MIPNLP stoaMINLP
This page is part of the MIPNLP Manual. See MIPNLP Manual. |
Purpose
stoaMINLP solves convex mixed-integer nonlinear programming problems (MINLP).
stoaMINLP solves problems of the form
where , , and
. The variables , the
index subset of are restricted to be integers.
Calling Syntax
Recommended is to first set IterPrint, to get information each iteration
Prob.optParam.IterPrint = 1;
Driver call, including printing with level 2:
Result = tomRun('stoaMINLP',Prob,2);
Direct solver call:
Result = stoaMINLP(Prob);
PrintResult(Result);
Result = tomRun('stoaMINLP',Prob,...)
Warm Start
To make a restart (warm start), just set the warm start flag, and call stoaMINLP once again:
Prob.WarmStart = 1;
Result = tomRun('stoaMINLP', Prob, 2);
stoaMINLP will read warm start information from the stoaMINLPSave.mat file. Another warm start (with same MaxFunc) is made by just calling tomRun again:
Result = tomRun('stoaMINLP', Prob, 2);
To make a restart from the warm start information in the Result structure, make a call to WarmDefGLOBAL before calling stoaMINLP. WarmDefGLOBAL moves information from the Result structure to the Prob structure and sets the warm start flag, Prob.WarmStart = 1;
Prob = WarmDefGLOBAL('stoaMINLP', Prob, Result);
where Result is the result structure returned by the previous run. A warm start (with same MaxIter) is done by just calling tomRun again:
Result = tomRun('stoaMINLP', Prob, 2);
To make another warm start with new MaxIter 100, say, redefine MaxIter as:
Prob.optParam.MaxIter = 100;
Then repeat the two lines:
Prob = WarmDefGLOBAL('stoaMINLP', Prob, Result);
Result = tomRun('stoaMINLP', Prob, 2);
Inputs
Prob structure
The TOMLAB problem structure
The following fields are used in Prob: | |
---|---|
Field | Description |
x_L | Lower bounds on x. |
x_U | Upper bounds on x. |
A | The linear constraint matrix. |
b_L | Lower bounds on linear constraints. |
b_U | Upper bounds on linear constraints. |
c_L | Lower bounds on nonlinear constraints. |
c_U | Upper bounds on nonlinear constraints. |
x_0 | Starting point. |
Convex | If Convex==1, assume NLP problems are convex, and only one local NLP solver call is used at each node. If Convex==0 (Default), multiMin is used to do many calls to a local solver to determine the global minima at each node. The global minimum with most components integer valued is chosen. |
MaxCPU | Maximal CPU Time (in seconds) to be used by stoaMINLP, stops with best point found |
PriLev | Print level in stoaMINLP (default 1). Also see optParam.IterPrint |
PriLevOpt | Print level in sub-solvers (SNOPT and other NLP solvers): =0 No output; >0 Convergence results. >1 Output every iteration, >2 Output each step in the NLP alg For other NLP solvers, see the documentation for the solver |
WarmStart | If true, >0, stoaMINLP reads the output from the last run from Prob.stoaMINLP, if it exists. If it doesn't exist, stoaMINLP attempts to open and read warm start data from mat-file stoaMINLPSave.mat. stoaMINLP uses the warm start information to continue from the last run. The mat-file minlp- SolveSave.mat is saved every Prob.MIP.SaveFreq iteration. |
SolverNLP | Name of the solver used for NLP subproblems. If empty, the default solver is found calling GetSolver('con',1); If TOMLAB /SOL installed, SNOPT is the default solver. If SolverNLP is a SOL solver (SNOPT, MINOS or NPSOL), the SOL.optPar and SOL.PrintFile is used: See help minosTL.m, npsolTL.m or snoptTL.m for how to set these parameters |
SolverNLP0 | Name of the solver used for the initial NLP-problem. If empty, SolverNLP is used. |
SolverLP | Name of the solver used for LP subproblems. If empty, the default solver is found calling GetSolver('lp',1). If TOMLAB /SOL or /SNOPT or /NPSOL installed, MINOS is the default solver. If SolverLP is a SOL solver (MINOS, SNOPT or NPSOL), the SOL.optPar and SOL.PrintFile is used: See help minosTL.m, npsolTL.m or snoptTL.m for how to set these parameters. |
RandState | See help rngset for how to initialize the random generator. Default is RandState = -1 If Convex == 0 and globalSolver == 'multiMin', RandState is sent to multiMin to initizalize the random generator. |
xInit | Parameter sent to the solver multiMin which is used to solve relaxed sub-problems for nonconvex problems (with Prob.Convex set to false). xInit determines the way initial points are generated and is set as follows:
|
xInit0 | Parameter sent to the solver multiMin when solving the initial relaxed NLP problem at the root node. Default value for xInit0 is min(3000,max(100,N*10)) |
MIP | Structure defining integer optimization parameters. See the table below for a description of each field used in Prob.MIP. |
STOAMINLP | Structure with solver-specific options. See the table below with descriptions of the fields used in Prob.STOAMINLP. |
optParam | Structure with general optimization parameters. See the table below with descriptions of the fields used in Prob.optParam. |
MIP structure
Substructure in Prob with parameters related to mixed integer programming.
