Features Guide for MPbased AMPL Solvers¶
The MP framework defines standard solver features that solvers might support; these are usually characterized by a set of options used to control the feature, sometimes suffixes to pass required data and results, and may change the behaviour of the solution process. Much of the biolerplate code is written already, so that the behaviour becomes automatically standardized across all solvers.
This page presents the semantics of the most common solver features; for a development reference see HOWTO hook your solver to AMPL MP.
General features¶
Output level¶
All solvers print some information during the solution process. For the sake of clarity,
when using the solvers from AMPL the information is mostly ommitted, and only the solver message
is
displayed, which describes the outcome of the optimization process.
The amount of information printed is controlled by the option outlev
:
option <solver>_options 'outlev=1';
In case of repeated executions it is often desiderable to hide all solver output. The solver message
can be suppressed by setting the option solver_msg
to 0. The solver banner is displayed anyway;
to suppress it a redirection is needed:
option solver_msg 0;
solve > NUL;
Option 

Applicability 
All models 
Values 
Values:

Model export¶
Most solvers can export the model before solving. This is usually
controlled by the option writeprob
:
option <solver>_options 'writeprob=/tmp/diet.lp';
The format is solverdependent and determined by the file extension (‘.lp’ in the example).
Option 

Applicability 
All models 
Values 
Values:

Warm start¶
Solution process can often benefit of a solution (a set of variable values) to start the algorithm. This is passed to supporting solver automatically if the option is activated and variables in AMPL have a value assigned. Note that, for LP problems, also the dual values can be passed.
This option controls whether to use incoming primal (and dual, for LP) variable values in a warmstart.
Option 

Applicability 
LP and MIP models 
Input 
Variable values 
Output 
None 
Values 
Sum of:

Example 
Use this model Execute: option <solver>_options "alg:start=1";
let n:=250; # increase the size of the model to have noticeable solution times
solve;
printf "Solution without warm start took %fs\n", _solve_time;
# Now an optimal solution is already present, we pass it to the solver
# which would use to start the solution process
solve;
printf "Solution with warm start took %fs\n", _solve_time;
Output: ...
Solution without warm start took 2.89062s
...
Solution with warm start took 0.671875s

Input and output basis¶
A basis is a set of variable values representing a feasible and extreme solution. Simplex solvers normally calculate this as part of the solution process, while interior point methods must perform additional steps (crossover) to get it. In a way similar to warm start, a basis can also be passed to the solver, which will use it as starting point for searching for a solution.
This option controls whether to use or return a basis.
Option 

Applicability 
LP and MIP models 
Input 
Suffixes:

Output 
Suffixes:

Values 
Sum of:

Example 
Use this model Execute: option gurobi_options "alg:start=0 outlev=1"; # disable passing the solution
solve;
display Buy.sstatus; # display basis status
solve; # second solve with take much less although a solution is not provided
In the solver logs, we can see the expected behaviour: xGurobi 9.5.2: optimal solution; objective 74.27382022
3 simplex iterations
Objective = total_cost['A&P']
ampl: display Buy.sstatus;
Buy.sstatus [*] :=
BEEF low
CHK upp
FISH low
HAM low
MCH low
MTL bas
SPG bas
TUR low;
... # second solve:
Solved in 0 iterations and 0.00 seconds (0.00 work units)

Feasibility Relaxation¶
The feasibility relaxation functionality enables the solver to find a feasible solution even if the original model is unfeasible without explicitly adding slack variables to the constraints. In the feasibility relaxation problem,
Each variable \(x\) can violate its bounds (\(lb \leq x \leq ub\)):
Violation of lower bound \(lbv = max(0, lbx)\)
Violation of upper bund \(ubv = max(0, xub)\)
Each constraint body \(c\) can violate its bounds also (\(c \leq rhs\))
Constraint violation \(rhsv = max(0, crhs)\)
The objective then becomes to minimize some function of the
violations (e.g. the number of violations, or their sum  possibly weighted by some
penalty values).
The penalty values (used in some kinds of feasibility relaxation problmes) can be
controlled with macro defaults (e.g. option alg:ubpen
sets the penalty weight for
all upper buonds violations, and its default values is 1) or, with more granularity,
on each entity via suffix values (e.g. variable suffix ubpen
on variables, default
value 0).
Penaly weights < 0 are treated as Infinity, allowing no violation.
Option 

