AMPL Interface¶
AMPL is an algebraic modeling language for describing
largescale complex mathematical problems, it was hooked to many commercial
and opensource mathematical optimizers, with various data interfaces and
extensions, and received high popularity among both industries and institutes,
see Who uses AMPL? for more information.
The solver coptampl
uses Cardinal Optimizer to solve linear programming,
convex quadratic programming, convex quadratic constrainted programming and
mixed integer programming problems. Normally coptampl
is invoked
by AMPL’s solve command, which gives the invocation:
coptampl stub AMPL
in which stub.nl
is an AMPL generic output file (possibly written by
'ampl obstub'
or 'ampl ogstub'
). After solving the problem,
coptampl
writes a stub.sol
file for use by AMPL’s solve and solution
commands. When you run AMPL, this all happens automatically if you
give the AMPL commands:
ampl: option solver coptampl;
ampl: solve;
Installation Guide¶
To use coptampl
in AMPL, you must have a valid AMPL license and make sure
that you have installed Cardinal Optimizer and setup its license properly,
see How to install Cardinal Optimizer for details.
Be sure to check if it satisfies the following requirements for different
operating systems.
Windows¶
On Windows platform, the coptampl.exe
utility and the copt.dll
dynamic
library contained in the Cardinal Optimizer must appear somewhere in your
user or system PATH
environment variable (or in the current directory).
To test if your setting meets the above requirements, you can check it by executing commands below in command prompt:
coptampl v
And you are expected to see output similar to the following on screen:
AMPL/xCOPT Optimizer [7.1.1] (windowsx86), driver(20220526), MP(20220526)
If the commands failed, then you should recheck your settings.
Linux¶
On Linux platform, the coptampl
utility must appears somewhere in your
$PATH
environment variable, while the libcopt.so
shared library must
appears somewhere in your $LD_LIBRARY_PATH
environment variable.
Similarly, to test if your setting meets the above requirements, just execute commands below in shell:
coptampl v
And you are expected to see output similar to the following on screen:
AMPL/xCOPT Optimizer [7.1.1] (linuxx86), driver(20220526), MP(20220526)
If the commands failed, please recheck your settings.
MacOS¶
On MacOS platform, the coptampl
utility must appears somewhere in your
$PATH
environment variable, while the libcopt.dylib
dynamic library
must appears somewhere in your $DYLD_LIBRARY_PATH
environment variable.
You can execute commands below in shell to see if your settings meets the above requirements:
coptampl v
And you are expected to see output similar to the following on screen:
AMPL/xCOPT Optimizer [7.1.1] (macosx86), driver(20220526), MP(20220526)
If the commands failed, then please recheck your settings.
Solver Options and Exit Codes¶
The coptampl
utility offers some options to customize its behavior. Uers can
control it by setting the environment variable copt_options
or use AMPL’s
option
command. To see all available options, please invoke:
coptampl =
The supported parameters and their interpretation for current version are shown in Table 5:
Parameter 
Interpretation 
barhomogeneous 
whether to use homogeneous selfdual form in barrier 
bariterlimit 
iteration limit of barrier method 
barthreads 
number of threads used by barrier 
basis 
whether to use or return basis status 
bestbound 
whether to return best bound by suffix 
conflictanalysis 
whether to perform conflict analysis 
crossoverthreads 
number of threads used by crossover 
cutlevel 
level of cuttingplanes generation 
divingheurlevel 
level of diving heuristics 
dualize 
whether to dualize a problem before solving it 
dualperturb 
whether to allow the objective function perturbation 
dualprice 
specifies the dual simplex pricing algorithm 
dualtol 
the tolerance for dual solutions and reduced cost 
feastol 
the feasibility tolerance 
heurlevel 
level of heuristics 
iisfind 
whether to compute IIS and return result 
iismethod 
specify the IIS method 
inttol 
the integrality tolerance for variables 
logging 
whether to print solving logs 
logfile 
name of log file 
exportfile 
name of model file to be exported 
lpmethod 
method to solve the LP problem 
matrixtol 
input matrix coefficient tolerance 
mipstart 
whether to use initial values for MIP problem 
miptasks 
number of MIP tasks in parallel 
nodecutrounds 
rounds of cuttingplanes generation of tree node 
nodelimit 
node limit of the optimization 
objno 
objective number to solve 
count 
whether to count the number of solutions 
stub 
name prefix for alternative MIP solutions written 
presolve 
level of presolving before solving a problem 
relgap 
the relative gap of optimization 
absgap 
the absolute gap of optimization 
return_mipgap 
whether to return absolute/relative gap by suffix 
rootcutlevel 
level of cuttingplanes generation of root node 
rootcutrounds 
rounds of cuttingplanes generation of root node 
roundingheurlevel 
level of rounding heuristics 
scaling 
whether to perform scaling before solving a problem 
simplexthreads 
number of threads used by dual simplex 
sos 
whether to use ‘.sosno’ and ‘.ref’ suffix 
sos2 
whether to use SOS2 to represent piecewise linear terms 
strongbranching 
level of strong branching 
submipheurlevel 
level of SubMIP heuristics 
threads 
number of threads to use 
timelimit 
time limit of the optimization 
treecutlevel 
level of cuttingplanes generation of search tree 
wantsol 
whether to generate ‘.sol’ file 
Please refer to COPT Parameters for details.
