Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The quadratic knapsack problem (QKP) is a ll-known combinatorial optimization problem with numerous applications. Given its NP-hard nature, finding optimal solutions or even high quality suboptimal solutions to QKP in the general case is a highly challenging task. ,  propose an iterated "hyperplane exploration" approach (IHEA) to solve QKP approximately. Instead of considering the whole solution space, the proposed approach adopts the idea of searching over a set of hyperplanes defined by a cardinality constraint to delimit the search to promising areas of the solution space. To explore these hyperplanes efficiently, IHEA employs a variable fixing strategy to reduce each hyperplane-constrained sub-problem and then applies a dedicated tabu search procedure to locate high quality solutions within the reduced solution space. Extensive experimental studies over three sets of 220 QKP instances indicate that IHEA competes very favorably with the state-of-the-art algorithms both in terms of solution quality and computing efficiency.  provide additional information to gain insight into the key components of the proposed approach. HighlightsThe quadratic knapsack problem (QKP) is a ll-known optimization problem.A hyperplane constraint is introduced to obtain a reduced model of the original problem.A variable fixing strategy is employed to further reduce the search space.A dedicated tabu search procedure explores the hyperplane constrained subproblem.Computational results and comparisons are shown on three sets of 220 benchmark instances.
['Yuning Chen', 'Jin-Kao Hao']
I am writing a research paper on a idea An iterated hyperplane exploration approach for the quadratic knapsack problem
[{"from": "human", "value": "I am writing a research paper on a idea An iterated hyperplane exploration approach for the quadratic knapsack problem"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The quadratic knapsack problem (QKP) is a ll-known combinatorial optimization problem with numerous applications. Given its NP-hard nature, finding optimal solutions or even high quality suboptimal solutions to QKP in the general case is a highly challenging task. ,  propose an iterated \"hyperplane exploration\" approach (IHEA) to solve QKP approximately. Instead of considering the whole solution space, the proposed approach adopts the idea of searching over a set of hyperplanes defined by a cardinality constraint to delimit the search to promising areas of the solution space. To explore these hyperplanes efficiently, IHEA employs a variable fixing strategy to reduce each hyperplane-constrained sub-problem and then applies a dedicated tabu search procedure to locate high quality solutions within the reduced solution space. Extensive experimental studies over three sets of 220 QKP instances indicate that IHEA competes very favorably with the state-of-the-art algorithms both in terms of solution quality and computing efficiency.  provide additional information to gain insight into the key components of the proposed approach. HighlightsThe quadratic knapsack problem (QKP) is a ll-known optimization problem.A hyperplane constraint is introduced to obtain a reduced model of the original problem.A variable fixing strategy is employed to further reduce the search space.A dedicated tabu search procedure explores the hyperplane constrained subproblem.Computational results and comparisons are shown on three sets of 220 benchmark instances."}]