Solving mixed integer programming problems using automatic reformulation
Operations Research
Journal of Optimization Theory and Applications
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Links between linear bilevel and mixed 0-1 programming problems
Journal of Optimization Theory and Applications
On the choice of explicit stabilizing terms in column generation
Discrete Applied Mathematics
0-1 reformulations of the multicommodity capacitated network design problem
Discrete Applied Mathematics
SDP diagonalizations and perspective cuts for a class of nonseparable MIQP
Operations Research Letters
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Reformulation is one of the most useful and widespread activities in mathematical modeling, in that finding a “good” formulation is a fundamental step in being able so solve a given problem. Currently, this is almost exclusively a human activity, with next to no support from modeling and solution tools. In this paper we show how the reformulation system defined in [13] allows to automatize the task of exploring the formulation space of a problem, using a specific example (the Hyperplane Clustering Problem). This nonlinear problem admits a large number of both linear and nonlinear formulations, which can all be generated by defining a relatively small set of general Atomic Reformulation Rules (ARR). These rules are not problem-specific, and could be used to reformulate many other problems, thus showing that a general-purpose reformulation system based on the ideas developed in [13] could be feasible.