Difference between revisions of "MIPDECO"

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| [[Media:MeshDep-008-1.dat|MeshDep-008-1.dat]]
 
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| [[Media:MeshDep-008-2.dat|MeshDep-008-2.dat]]
 
| [[Media:MeshDep-008-2.dat|MeshDep-008-2.dat]]
 
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|+ align="bottom" | MIPDECOlib: Parabolic Robin Boundary Problem in One Spatial Dimension
 
|+ align="bottom" | MIPDECOlib: Parabolic Robin Boundary Problem in One Spatial Dimension

Revision as of 16:22, 20 March 2017

Mixed-Integer PDE Constrained Optimization (MIPDECO) Test Problems

This page links to sets of MIPDECO test problems written in AMPL and described in a companion report.

Each problem includes a characterization in terms of type of PDE, class of integers, type of objective, type of constraints, and discretization scheme.

A tar-ball with all ampl models, data, and command files is available here. A tar-ball with the corresponding stub.nl files is available here.

Laplace Source Inversion

Problem is to identify source to match an observed state, governed by Laplace equation with Dirichtlet boundary conditions.

Type of PDE Laplace equation on [0,1]^2 with Dirichlet boundary conditions
Class of Integers Mesh-dependent & mesh-independent binary variables
Type of Objective Least-squares (inverse problem) with possible regularization term
Type of Constraints Knapsack constraint on binary variables
Discretization Five-point finite difference stencil


NAME mod file dat file mesh optimal objective
SrcDetct-MeshDep-008-1 SrcDetct.mod MeshDep-008-1.dat 8x8 0.0022
SrcDetct-MeshDep-008-2 SrcDetct.mod MeshDep-008-2.dat 8x8 0.0001
SrcDetct-MeshDep-008-3 SrcDetct.mod MeshDep-008-3.dat 8x8 0.0001
SrcDetct-MeshDep-016-1 SrcDetct.mod MeshDep-016-1.dat 16x16 0.0076
SrcDetct-MeshDep-016-2 SrcDetct.mod MeshDep-016-2.dat 16x16 0.0000
SrcDetct-MeshDep-016-3 SrcDetct.mod MeshDep-016-3.dat 16x16 0.5675
SrcDetct-MeshDep-032-1 SrcDetct.mod MeshDep-032-1.dat 32x32 0.0298
SrcDetct-MeshDep-032-2 SrcDetct.mod MeshDep-032-2.dat 32x32 0.0000
SrcDetct-MeshDep-032-3 SrcDetct.mod MeshDep-032-3.dat 32x32 2.2180
SrcDetct-MeshInd-008-1 SrcDetct.mod MeshInd-008-1.dat 8x8 0.0002
SrcDetct-MeshInd-008-2 SrcDetct.mod MeshInd-008-2.dat 8x8 0.0001
SrcDetct-MeshInd-008-3 SrcDetct.mod MeshInd-008-3.dat 8x8 0.0001
SrcDetct-MeshInd-016-1 SrcDetct.mod MeshInd-016-1.dat 16x16 0.0006
SrcDetct-MeshInd-016-2 SrcDetct.mod MeshInd-016-2.dat 16x16 0.0004
SrcDetct-MeshInd-016-3 SrcDetct.mod MeshInd-016-3.dat 16x16 0.3271
SrcDetct-MeshInd-032-1 SrcDetct.mod MeshInd-032-1.dat 32x32 0.0023
SrcDetct-MeshInd-032-2 SrcDetct.mod MeshInd-032-2.dat 32x32 0.0015
SrcDetct-MeshInd-032-3 SrcDetct.mod MeshInd-032-3.dat 32x32 1.3068
MIPDECOlib: Parabolic Robin Boundary Problem in One Spatial Dimension


In this problem, the state variables, u, can be eliminated, resulting in a pure integer QP. The model that defines the problems without state variables is SrcDetctElim.mod, and the AMPL script, Presolve.ampl implements the presolve step. The calling sequence is

ampl: model SrcDetctElim.mod; data MeshDep-008-1.dat; include Presolve.ampl;

for the small example, SrcDetct-MeshDep-008-1.

Distributed Control with Neumann Boundary Conditions

Parabolic Robin Boundary Problem in One Spatial Dimension

This model is modified from OPTPDE library (http://www.optpde.uni-hamburg.de/result.php?id=8). The goal is to find the optimal state and control variables that satisfy the Heat equation with boundary conditions. There are two classes of models: one with binary controls, and one with controls in {-1,0,1}. Both L1 and L2 regularizations are used.

Type of PDE Heat equation on [0,1]x[0,1.58] with Robin and Neuman boundary conditions
Class of Integers Mesh-dependent & mesh-independent binary variables
Type of Objective Least-squares (inverse problem) with L1 or L2 regularization term
Type of Constraints Binary or integer controls
Discretization Crank-Nicolson formula


NAME mod file dat file mesh optimal objective
RobinBin-08 RobinBin.mod m08.dat 8x8 0.0305
RobinBin-16 RobinBin.mod m16.dat 16x16 0.0190
RobinBin-32 RobinBin.mod m32.dat 32x32 0.0145
RobinBinL1-08 RobinBinL1.mod m08.dat 8x8 0.0305
RobinBinL1-16 RobinBinL1.mod m16.dat 16x16 0.0190
RobinBinL1-32 RobinBinL1.mod m32.dat 32x32 0.0145
RobinInt-08 RobinInt.mod m08.dat 8x8 0.0305
RobinInt-16 RobinInt.mod m16.dat 16x16 0.0190
RobinInt-32 RobinInt.mod m32.dat 32x32 0.0145
RobinIntL1-08 RobinIntL1.mod m08.dat 8x8 0.0305
RobinIntL1-16 RobinIntL1.mod m16.dat 16x16 0.0190
RobinIntL1-32 RobinIntL1.mod m32.dat 32x32 0.0145
MIPDECOlib: Parabolic Robin Boundary Problem in One Spatial Dimension

Parabolic Robin Boundary Problem in Two Spatial Dimensions

Heat Equation Actuator-Placement

Subsurface Flow Well-Placement

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