fields used in Prob.MIP | |
---|---|
Field | Description |
IntVars | If empty, all variables are assumed non-integer. If islogical(IntVars) (=all elements are 0/1), then 1 = integer variable, 0 = continuous variable. If any element >1, IntVars is the indices for integer variables. |
VarWeight | Weight for each variable in the variable selection phase. A lower value gives higher priority. Setting Prob.MIP.VarWeight might improve convergence. VarWeight must be of length N, but the values corresponding to noninteger variables will be ignored. |
DualGap | stoaMINLP stops if the duality gap is less than DualGap. DualGap = 1, stop at first integer solution e.g. DualGap = 0.01, stop if solution < 1% from optimal solution. Note that a finite lower bound will only be set by the solver and thus generating a gap when Prob.Convex is set to true. If Prob.Convex is set to false, the lower bound will be -Inf. |
fIP | An upper bound on the IP value wanted. Makes it possible to cut branches and avoid node computations. Used even if xIP not given. |
xIP | The x-values giving the fIP value, if a solution (xIP,fIP) is known. |
NodeSel | Node selection method: = 1 Depth First. Priority on nodes with more integer components. Default = 2 Breadth First. Priority on nodes with more integer components. = 3 Pure LIFO (Last in, first out) Depth First. = 4 Pure FIFO (First in, first out) Breadth First. = 5 Maximize integer components. = 6 Best bound. = 7 Best estimate using pseudo-costs. = 8 Best projection. |
Backtrack | Switch node selection method during branch and bound. When set to any of the NodeSel methods, node selection method is changed to the Backtrack value when the backtracking criterion (see parameter BackCrit below) is fulfilled. |
BackCrit | Backtracking criterion, used when Backtrack > 0. = 0. Integer solution found. Default. |
VarSel | Variable selection method in branch and bound. = 1 Use variable with most fractional value. = 2 Use gradient and distance to nearest integer value. = 3 Pseudo-cost-based branching. |
KNAPSACK | If = 1, use a knapsack heuristic. Default 0. |
ROUNDH | If = 1, use a rounding heuristic. Default 0. |
SaveFreq | Warm start info saved on stoaMINLPSave.mat every SaveFreq iteration (default -1, i.e. no warm start info is saved) |
STOAMINLP structure
Substructure in Prob with solver-specific options
fields used in Prob.STOAMINLP | |
---|---|
Field | Description |
USE_CUTS | Flag to use cutting plane algorithm described in StoaMINLP#Algorithm. Using cuts is not recommended for nonconvex problems. Set nonzero to enable, zero to disable. By default, STOAMINLP.USE_CUTS is set to Prob.Convex. |
LoL_ecp | Parameter regulating likelihood of linearization using extended cutting plane. See StoaMINLP#Algorithm for more information. Default 10. |
TOD_ecp | Parameter regulating "tailing off" detection for extended cutting plane linearizations. See StoaMINLP#Algorithm for more information. Default 0.001. |
BCB_ecp | Parameter regulating the balance between branching the search tree and adding linearizations using extended cutting plane. See StoaMINLP#Algorithm for more information. Default 10. |
LoL_ff | Parameter regulating likelihood of linearization using fixed fractional integer decision variables. See StoaMINLP#Algorithm for more information. Default 10. |
TOD_ff | Parameter regulating "tailing off" detection for linearizations using fixed fractional integer decision variables. See StoaMINLP#Algorithm for more information. Default 0.001. |
BCB_ff | Parameter regulating the balance between branching the search tree and adding linearizations using fixed fractional integer decision variables. See StoaMINLP#Algorithm for more information. Default 10. |
LoL_nlpr | Parameter regulating likelihood of linearization using the solution of the relaxed NLP problem. See StoaMINLP#Algorithm for more information. Default 10. |
