"}. This record does not assert independent reproduction. ### HNN Optimality Gap (%): 17.45. Result ID: 69c11eda47f34ce924a975bf. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"2k","Base solver":"SCIP"}. This record does not assert independent reproduction. ### Neural QP Optimality Gap (%): 17.9. Result ID: 69c11eda47f34ce924a975a9. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"Mini","Base solver":"SCIP"}. This record does not assert independent reproduction. ### GNNQP Optimality Gap (%): 17.9. Result ID: 69c11eda47f34ce924a975af. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"Mini","Base solver":"SCIP"}. This record does not assert independent reproduction. ### HNN Optimality Gap (%): 17.93. Result ID: 69c11eda47f34ce924a975bb. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"Mini","Base solver":"SCIP"}. This record does not assert independent reproduction. ### TriGNN Optimality Gap (%): 18.26. Result ID: 69c11eda47f34ce924a975b9. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"2k","Base solver":"SCIP"}. This record does not assert independent reproduction. ### TriGNN Optimality Gap (%): 18.77. Result ID: 69c11eda47f34ce924a975b7. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"1k","Base solver":"SCIP"}. This record does not assert independent reproduction. ### Neural QP Optimality Gap (%): 19.44. Result ID: 69c11eda47f34ce924a975ab. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"1k","Base solver":"SCIP"}. This record does not assert independent reproduction. ### Exact solver Optimality Gap (%): 26.69. Result ID: 69c11eda47f34ce924a975a6. [Reporting paper]() Recorded evaluation configuration: {"Base solver":"Gurobi"}. This record does not assert independent reproduction. ### Exact solver Optimality Gap (%): 27.61. Result ID: 69c11eda47f34ce924a975a7. [Reporting paper]() Recorded evaluation configuration: {"Base solver":"SCIP"}. This record does not assert independent reproduction. ### GNNQP Optimality Gap (%): 31.12. Result ID: 69c11eda47f34ce924a975b3. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"2k","Base solver":"SCIP"}. This record does not assert independent reproduction. ### GNNQP Optimality Gap (%): 38.09. Result ID: 69c11eda47f34ce924a975b1. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"1k","Base solver":"SCIP"}. This record does not assert independent reproduction. ### GNNQP Optimality Gap (%): 38.95. Result ID: 69c11eda47f34ce924a975b0. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"1k","Base solver":"Gurobi"}. This record does not assert independent reproduction. ### GNNQP Optimality Gap (%): 39.05. Result ID: 69c11eda47f34ce924a975b2. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"2k","Base solver":"Gurobi"}. This record does not assert independent reproduction. Page 1 of 1. This is an index page, not the full collection.