MIPNLP stoaMINLP
This page is part of the MIPNLP Manual. See MIPNLP Manual. 
Contents
Purpose
stoaMINLP solves convex mixedinteger 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 subsolvers (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 matfile stoaMINLPSave.mat. stoaMINLP uses the warm start information to continue from the last run. The matfile 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 NLPproblem. 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 the wikimanuals or the inMATLAB help of 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 subproblems 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 solverspecific 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 noninteger. 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 xvalues 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 pseudocosts. = 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 Pseudocostbased 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 solverspecific 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 Two lines at each node with an improved integer solution:
> 1 Two lines 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. Default 1.0e6 
cTol  Constraint violation convergence tolerance. Default 1.0e6 
fTol  Optimality tolerance. Default 3.0e13 
xTol  Variable convergence tolerance. Default 2.2204e13 
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,fIPMinfLB)/fIPMin, if fIPMin =0; max(0,fIPMinfLB) 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. 