# Quadratic Multiple Knapsack Problem on QMKP 1k Source: [Quadratic Multiple Knapsack Problem on QMKP 1k]() Collection index: [llms.txt]() Data updated: 2026-03-23T11:07:11.225Z Evaluation of algorithms solving the Quadratic Multiple Knapsack Problem using the QMKP 1k instance set, measured by optimality 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 1k | | Metric | Optimality Gap (%) | | Unit | PERCENT | | Direction | Lower is better | | Results loaded | 18 of 18 | | 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 | | --- | --- | --- | --- | | HNN | 0.16 | Not recorded | 69c0c9030636e5bf4afc3b6f | | HNN | 0.18 | Not recorded | 69c0c9030636e5bf4afc3b6f | | HNN | 0.31 | Not recorded | 69c0c9030636e5bf4afc3b6f | | HNN | 0.33 | Not recorded | 69c0c9030636e5bf4afc3b6f | | Neural QP | 0.35 | Not recorded | 69c0c9030636e5bf4afc3b6f | | Neural QP | 0.35 | Not recorded | 69c0c9030636e5bf4afc3b6f | | Exact solver | 0.38 | Not recorded | 69c0c9030636e5bf4afc3b6f | | Neural QP | 0.38 | Not recorded | 69c0c9030636e5bf4afc3b6f | | TriGNN | 0.43 | Not recorded | 69c0c9030636e5bf4afc3b6f | | GNNQP | 0.45 | Not recorded | 69c0c9030636e5bf4afc3b6f | | TriGNN | 0.46 | Not recorded | 69c0c9030636e5bf4afc3b6f | | TriGNN | 0.47 | Not recorded | 69c0c9030636e5bf4afc3b6f | | GNNQP | 0.49 | Not recorded | 69c0c9030636e5bf4afc3b6f | | GNNQP | 0.52 | Not recorded | 69c0c9030636e5bf4afc3b6f | | TriGNN | 0.52 | Not recorded | 69c0c9030636e5bf4afc3b6f | | Neural QP | 0.54 | Not recorded | 69c0c9030636e5bf4afc3b6f | | GNNQP | 0.54 | Not recorded | 69c0c9030636e5bf4afc3b6f | | Exact solver | 5.15 | Not recorded | 69c0c9030636e5bf4afc3b6f | ### HNN Optimality Gap (%): 0.16. Result ID: 69c11eda47f34ce924a9756e. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"Mini","Base solver":"Gurobi"}. This record does not assert independent reproduction. ### HNN Optimality Gap (%): 0.18. Result ID: 69c11eda47f34ce924a9756f. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"Mini","Base solver":"SCIP"}. This record does not assert independent reproduction. ### HNN Optimality Gap (%): 0.31. Result ID: 69c11eda47f34ce924a97570. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"1k","Base solver":"Gurobi"}. This record does not assert independent reproduction. ### HNN Optimality Gap (%): 0.33. Result ID: 69c11eda47f34ce924a97571. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"1k","Base solver":"SCIP"}. This record does not assert independent reproduction. ### Neural QP Optimality Gap (%): 0.35. Result ID: 69c11eda47f34ce924a97562. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"Mini","Base solver":"Gurobi"}. This record does not assert independent reproduction. ### Neural QP Optimality Gap (%): 0.35. Result ID: 69c11eda47f34ce924a97564. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"1k","Base solver":"Gurobi"}. This record does not assert independent reproduction. ### Exact solver Optimality Gap (%): 0.38. Result ID: 69c11eda47f34ce924a97560. [Reporting paper]() Recorded evaluation configuration: {"Base solver":"Gurobi"}. This record does not assert independent reproduction. ### Neural QP Optimality Gap (%): 0.38. Result ID: 69c11eda47f34ce924a97565. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"1k","Base solver":"SCIP"}. This record does not assert independent reproduction. ### TriGNN Optimality Gap (%): 0.43. Result ID: 69c11eda47f34ce924a9756a. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"Mini","Base solver":"Gurobi"}. This record does not assert independent reproduction. ### GNNQP Optimality Gap (%): 0.45. Result ID: 69c11eda47f34ce924a97566. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"Mini","Base solver":"Gurobi"}. This record does not assert independent reproduction. ### TriGNN Optimality Gap (%): 0.46. Result ID: 69c11eda47f34ce924a9756c. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"1k","Base solver":"Gurobi"}. This record does not assert independent reproduction. ### TriGNN Optimality Gap (%): 0.47. Result ID: 69c11eda47f34ce924a9756d. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"1k","Base solver":"SCIP"}. This record does not assert independent reproduction. ### GNNQP Optimality Gap (%): 0.49. Result ID: 69c11eda47f34ce924a97568. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"1k","Base solver":"Gurobi"}. This record does not assert independent reproduction. ### GNNQP Optimality Gap (%): 0.52. Result ID: 69c11eda47f34ce924a97569. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"1k","Base solver":"SCIP"}. This record does not assert independent reproduction. ### TriGNN Optimality Gap (%): 0.52. Result ID: 69c11eda47f34ce924a9756b. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"Mini","Base solver":"SCIP"}. This record does not assert independent reproduction. ### Neural QP Optimality Gap (%): 0.54. Result ID: 69c11eda47f34ce924a97563. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"Mini","Base solver":"SCIP"}. This record does not assert independent reproduction. ### GNNQP Optimality Gap (%): 0.54. Result ID: 69c11eda47f34ce924a97567. [Reporting paper]() [Method origin paper]() Recorded evaluation configuration: {"Train":"Mini","Base solver":"SCIP"}. This record does not assert independent reproduction. ### Exact solver Optimality Gap (%): 5.15. Result ID: 69c11eda47f34ce924a97561. [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.