AMPL uses suffix to store or pass model and solution information, and also some
extension features, such as support for SOS constraints. Currently, coptampl
support suffix information as shown in Suffix supported by coptampl :
Suffix 
Interpretation 
absmipgap 
absolute gap for MIP problem 
bestbound 
best bound for MIP problem 
iis 
store IIS status of variables or constraints 
nsol 
number of pool solutions written 
ref 
weight of variable in SOS constraint 
relmipgap 
relative gap for MIP problem 
sos 
store type of SOS constraint 
sosno 
type of SOS constraint 
sosref 
store variable weight in SOS constraint 
sstatus 
basis status of variables and constraints 
Users who want to know how to use SOS constraints in AMPL, please refer to resources in AMPL’s website: How to use SOS constraints in AMPL .
When solving finished, coptampl
will display a status message and return
exit code to AMPL. The exit code can be displayed by:
ampl: display solve_result_num;
If no solution was found or something unexpected happened, coptampl
will
return nonzero code to AMPL from Table 7:
Exit Code 
Interpretation 
0 
optimal solution 
200 
infeasible 
300 
unbounded 
301 
infeasible or unbounded 
600 
user interrupted 
Example Usage¶
The following section will illustrate the use of AMPL by a wellknown example called “Diet problem”, which finds a mix of foods that satisfies requirements on the amounts of various vitamins, see AMPL book for details.
Suppose the following kinds of foods are available for the following prices per unit, see Table 8:
Food 
Price 
BEEF 
3.19 
CHK 
2.59 
FISH 
2.29 
HAM 
2.89 
MCH 
1.89 
MTL 
1.99 
SPG 
1.99 
TUR 
2.49 
These foods provide the following percentages, per unit, of the minimum daily requirements for vitamins A, C, B1 and B2, see Table 9:
A 
C 
B1 
B2 

BEEF 
60% 
20% 
10% 
15% 
CHK 
8 
0 
20 
20 
FISH 
8 
10 
15 
10 
HAM 
40 
40 
35 
10 
MCH 
15 
35 
15 
15 
MTL 
70 
30 
15 
15 
SPG 
25 
50 
25 
15 
TUR 
60 
20 
15 
10 
The problem is to find the cheapest combination that meets a week’s requirements, that is, at least 700% of the daily requirements for each nutrient.
To summarize, the mathematical form for the above problem can be modeled as shown in Eq. 6:
The AMPL model for above problem is shown in diet.mod
,
see Listing 7:
1# The code is adopted from:
2#
3# https://github.com/Pyomo/pyomo/blob/master/examples/pyomo/amplbook2/diet.mod
4#
5# with some modification by developer of the Cardinal Optimizer
6
7set NUTR;
8set FOOD;
9
10param cost {FOOD} > 0;
11param f_min {FOOD} >= 0;
12param f_max {j in FOOD} >= f_min[j];
13
14param n_min {NUTR} >= 0;
15param n_max {i in NUTR} >= n_min[i];
16
17param amt {NUTR, FOOD} >= 0;
18
19var Buy {j in FOOD} >= f_min[j], <= f_max[j];
20
21minimize Total_Cost:
22 sum {j in FOOD} cost[j] * Buy[j];
23
24subject to Diet {i in NUTR}:
25 n_min[i] <= sum {j in FOOD} amt[i, j] * Buy[j] <= n_max[i];
The data file for above problem is shown in diet.dat
,
see Listing 8:
1# The data is adopted from:
2#
3# https://github.com/Pyomo/pyomo/blob/master/examples/pyomo/amplbook2/diet.dat
4#
5# with some modification by developer of the Cardinal Optimizer
6
7data;
8
9set NUTR := A B1 B2 C ;
10set FOOD := BEEF CHK FISH HAM MCH MTL SPG TUR ;
11
12param: cost f_min f_max :=
13 BEEF 3.19 0 100
14 CHK 2.59 0 100
15 FISH 2.29 0 100
16 HAM 2.89 0 100
17 MCH 1.89 0 100
18 MTL 1.99 0 100
19 SPG 1.99 0 100
20 TUR 2.49 0 100 ;
21
22param: n_min n_max :=
23 A 700 10000
24 C 700 10000
25 B1 700 10000
26 B2 700 10000 ;
27
28param amt (tr):
29 A C B1 B2 :=
30 BEEF 60 20 10 15
31 CHK 8 0 20 20
32 FISH 8 10 15 10
33 HAM 40 40 35 10
34 MCH 15 35 15 15
35 MTL 70 30 15 15
36 SPG 25 50 25 15
37 TUR 60 20 15 10 ;
To solve the problem with coptampl
in AMPL, just type commands in command
prompt on Windows or shell on Linux and MacOS:
ampl: model diet.mod;
ampl: data diet.dat;
ampl: option solver coptampl;
ampl: option copt_options 'logging 1';
ampl: solve;
coptampl
solve it quickly and display solving log and status message on screen:
xCOPT 5.0.1: optimal solution; objective 88.2
1 simplex iterations
So coptampl
claimed it found the optimal solution, and the minimal cost is
88.2 units. You can further check the solution by:
ampl: display Buy;
And you will get:
Buy [*] :=
BEEF 0
CHK 0
FISH 0
HAM 0
MCH 46.6667
MTL 0
SPG 0
TUR 0
;
So if we buy 46.667 units of MCH, we will have a minimal cost of 88.2 units.