Applicability 
LP and MIP models 
Input 

Output 
None 
Values 
Sum of:

Example 
Use this model Solve the model changing the penalties to get different solutions: options <solver>_options "alg:feasrelax=1";
option presolve 0; # otherwise the model could be oversimplified
solve; display x,y;
Gives:
Now we want to force all variable lower bounds to be respected: options <solver>_options "alg:feasrelax=1 alg:lbpen=1";
solve; display x,y;
Gives, as expected x=5 (it had a lower bound of 5):
Single violations can be controlled via suffixes; in this case we want to control the constraints violations: options <solver>_options "alg:feasrelax=1 alg:lbpen=1"; # allow lower bounds to be violated again
suffix rhspen IN;
let C1.rhspen := 1; # normal weight
let C2.rhspen := 1; # C2 can NOT be violated
let C3.rhspen := 10; # We'd rather not violate C3
solve;
display C1.slack, C2.slack, C3.slack;
Gives:
C1 is violated  which makes sense as we specified that C2 cannot be violated and we gave an higher avoidance weight to C2. If we want to violate C1 instead, we can: let C1.rhspen := 10; # We'd rather not violate C1
let C2.rhspen := 1; # C2 can be violated
let C3.rhspen := 1; # Normal weight
solve;
display C1.slack, C2.slack, C3.slack;
Which gives, as expected:

Multiple solutions¶
More often than not, optimization problems have more than one optimal solution; moreover, during the solution process, MIP solvers usually find suboptimal solutions, which are normally discarded. They can be however be kept, and in most cases there are solverspecific options to control how the search for additional solutions is performed.
The main (and generic) options that controls the search are sol:stub
amd sol:count
, which
control respecitvely the basename for the files where additional solution will be stored and
if to count additional solutions and return them in the nsol
problem suffix.
Specifying a stub name automatically enables the solutions count; found solutions are written to
files [solutionstub1.sol'
, … solutionstub<nsol>.sol
].
Option 

Applicability 
MIP models 
Input 
None 
Output 
Suffixes 
Values 
The name used as base file name for the alternative solutions 
Example 
Use this model Execute: option gurobi_options "sol:stub=queentake";
solve;
printf "I have found %d solutions\n", Initial.nsol;
printf "Displaying solution 1";
solution queentake1.sol;
display X;
printf "Displaying solution 2";
solution queentake2.sol;
display X;
Output: xGurobi 9.5.2: sol:stub=queentake
xGurobi 9.5.2: optimal solution; objective 10
355 simplex iterations
23 branching nodes
suffix nsol OUT;
suffix npool OUT;
I have found 10 solutions
Displaying solution 1
xGurobi 9.5.2: Alternative solution; objective 10
X [*,*]
: 1 2 3 4 5 6 7 8 9 10 :=
1 0 0 0 0 0 0 1 0 0 0
2 1 0 0 0 0 0 0 0 0 0
3 0 0 0 1 0 0 0 0 0 0
4 0 0 0 0 0 1 0 0 0 0
5 0 0 0 0 0 0 0 0 1 0
6 0 0 1 0 0 0 0 0 0 0
7 0 0 0 0 0 0 0 0 0 1
8 0 0 0 0 0 0 0 1 0 0
9 0 1 0 0 0 0 0 0 0 0
10 0 0 0 0 1 0 0 0 0 0;
Displaying solution 2
xGurobi 9.5.2: Alternative solution; objective 10
X [*,*]
: 1 2 3 4 5 6 7 8 9 10 :=
1 0 0 1 0 0 0 0 0 0 0
2 0 0 0 0 0 1 0 0 0 0
3 0 0 0 0 0 0 0 0 1 0
4 1 0 0 0 0 0 0 0 0 0
5 0 0 0 1 0 0 0 0 0 0
6 0 0 0 0 0 0 1 0 0 0
7 0 0 0 0 0 0 0 0 0 1
8 0 0 0 0 0 0 0 1 0 0
9 0 1 0 0 0 0 0 0 0 0
10 0 0 0 0 1 0 0 0 0 0

Sensitivity analysis¶
It is often useful to know the ranges of variables and constraint bodies for which the optimal basis remains optimal. Solvers supporting this feature return such ranges in suffixes after solving to optimum. This option controls whether to calculate these values and return them in the suffixes listed below.
Option 

Applicability 
LP and MIP models 
Input 
None 
Output 
Suffixes for variables only:
Suffixes for variables and constraints:

Values 
Sum of:

Example 
Use Multi objective diet model Execute: options <solver>_options "alg:sens=1";
option presolve 0; # disable model transformations in AMPL
solve;
Then the ranges for variables and constraints can be examined: display Buy, Buy.sstatus, Buy.sensublo, Buy.sensubhi;
Which gives: display Buy.sensublo, Buy.sensubhi, Buy.sstatus, Buy;
: Buy.sensublo Buy.sensubhi Buy.sstatus Buy :=
BEEF 2 1e+100 low 2
CHK 9.12987 10.9792 upp 10
FISH 2 1e+100 low 2
HAM 2 1e+100 low 2
MCH 2 1e+100 low 2
MTL 6.23596 1e+100 bas 6.23596
SPG 5.25843 1e+100 bas 5.25843
TUR 2 1e+100 low 2;

Kappa¶
Kappa is the condition number for the current LP basis matrix. It is a measure of the stability of the current solution \(Ax=b\) measuring the rate at which the solution \(x\) will change with respect to a change in \(b\). It is only available for basic solutions, therefore it is not available for barrier method if crossover is not applied.
Option 

Applicability 
LP and MIP models with optimal basis 
Input 
None 
Output 
Additional text in

Values 
Sum of:

Example 
Use Multi objective diet model Solve the model and report kappa: options <solver>_options "alg:kappa=3";
solve;
display Initial.kappa, total_number.kappa;
Gives: xGurobi 9.5.2: optimal solution; objective 30.92537313
kappa value: 53.5399
5 simplex iterations
suffix kappa OUT;
Initial.kappa = 53.5399
total_number.kappa = 53.5399

Unbounded rays¶
When a model is unbounded, a vector \(r\) (unbounded ray) can be found such that
when added to any feasible solution \(x\), the resulting vector is a feasible solution
with an improved objective value.
When a model is infeasible, the dual solution is unbounded and the same as above can be applied
to constraints.
This option controls whether to return suffix unbdd
if the objective is unbounded
or suffix dunbdd
if the constraints are infeasible.
Option 

Applicability 
Unbounded/unfeasible LP and MIP linear models 
Input 
None 
Output 
Suffixes:

Values 
Sum of:

Example 
Use this model Solve the (infeasible) model and report the options gurobi_options "alg:rays=3"; # it is default already
option presolve 0; # else the model could be oversimplified
solve;
display c1.dunbdd, c2.dunbdd, c3.dunbdd;
Output: xGurobi 9.5.2: alg:rays=3
xGurobi 9.5.2: infeasible problem
suffix dunbdd OUT;
c1.dunbdd = 1
c2.dunbdd = 0
c3.dunbdd = 0

Multiple objectives¶
Many real world problems have multiple objectives; often this scenario is tackled by blending all the objectives
by linear combination when formulating the model, or by minimizing each unwanted objective deviations from a prespecified
goal.
Many solvers can facilitate the formulation; the available functionalities are solverspecific; at MP level
they accessible via the main option obj:multi
. Consult the solver documentation for the functionalities available
on your solver.
Option 

Applicability 
LP and MIP models 
Input 
None 
Output 
All objectives are reported in 
Values 
Values:

Example 
Use Multi objective diet model Execute: options <solver>_options "obj:multi=1";
solve;
Output: xGurobi 9.5.1: obj:multi=1
xGurobi 9.5.1: optimal solution; objective 74.27382022
Individual objective values:
_sobj[1] = 74.27382022
_sobj[2] = 75.01966292
_sobj[3] = 79.59719101
_sobj[4] = 31.49438202

Irreducible Inconsistent Subset (IIS)¶
Given an infeasible model, it is useful to know where the infeasibility comes from, that is, which bounds and/or constraints are incompatible. An IIS is a subset of constraints and variables that is still infeasible and where if a member is removed the subsystem becaomes feasible. Note that an infeasible model can have more than one IIS.
This options controls whether to perform the additional computational steps required to find an IIS.
Option 

Applicability 
LP and MIP models 
Input 
None 
Output 
Suffix 
Values 
Values:

Example 
Use this model Execute: option <solver>_options "iisfind=1";
option presolve 0; # else the model could be oversimplified
solve;
display c1.iis, c2.iis, c3.iis;
Output: xGurobi 9.5.2: alg:iisfind=1
xGurobi 9.5.2: infeasible problem
2 simplex iterations
suffix iis symbolic OUT;
suffix dunbdd OUT;
c1.iis = mem
c2.iis = mem
c3.iis = mem

