ReLU networks as surrogate models in mixed-integer linear programs
We consider the embedding of piecewise-linear deep neural networks (ReLU networks) as surrogate models in mixed-integer linear programming (MILP) problems. A MILP formulation of ReLU networks has recently been applied by many authors to probe for various model properties subject to input bounds. The...
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| Published in | Computers & chemical engineering Vol. 131; p. 106580 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
05.12.2019
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| Abstract | We consider the embedding of piecewise-linear deep neural networks (ReLU networks) as surrogate models in mixed-integer linear programming (MILP) problems. A MILP formulation of ReLU networks has recently been applied by many authors to probe for various model properties subject to input bounds. The formulation is obtained by programming each ReLU operator with a binary variable and applying the big-M method. The efficiency of the formulation hinges on the tightness of the bounds defined by the big-M values. When ReLU networks are embedded in a larger optimization problem, the presence of output bounds can be exploited in bound tightening. To this end, we devise and study several bound tightening procedures that consider both input and output bounds. Our numerical results show that bound tightening may reduce solution times considerably, and that small-sized ReLU networks are suitable as surrogate models in mixed-integer linear programs. |
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| AbstractList | We consider the embedding of piecewise-linear deep neural networks (ReLU networks) as surrogate models in mixed-integer linear programming (MILP) problems. A MILP formulation of ReLU networks has recently been applied by many authors to probe for various model properties subject to input bounds. The formulation is obtained by programming each ReLU operator with a binary variable and applying the big-M method. The efficiency of the formulation hinges on the tightness of the bounds defined by the big-M values. When ReLU networks are embedded in a larger optimization problem, the presence of output bounds can be exploited in bound tightening. To this end, we devise and study several bound tightening procedures that consider both input and output bounds. Our numerical results show that bound tightening may reduce solution times considerably, and that small-sized ReLU networks are suitable as surrogate models in mixed-integer linear programs. |
| ArticleNumber | 106580 |
| Author | Grimstad, Bjarne Andersson, Henrik |
| Author_xml | – sequence: 1 givenname: Bjarne surname: Grimstad fullname: Grimstad, Bjarne email: bjarne.grimstad@gmail.com organization: Solution Seeker AS, Gaustadalléen 21, Oslo 0349, Norway – sequence: 2 givenname: Henrik surname: Andersson fullname: Andersson, Henrik organization: Department of Industrial Economics and Technology Management, Norwegian University of Science and Technology,Trondheim NO-7491, Norway |
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| Keywords | Mixed-Integer linear programming Regression Deep neural networks ReLU networks Surrogate modeling |
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