Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:   consider a multicommodity network flow problem with flow routing and discrete capacity expansion decisions. The problem involves trading off congestion and capacity assignment (or expansion) costs. In particular,  consider congestion costs involving convex, increasing por functions of flows on the arcs.  first observe that under certain conditions the congestion cost can be formulated as a convex function of the capacity level and the flow. Then,  show that the problem can be efficiently formulated by using conic quadratic inequalities. As most of the research on this problem is devoted to heuristic approaches, this study differs in showing that the problem can be solved to optimum by branch-and-bound solvers implementing the second-order cone programming (SOCP) algorithms. Computational experiments on the test problems from the literature show that the continuous relaxation of the formulation gives a tight lor bound and leads to optimal or near optimal integer solutions within reasonable CPU times.
['Sinan Gürel']
I am writing a research paper on a idea A conic quadratic formulation for a class of convex congestion functions in network flow problems
[{"from": "human", "value": "I am writing a research paper on a idea A conic quadratic formulation for a class of convex congestion functions in network flow problems"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:   consider a multicommodity network flow problem with flow routing and discrete capacity expansion decisions. The problem involves trading off congestion and capacity assignment (or expansion) costs. In particular,  consider congestion costs involving convex, increasing por functions of flows on the arcs.  first observe that under certain conditions the congestion cost can be formulated as a convex function of the capacity level and the flow. Then,  show that the problem can be efficiently formulated by using conic quadratic inequalities. As most of the research on this problem is devoted to heuristic approaches, this study differs in showing that the problem can be solved to optimum by branch-and-bound solvers implementing the second-order cone programming (SOCP) algorithms. Computational experiments on the test problems from the literature show that the continuous relaxation of the formulation gives a tight lor bound and leads to optimal or near optimal integer solutions within reasonable CPU times."}]