MIPonly features¶
Return MIP gap¶
The MIP gap describes how far the reported solution for the MIP model is from the best bound found. It is defined as:
\(absgap =  objective  bestbound \)
\(relmipgap = absgap /  objective \)
It gives a measure of how far the current solution is from the
theoretical optimum.
The AMPL option controls whether to return mipgap suffixes or include mipgap values
in the solve_message. Returned suffix values are +Infinity
if no integerfeasible
solution has been found, in which case no mipgap values are reported in the solve_message.
Option 

Applicability 
MIP models 
Input 
None 
Output 
Additional text in

Values 
Sum of:

Example 
Use this model Execute: # 3 = return both absolute and relative MIP gap, and also report them
# in the solve_message
option <solver>_options "return_mipgap=3";
solve;
display max_queens.relmipgap, max_queens.absmipgap;
display Initial.relmipgap, Initial.absmipgap;
Output: xGurobi 9.5.2: mip:return_gap=3
xGurobi 9.5.2: optimal solution; objective 10
suffix absmipgap OUT;
max_queens.relmipgap = 0
max_queens.absmipgap = 0
Initial.relmipgap = 0
Initial.absmipgap = 0

Return best dual bound¶
The best dual bound (on the objective) represents what is the currently proven best value that the objective value can assume. Usually solvers terminate when the current solution is close enough to the best bound.
This option controls whether to return suffix .bestbound for the best known MIP dual bound on the objective value. The returned value is Infinity for minimization problems and +Infinity for maximization problems if there are no integer variables or if a dual bound is not available.
Option 

Applicability 
MIP models 
Input 
None 
Output 
Suffix:

Values 
Sum of:

Example 
Use this model Execute: option <solver>_options "mip:bestbound=3";
solve;
display max_queens.bestbound, Initial.bestbound;
Output: xGurobi 9.5.2: mip:bestbound=1
xGurobi 9.5.2: optimal solution; objective 10
max_queens.bestbound = 10
Initial.bestbound = 10

Lazy constraints and user cuts¶
The solution process of a MIP model can be helped by further specifying its structure.
Specifically, constraints can be marked as lazy
or as user cuts
.
Such constraints are not included initially, then:
Lazy constraints
are pulled in when a feasible solution is found; if the solution violates
them, it is cut off. They are integral part of the model, as they can cut off integerfeasible
solutions.
User cuts
are pulled in also, but they can only cut off relaxation solutions; they are
consider redundant in terms of specifying integer feasibility.
This option controls whether to recognize the suffx lazy
on constraints, which should then be
positive to denote a lazy constraint and negative to mark a contraint as a user cut.
Option 

Applicability 
MIP models 
Input 
Suffix:

Output 
None 
Values 
Sum of:

Example 
Following ampl model TODO Model
end of code block option presolve 0; # disable model transformations in AMPL
suffix lazy IN;
let c1.lazy := 1; # lazy constraint
let c2.lazy := 1; # user cut, must be redundant as it might never be pulled in
solve;
# TODO SHOW OUTPUT

Variable priorities¶
Solution of MIP models via branch and bound can often be helped by providing
preferences on which variables to branch on. Those can be specified in AMPL via the suffix
priority
.
This option controls whether to read those values and use them in the solution process.
Option 

Applicability 
MIP models 
Input 
Suffix:

Output 
None 
Values 
Values:

Example 
Following AMPL model TODO Model
end of code block option presolve 0; # disable model transformations in AMPL
let x.priority := 1;
let y.priority := 5;
solve;
# TODO SHOW OUTPUT

Fixed model (return basis for MIP)¶
At the end of the solution process for a MIP model, a continuous relaxation of the model with all the integer variables fixed at their integeroptimum value. Some continuous variables can also be fixed to satisfy SOS or general constraints. The model can therefore be solved without these types of restrictions to calculate a basis, dual values or sensitivity information that wouldn’t normally be available for MIP problems.
This option controls if to generate and solve the fixed model after solving the integer problem.
Option 

Applicability 
MIP models 
Input 
None 
Output 
Suffixes:

Values 
Values

Example 
Following ampl model TODO Model
end of code block option <solver>_options "mip:basis=1";
# TODO SHOW OUTPUT

Round