TOD_nlpr | Parameter regulating "tailing off" detection for linearizations using the solution of the relaxed NLP problem. See StoaMINLP#Algorithm for more information. Default 0.001. |
BCB_nlpr | Parameter regulating the balance between branching the search tree and adding linearizations using the solution of the relaxed NLP problem. See StoaMINLP#Algorithm for more information. Default 10. |
rTYPE | = 0 r is fixed to the value in rVALUE. = 1 r is a uniformly distributed random number in the interval [0,1]. Default. |
rVALUE | Defines the value of r when rTYPE is set to zero. Default is 0.5. |
CUTPOOL | = 0 All linearizations constraints are kept in the master problem. = 1 Manage a pool with inactive linearization constraints. If an inactive constraint gets violated, it is brought back from the pool. Default. |
CutDelBnd | The number of consecutive times a linearization can be inactive before it gets removed and put into the inactive pool. Default is 15 times. |
LIM_DEL_CUT | = 0 No extra deletion of cuts. Default when Prob.Convex == 1. = 1 Delete any cuts limiting the true feasible region whenever detected. Such cuts will appear if the problem has nonlinear constraints. Default when Prob.Convex == 0. |
PsCoItLim | Limit on time spent per node calculating initial pseudo costs when MIP.VarSel == 3. Default is 120 (s). |
PrintLin | Set nonzero to print short information about the type of linearization added. Default 0. Enabled when IterPrint > 3. |
PRINTPOOL | Set nonzero to print Set nonzero to print the decisions taken in the cutpool management.Default 0. Enabled when IterPrint > 4. |
optParam structure
Substructure in Prob with general optimization parameters.
fields used in Prob.optParam: | |
---|---|
Field | Description |
MaxIter | Maximal number of iterations, default 10000 |
IterPrint | Print short information each iteration. Setting PriLev > 1 also enables IterPrint, setting it to 1. The information printed for different levels is as follows: >0 A line at each evaluated node with the following: > 1 A line at each evaluated node with the information described above. >2 Depth, number of integer components and lower bound on objective for each node in L. |
bTol | Linear constraint violation convergence tolerance. |
cTol | Constraint violation convergence tolerance. |
fTol | Optimality tolerance. |
Outputs
Result | Structure with result from optimization. The following fields are changed: | |
---|---|---|
Iter | Number of iterations. | |
ExitFlag | Exit flag. 0: Global optimal solution found, or integer solution with duality gap less than user tolerance. 1: Maximal number of iterations reached. 2: Empty feasible set, no integer solution found. 4: No feasible point found running NLP relaxation. 5: Illegal x_0 found in NLP relaxation. 99: Maximal CPU Time used (cputime > Prob.MaxCPU). | |
Inform | Code telling type of convergence, returned from subsolver. | |
ExitText | Text string giving ExitFlag and Inform information. | |
DualGap | Relative duality gap, max(0,fIPMin-fLB)/-fIPMin-, if fIPMin =0; max(0,fIPMin-fLB) if fIPMin == 0. If fIPMin =0: Scale with 100, 100*Dual- Gap, to get the percentage duality gap. For absolute value duality gap: scale with fIPMin, fIPMin * DualGap | |
x_k | Solution. | |
v_k | Lagrange multipliers. Bounds, Linear and Nonlinear Constraints, size n + mLin + mNonLin. | |
f_k | Function value at optimum. | |
g_k | Gradient vector at optimum. | |
x_0 | Starting point x_0. | |
f_0 | Function value at start. | |
c_k | Constraint values at optimum. | |
cJac | Constraint derivative values at optimum. | |
xState | State of each variable, described in TOMLAB Appendix B. | |
bState | State of each constraint, described in TOMLAB Appendix B. | |
cState | State of each general constraint, described in TOMLAB Appendix B. | |
Solver | Solver used ('stoaMINLP'). | |
SolverAlgorithm | Description of method used. | |
Prob | Problem structure used. | |
stoaMINLP | A structure with warm start information. Use with WarmDefGLOBAL, see example here. |