GNU MathProg是一种用于描述线性数学规划模型的建模语言。用GNU MathProg语言编写的模型描述由一组语句和数据块组成。
在MathProg中，模型以集合、参数、变量、约束和目标(sets, parameters, variables, constraints, objectives称为模型对象)的形式进行描述。
在MathProg中，模型描述(model description)由两部分组成：模型部分和数据部分
(1).模型部分是模型描述的主要部分，包含模型对象的声明，并且对于基于相应模型的所有问题都是通用的。
(2).数据部分是模型描述的可选部分，包含特定于特定问题实例的数据。
模型描述采用ASCII字符集的纯文本格式编码。
这里使用 https://blog.csdn.net/fengbingchun/article/details/147855898 中饮食问题的数据生成diet.mod，内容如下所示：
# sets
set Foods := {'food1', 'food2', 'food3', 'food4', 'food5', 'food6', 'food7', 'food8', 'food9'};
set Nutrients := {'nutrient1', 'nutrient2', 'nutrient3', 'nutrient4'};
# parameters
param unit_prices{Foods};
param nutrient_values{Foods, Nutrients};
param min_bounds{Foods};
param max_bounds{Foods};
param min_nutrient{Nutrients};
param max_untrient{Nutrients};
# variable
var quantity{Foods} >= 0;
var select{Foods} binary;
# objective function
minimize total_cost: sum{f in Foods} unit_prices[f] * quantity[f];
# constraint
s.t. quantity_min{f in Foods}: quantity[f] >= min_bounds[f] * select[f];
s.t. quantity_max{f in Foods}: quantity[f] <= max_bounds[f] * select[f];
s.t. nutrient_min{n in Nutrients}: sum{f in Foods} nutrient_values[f, n] * quantity[f] >= min_nutrient[n];
s.t. nutrient_max{n in Nutrients}: sum{f in Foods} nutrient_values[f, n] * quantity[f] <= max_untrient[n];
s.t. total_quantity: sum{f in Foods} quantity[f] = 99.0;
s.t. mandatory_food: select['food5'] = 1;
s.t. num_select_foods: sum{f in Foods} select[f] = 5;
solve;
printf "total cost: %.4f\n", total_cost;
printf {f in Foods: select[f] > 0.5}: "selected: %s: %.4f, limit: [%.1f, %.1f]\n", f, quantity[f], min_bounds[f], max_bounds[f];
printf "total quantity: %.1f\n", sum{f in Foods} quantity[f];
# data
data;
param unit_prices :=
'food1' 0.886
'food2' 0.863
'food3' 0.855
'food4' 0.917
'food5' 0.237
'food6' 0.856
'food7' 0.833
'food8' 0.904
'food9' 0.876;
param nutrient_values : 'nutrient1' 'nutrient2' 'nutrient3' 'nutrient4' :=
'food1' 0.21 65.10 0.72 88.5
'food2' 0.08 64.58 0.63 76.9
'food3' 0.22 64.81 0.53 86.1
'food4' 0.58 65.84 1.09 57.8
'food5' 0.033 46.07 14.15 0
'food6' 0.059 65.25 0.39 87.2
'food7' 0.14 64.25 0.57 93.7
'food8' 0.033 63.06 1.36 79.0
'food9' 0.076 65.20 0.59 99.0;
param min_bounds :=
'food1' 1.0
'food2' 1.0
'food3' 1.0
'food4' 1.0
'food5' 7.0
'food6' 1.0
'food7' 1.0
'food8' 1.0
'food9' 1.0;
param max_bounds :=
'food1' 55.0
'food2' 55.0
'food3' 55.0
'food4' 55.0
'food5' 9.0
'food6' 55.0
'food7' 55.0
'food8' 55.0
'food9' 55.0;
param min_nutrient :=
'nutrient1' 0.
'nutrient2' 6200.
'nutrient3' 9.9
'nutrient4' 6500.;
param max_untrient :=
'nutrient1' 49.
'nutrient2' 6230.
'nutrient3' 782.
'nutrient4' 7000.;
end;.mod文件：模型文件(model file)，纯文本文件，由GNU MathProg建模语言编写。
(1).可在.mod中使用printf打印中间结果
(2).数据既可以放在.mod文件中，也可以存放于单独的.dat文件中
glpsol.exe调用.mod：
(1).可通过执行"glpsol.exe --help"查看glpsol.exe支持的参数
(2).执行"glpsol.exe -m diet.mod -o result.txt",执行结果如下图所示：与之前结果相同
C API调用.mod实现：
int test_glpk_mod()
{
auto tran = glp_mpl_alloc_wksp();
const char* model_file{ "../../../testdata/diet.mod" };
if (auto ret = glp_mpl_read_model(tran, model_file, 0); ret != 0) {
std::cerr << "Error: failed to read model: " << model_file << ", error code: " << ret << std::endl;
return ret;
}
if (auto ret = glp_mpl_generate(tran, nullptr); ret != 0) {
std::cerr << "Error: failed to generate model: " << model_file << ", error code: " << ret << std::endl;
return ret;
}
auto lp = glp_create_prob();
glp_mpl_build_prob(tran, lp);
glp_iocp parm;
glp_init_iocp(&parm);
parm.presolve = GLP_ON;
parm.msg_lev = GLP_MSG_ERR;
auto ret = glp_intopt(lp, &parm);
if (ret != 0) {
std::cerr << "Error: failed to solve: error code: " << ret << std::endl;
glp_delete_prob(lp);
glp_mpl_free_wksp(tran);
return ret;
}
ret = ret = glp_mip_status(lp);
if (ret != GLP_OPT) {
std::cerr << "Error: there is no optimal solution, status: " << ret << std::endl;
glp_delete_prob(lp);
glp_mpl_free_wksp(tran);
return ret;
}
glp_mpl_postsolve(tran, lp, GLP_MIP); // GLP_SOL: LP, glp_simplex; GLP_MIP: MIP, glp_intopt; execute the printf statement in the mod file
std::cout << "minimum cost: " << glp_mip_obj_val(lp) << std::endl; // LP: glp_get_obj_val; MIP: glp_mip_obj_val
for (auto j = 0; j < foods.size(); ++j) {
if (auto ret = glp_mip_col_val(lp, j+1); ret > 0.5)
std::cout << foods[j] << ": quantity: " << ret << ", limit: [" << bounds[j][0] << "," << bounds[j][1] << "]" << std::endl;
}
glp_delete_prob(lp);
glp_mpl_free_wksp(tran);
return 0;
}执行结果如下图所示：与之前结果相同
