7.2. AMPL¶

AMPL (A Mathematical Programming Language) is an algebraic modeling language designed to simplify complex optimization problems into abstract algebraic expressions. Users only need to focus on the construction of the algebraic model, and then import data separately after the model is completed. This not only speeds up the development, but also effectively reduces the possibility of model input errors.

Currently, MindOpt can solve Linear Programming models constructed by AMPL on Windows/Linux/macOS platforms. For more information about AMPL, please refer to AMPL official document.

In this section we describe how to use MindOpt’s mindoptampl application to solve AMPL models.

7.2.1. Install mindoptampl¶

The mindoptampl application is automatically generated during MindOpt installation. For installation and configuration of MindOpt, please refer to Software Installation.

Verify the mindoptampl application as follows:

After MindOpt is installed, the path of mindoptampl is as follows:
<MDOHOME>\<VERSION>\<PLATFORM>\bin\mindoptampl
Users can verify whether the mindoptampl application is available with the following command line:
mindoptampl --version
If the version information of MindOpt and mindoptampl similar to the following is returned, the installation is successful:
2.0.0 (Darwin x86_64), driver(20230713), ASL(20201107)
mindoptampl supports direct command line to solve .nl format files, you can directly run the following command on the command line to solve.
mindoptampl <MDOHOME>\<VERSION>\examples\ampl\diet.nl

7.2.2. Install AMPL¶

Users can download and install AMPL from the official website, such as: TRY AMPL.

7.2.3. Parameters and Return Values¶

mindoptampl provides some configurable parameters, mindoptampl_options, that can be set through the option command of AMPL, such as:

ampl: option mindoptampl_options 'num_threads=4 max_time=3600';

All parameters supported by mindoptampl can be obtained through the following command:

mindoptampl -=

For detailed description of MindOpt parameters, please refer to Parameters.

MindOpt AMPL interface parameters¶
Parameters	Description
dualization	Set whether to dualize the model
enable_network_flow	Set whether to enable network simplex method
enable_stochastic_lp	Set whether to enable the detection of random LP structure, which can be accelerated when the specific problem structure is turned on
ipm_dual_tolerance	Sets the dual feasibility (relative) tolerance used by the interior point method
ipm_gap_tolerance	Set the dual gap (relative) tolerance in the interior point method
ipm_max_iterations	Set the maximum number of iterations in the interior point method
ipm_primal_tolerance	Sets the primitive feasibility (relative) tolerance used by the interior point method
max_time	Set the maximum solution time for the optimizer in seconds
method	Set the algorithm used in the optimizer
mip_allow_dual_presolve	Specify whether to enable the dual presolve method of MIP
mip_auto_configuration	Set whether to enable MIP automatic parameter configuration
mip_cutoff	Sets the cutoff value of the objective value to prevent finding solutions worse than this value
mip_detect_disconnected_components	Specify whether to enable disconnected components policy in MIP
mip_gap_abs	Set absolute MIP gap tolerance
mip_gap_rel	Set relative MIP gap tolerance
mip_integer_tolerance	Set integer decision precision in MIP solution
mip_linearization_big_m	Set the maximum coefficient when rearranging nonlinear functions in MIP
mip_max_stalling_nodes	Set the maximum number of nodes that are allowed to stall
mip_max_nodes	Set maximum node limit in MIP
mip_max_sols	Set the maximum number of solutions in MIP
mip_objective_tolerance	Set the comparison accuracy of objective value in MIP solution
mip_root_parallelism	Set the maximum number of concurrent threads allowed by the root node in the MIP solver
mip_solution_pool_size	Set the maximum size of the solution pool
num_threads	Set the maximum number of threads used when optimizing the solution
presolve	Set presolver level
print	Set print level
spx_crash_start	Set whether to use the initial basis solution generation method in the simplex method
spx_column_generation	Set whether to use column generation in the simplex method
spx_dual_pricing	Set dual pricing strategy in simplex method
spx_dual_tolerance	Sets the dual feasibility (relative) tolerance used by the simplex method
spx_max_iterations	Set the maximum number of iterations in the simplex method
spx_primal_pricing	Set primitive pricing strategy in simplex method
spx_primal_tolerance	Set the primitive feasibility tolerance used by the simplex method
wantsol	Set whether to return the result (without -AMPL), 1 write the .sol file, 2 print the value of the variable, 8 do not print the solution information.

When MindOpt finishes computing, status information will be returned to AMPL in the form of exit code. Users can obtain status information in the following ways:

ampl: display solve_result_num;

7.2.4. An Example of AMPL Calling MindOpt¶

The following will take the Diet problem as an example to illustrate how to create an AMPL model and call the mindoptampl application to solve it.

The Diet question uses data from the following two tables: Prices of foods and Nutrition of foods .

Prices of foods¶
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

Nutrition of foods¶
Food	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 goal of the Diet problem is to match the food combination that satisfies the nutritional needs at the lowest price; the algebraic mathematical model of the problem is as follows:

\[\begin{split}\begin{eqnarray} &\min & \sum_{j \in J} \mbox{cost}_j \times \mbox{buy}_j \\ &\mbox{s.t.} & \mbox{n_min}_i \leq \sum_{j \in J} \mbox{amt}_{i,j} \times \mbox{buy}_j \leq \mbox{n_max}_i, \forall i \in I, \\ & & \mbox{f_min}_j \leq \mbox{buy}_j \leq \mbox{f_max}_j, \forall j \in J. \end{eqnarray}\end{split}\]

Here,

\(\mbox{buy}\) is the decision variable,
\(\mbox{f_min}\) and \(\mbox{f_max}\) are the lower and upper bounds of \(\mbox{buy}\) respectively,
\(\mbox{cost}\) is the coefficient in the objective function,
\(\mbox{amt}\) is the constraint matrix,
\(\mbox{n_min}\) and \(\mbox{n_max}\) are the lower and upper bounds of the constraints, respectively.

Before using AMPL, first convert the algebraic mathematical model of the above Diet problem into the following AMPL model

The abstract algebraic model diet.mod,
The data file diet.dat.

Next, load the above file in AMPL and call the mindoptampl application to solve the problem:

ampl: model diet.mod;
ampl: data diet.dat;
ampl: option solver mindoptampl;
ampl: option mindoptampl_options 'numthreads=4 maxtime=1e+4';
ampl: solve;

After the solution is computed, the user can view the results through the display command of AMPL:

ampl: display Buy;

Buy [*] :=
BEEF   0
CHK    0
FISH   0
HAM    0
MCH    46.6667
MTL    0
SPG    0
TUR    0
;