Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Given a matrix of ights, the linear ordering problem (LOP) consists of finding a permutation of the columns and rows in order to maximize the sum of the ights in the upper triangle. This NP-complete problem can also be formulated in terms of graphs, as finding an acyclic tournament with a maximal sum of arc ights in a complete ighted graph. ,  first review the previous methods for the LOP and then propose a heuristic algorithm based on the variable neighborhood search (VNS) methodology. The method combines different neighborhoods for an efficient exploration of the search space.  explore different search strategies and propose a hybrid method in which the VNS is coupled with a short-term tabu search for improved outcomes. Our extensive experimentation with both real and random instances shows that the proposed procedure competes with the best-known algorithms in terms of solution quality, and has reasonable computing-time requirements.Variable neighborhood search (VNS) is a metaheuristic method that has recently been shown to yield promising outcomes for solving combinatorial optimization problems. Based on a systematic change of neighborhood in a local search procedure, VNS uses both deterministic and random strategies in search for the global optimum.,  present a VNS implementation designed to find high quality solutions for the NP-hard LOP, which has a significant number of applications in practice. The LOP, for example, is equivalent to the so-called triangulation problem for input-output tables in economics. Our implementation incorporates innovative mechanisms to include memory structures within the VNS methodology. Moreover  study the hybridization with other methodologies such as tabu search.
['Carlos G. Garcia', 'Dionisio Pérez-Brito', 'Vicente Campos', 'Rafael Martí']
I am writing a research paper on a idea Variable neighborhood search for the linear ordering problem
[{"from": "human", "value": "I am writing a research paper on a idea Variable neighborhood search for the linear ordering problem"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Given a matrix of ights, the linear ordering problem (LOP) consists of finding a permutation of the columns and rows in order to maximize the sum of the ights in the upper triangle. This NP-complete problem can also be formulated in terms of graphs, as finding an acyclic tournament with a maximal sum of arc ights in a complete ighted graph. ,  first review the previous methods for the LOP and then propose a heuristic algorithm based on the variable neighborhood search (VNS) methodology. The method combines different neighborhoods for an efficient exploration of the search space.  explore different search strategies and propose a hybrid method in which the VNS is coupled with a short-term tabu search for improved outcomes. Our extensive experimentation with both real and random instances shows that the proposed procedure competes with the best-known algorithms in terms of solution quality, and has reasonable computing-time requirements.Variable neighborhood search (VNS) is a metaheuristic method that has recently been shown to yield promising outcomes for solving combinatorial optimization problems. Based on a systematic change of neighborhood in a local search procedure, VNS uses both deterministic and random strategies in search for the global optimum.,  present a VNS implementation designed to find high quality solutions for the NP-hard LOP, which has a significant number of applications in practice. The LOP, for example, is equivalent to the so-called triangulation problem for input-output tables in economics. Our implementation incorporates innovative mechanisms to include memory structures within the VNS methodology. Moreover  study the hybridization with other methodologies such as tabu search."}]