# Quadratic Multiple Knapsack Problem on QMKP 5k Source: [Quadratic Multiple Knapsack Problem on QMKP 5k]() Collection index: [llms.txt]() Data updated: 2026-03-23T11:07:11.283Z Evaluation of algorithms solving the Quadratic Multiple Knapsack Problem using the QMKP 5k instance set, measured by gap percentage. 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 5k | | Metric | 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 - [Gap %](): Lower is better; unit: PERCENT. ## Recorded results | Method | Gap % | Result date | Report paper | | --- | --- | --- | --- | | Neural QP | 0.03 | Not recorded | 69c0c9030636e5bf4afc3b6f | | TriGNN | 0.03 | Not recorded | 69c0c9030636e5bf4afc3b6f | | TriGNN | 0.03 | Not recorded | 69c0c9030636e5bf4afc3b6f | | HNN | 0.03 | Not recorded | 69c0c9030636e5bf4afc3b6f | | Neural QP | 0.04 | Not recorded | 69c0c9030636e5bf4afc3b6f | | TriGNN | 0.04 | Not recorded | 69c0c9030636e5bf4afc3b6f | | Neural QP | 0.05 | Not recorded | 69c0c9030636e5bf4afc3b6f | | GNNQP | 0.05 | Not recorded | 69c0c9030636e5bf4afc3b6f | | GNNQP | 0.05 | Not recorded | 69c0c9030636e5bf4afc3b6f | | HNN | 0.05 | Not recorded | 69c0c9030636e5bf4afc3b6f | | HNN | 0.05 | Not recorded | 69c0c9030636e5bf4afc3b6f | | GNNQP | 0.06 | Not recorded | 69c0c9030636e5bf4afc3b6f | | TriGNN | 28.63 | Not recorded | 69c0c9030636e5bf4afc3b6f | | TriGNN | 28.66 | Not recorded | 69c0c9030636e5bf4afc3b6f | | HNN | 28.67 | Not recorded | 69c0c9030636e5bf4afc3b6f | | Neural QP | 28.68 | Not recorded | 69c0c9030636e5bf4afc3b6f | | TriGNN | 28.7 | Not recorded | 69c0c9030636e5bf4afc3b6f | | Exact solver | 29.08 | Not recorded | 69c0c9030636e5bf4afc3b6f | | HNN | 29.33 | Not recorded | 69c0c9030636e5bf4afc3b6f | | Neural QP | 29.38 | Not recorded | 69c0c9030636e5bf4afc3b6f | | GNNQP | 29.38 | Not recorded | 69c0c9030636e5bf4afc3b6f | | HNN | 29.41 | Not recorded | 69c0c9030636e5bf4afc3b6f | | GNNQP | 29.48 | Not recorded | 69c0c9030636e5bf4afc3b6f | | GNNQP | 29.53 | Not recorded | 69c0c9030636e5bf4afc3b6f | | Neural QP | 29.54 | Not recorded | 69c0c9030636e5bf4afc3b6f | | Exact solver | 35.73 | Not recorded | 69c0c9030636e5bf4afc3b6f | ### Neural QP Gap %: 0.03. Result ID: 69c11eda47f34ce924a9758e. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"Mini","Base solver":"Gurobi"}. This record does not assert independent reproduction. ### TriGNN Gap %: 0.03. Result ID: 69c11eda47f34ce924a9759c. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"1k","Base solver":"Gurobi"}. This record does not assert independent reproduction. ### TriGNN Gap %: 0.03. Result ID: 69c11eda47f34ce924a9759e. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"2k","Base solver":"Gurobi"}. This record does not assert independent reproduction. ### HNN Gap %: 0.03. Result ID: 69c11eda47f34ce924a975a0. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"Mini","Base solver":"Gurobi"}. This record does not assert independent reproduction. ### Neural QP Gap %: 0.04. Result ID: 69c11eda47f34ce924a97590. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"1k","Base solver":"Gurobi"}. This record does not assert independent reproduction. ### TriGNN Gap %: 0.04. Result ID: 69c11eda47f34ce924a9759a. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"Mini","Base solver":"Gurobi"}. This record does not assert independent reproduction. ### Neural QP Gap %: 0.05. Result ID: 69c11eda47f34ce924a97592. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"2k","Base solver":"Gurobi"}. This record does not assert independent reproduction. ### GNNQP Gap %: 0.05. Result ID: 69c11eda47f34ce924a97594. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"Mini","Base solver":"Gurobi"}. This record does not assert independent reproduction. ### GNNQP Gap %: 0.05. Result ID: 69c11eda47f34ce924a97598. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"2k","Base solver":"Gurobi"}. This record does not assert independent reproduction. ### HNN Gap %: 0.05. Result ID: 69c11eda47f34ce924a975a2. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"1k","Base solver":"Gurobi"}. This record does not assert independent reproduction. ### HNN Gap %: 0.05. Result ID: 69c11eda47f34ce924a975a4. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"2k","Base solver":"Gurobi"}. This record does not assert independent reproduction. ### GNNQP Gap %: 0.06. Result ID: 69c11eda47f34ce924a97596. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"1k","Base solver":"Gurobi"}. This record does not assert independent reproduction. ### TriGNN Gap %: 28.63. Result ID: 69c11eda47f34ce924a9759d. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"1k","Base solver":"SCIP"}. This record does not assert independent reproduction. ### TriGNN Gap %: 28.66. Result ID: 69c11eda47f34ce924a9759f. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"2k","Base solver":"SCIP"}. This record does not assert independent reproduction. ### HNN Gap %: 28.67. Result ID: 69c11eda47f34ce924a975a1. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"Mini","Base solver":"SCIP"}. This record does not assert independent reproduction. ### Neural QP Gap %: 28.68. Result ID: 69c11eda47f34ce924a97591. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"1k","Base solver":"SCIP"}. This record does not assert independent reproduction. ### TriGNN Gap %: 28.7. Result ID: 69c11eda47f34ce924a9759b. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"Mini","Base solver":"SCIP"}. This record does not assert independent reproduction. ### Exact solver Gap %: 29.08. Result ID: 69c11eda47f34ce924a9758c. [Reporting paper]() Recorded evaluation configuration: {"Base solver":"Gurobi"}. This record does not assert independent reproduction. ### HNN Gap %: 29.33. Result ID: 69c11eda47f34ce924a975a3. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"1k","Base solver":"SCIP"}. This record does not assert independent reproduction. ### Neural QP Gap %: 29.38. Result ID: 69c11eda47f34ce924a9758f. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"Mini","Base solver":"SCIP"}. This record does not assert independent reproduction. ### GNNQP Gap %: 29.38. Result ID: 69c11eda47f34ce924a97595. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"Mini","Base solver":"SCIP"}. This record does not assert independent reproduction. ### HNN Gap %: 29.41. Result ID: 69c11eda47f34ce924a975a5. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"2k","Base solver":"SCIP"}. This record does not assert independent reproduction. ### GNNQP Gap %: 29.48. Result ID: 69c11eda47f34ce924a97597. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"1k","Base solver":"SCIP"}. This record does not assert independent reproduction. ### GNNQP Gap %: 29.53. Result ID: 69c11eda47f34ce924a97599. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"2k","Base solver":"SCIP"}. This record does not assert independent reproduction. ### Neural QP Gap %: 29.54. Result ID: 69c11eda47f34ce924a97593. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"2k","Base solver":"SCIP"}. This record does not assert independent reproduction. ### Exact solver Gap %: 35.73. Result ID: 69c11eda47f34ce924a9758d. [Reporting paper]() Recorded evaluation configuration: {"Base solver":"SCIP"}. This record does not assert independent reproduction. Page 1 of 1. This is an index page, not the full collection.