MIPDECO

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

MIPDECOlib: Parabolic Robin Boundary Problem in One Spatial Dimension

NAME	mod file	dat file	mesh	optimal objective
SrcDetct-MeshDep-008-1	SrcDetct.mod	MeshDep-008-1.dat	8x8	???
SrcDetct-MeshDep-008-2	SrcDetct.mod	MeshDep-008-2.dat	8x8	???
SrcDetct-MeshDep-008-3	SrcDetct.mod	MeshDep-008-3.dat	8x8	???
SrcDetct-MeshDep-016-1	SrcDetct.mod	MeshDep-016-1.dat	16x16	???
SrcDetct-MeshDep-016-2	SrcDetct.mod	MeshDep-016-2.dat	16x16	???
SrcDetct-MeshDep-016-3	SrcDetct.mod	MeshDep-016-3.dat	16x16	???
SrcDetct-MeshDep-032-1	SrcDetct.mod	MeshDep-032-1.dat	32x32	???
SrcDetct-MeshDep-032-2	SrcDetct.mod	MeshDep-032-2.dat	32x32	???
SrcDetct-MeshDep-032-3	SrcDetct.mod	MeshDep-032-3.dat	32x32	???
SrcDetct-MeshInd-008-1	SrcDetct.mod	MeshInd-008-1.dat	8x8	???
SrcDetct-MeshInd-008-2	SrcDetct.mod	MeshInd-008-2.dat	8x8	???
SrcDetct-MeshInd-008-3	SrcDetct.mod	MeshInd-008-3.dat	8x8	???
SrcDetct-MeshInd-016-1	SrcDetct.mod	MeshInd-016-1.dat	16x16	???
SrcDetct-MeshInd-016-2	SrcDetct.mod	MeshInd-016-2.dat	16x16	???
SrcDetct-MeshInd-016-3	SrcDetct.mod	MeshInd-016-3.dat	16x16	???
SrcDetct-MeshInd-032-1	SrcDetct.mod	MeshInd-032-1.dat	32x32	???
SrcDetct-MeshInd-032-2	SrcDetct.mod	MeshInd-032-2.dat	32x32	???
SrcDetct-MeshInd-032-3	SrcDetct.mod	MeshInd-032-3.dat	32x32	???

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.

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

MIPDECOlib: Parabolic Robin Boundary Problem in One Spatial Dimension

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