8.3. C API¶
本章节提供MindOpt的C API手册，内容见下文。
8.3.6. Examples¶
8.3.6.1. 定制食谱¶
//include <stdio.h>
#include "Mindopt.h"
#include <stdlib.h>
#define CHECK_RESULT(code) { int res = code; if (res != 0) { fprintf(stderr, "Bad code: %d \n", res); exit(res); } }
#define NFOOD 9
#define NNUTRITION 8
#define MODEL_NAME "diet"
#define MODEL_SENSE "ModelSense"
#define STATUS "Status"
#define OBJ_VAL "ObjVal"
#define X "X"
int main(void) {
MDOenv *env;
MDOemptyenv(&env);
MDOstartenv(env);
// 建立模型
MDOmodel *m;
// 初始化数据
double demand_ub[] = {MDO_INFINITY, 375, MDO_INFINITY, MDO_INFINITY, MDO_INFINITY, MDO_INFINITY, MDO_INFINITY, 75};
double demand_lb[] = {2000, 350, 55, 100, 100, 100, 100, -MDO_INFINITY};
const char *nutrition_name[] = {"Calories", "Carbohydrates", "Protein", "VitA", "VitC", "Calcium", "Iron", "Volume"};
char *food_name[] = {"Cheeseburger", "HamSandwich", "Hamburger", "FishSandwich", "ChickenSandwich", "Fries",
"SausageBiscuit", "LowfatMilk", "OrangeJuice"};
double food_price[] = {1.84, 2.19, 1.84, 1.44, 2.29, 0.77, 1.29, 0.60, 0.72};
double req_value[NFOOD][NNUTRITION] = {
{510.0, 34.0, 28.0, 15.0, 6.0, 30.0, 20.0, 4.0},
{370.0, 35.0, 24.0, 15.0, 10.0, 20.0, 20.0, 7.5},
{500.0, 42.0, 25.0, 6.0, 2.0, 25.0, 20.0, 3.5},
{370.0, 38.0, 14.0, 2.0, 0.0, 15.0, 10.0, 5.0},
{400.0, 42.0, 31.0, 8.0, 15.0, 15.0, 8.0, 7.3},
{220.0, 26.0, 3.0, 0.0, 15.0, 0.0, 2.0, 2.6},
{345.0, 27.0, 15.0, 4.0, 0.0, 20.0, 15.0, 4.1},
{110.0, 12.0, 9.0, 10.0, 120.0, 30.0, 0.0, 8.0},
{80.0, 20.0, 1.0, 2.0, 4.0, 2.0, 2.0, 12.0}};
int *cbeg, *cind, idx;
double *cval;
int i, j, status;
double obj, x;
// 初始化模型同时添加决策变量
CHECK_RESULT(MDOnewmodel(env, &m, MODEL_NAME, NFOOD, food_price, 0, NULL, NULL, NULL));
// 添加约束
// 应满足每日获取的各种营养素在建议的范围内
cbeg = (int *)malloc(sizeof(int) * NNUTRITION);
cind = (int *)malloc(sizeof(int) * NNUTRITION * (NFOOD));
cval = (double *)malloc(sizeof(double) * NNUTRITION * (NFOOD));
idx = 0;
for (i = 0; i < NNUTRITION; i++) {
// Start index of each constraint
cbeg[i] = idx;
for (j = 0; j < NFOOD; ++j) {
cind[idx] = j;
cval[idx++] = req_value[j][i];
}
}
CHECK_RESULT(MDOaddrangeconstrs(m, NNUTRITION, idx, cbeg, cind, cval, demand_lb, demand_ub, nutrition_name));
// 添加目标函数
CHECK_RESULT(MDOsetintattr(m, MODEL_SENSE, MDO_MINIMIZE));
CHECK_RESULT(MDOoptimize(m));
// 打印结果
CHECK_RESULT(MDOgetintattr(m, STATUS, &status));
if (status == MDO_OPTIMAL) {
CHECK_RESULT(MDOgetdblattr(m, OBJ_VAL, &obj));
printf("The total cost is %f \n", obj);
for (i = 0; i < NFOOD; ++i) {
CHECK_RESULT(MDOgetdblattrelement(m, X, i, &x));
printf("You should buy %f unit of %s \n", x, food_name[i]);
}
} else {
printf("No feasible solution exists \n");
}
// 释放被分配的内存
free(cbeg);
free(cind);
free(cval);
MDOfreemodel(m);
MDOfreeenv(env);
return 0;
}
8.3.6.2. 设施选址¶
#include <stdio.h>
#include "Mindopt.h"
#include <stdlib.h>
#define CHECK_RESULT(code) { int res = code; if (res != 0) { fprintf(stderr, "Bad code: %d \n", res); exit(res); } }
#define FACILITY_NUM 8
#define MARKET_NUM 2
#define MODEL_NAME "facility"
#define VAR_TYPE "VType"
#define MODEL_SENSE "ModelSense"
#define STATUS "Status"
#define OBJ "Obj"
#define OBJ_VAL "ObjVal"
#define VAR_NAME "VarName"
#define X "X"
double calculate_transportation_fee(double *pos1, double *pos2, double transport_fee_per_m) {
double x1 = pos1[0] - pos2[0];
double x2 = pos1[1] - pos2[1];
return (x1 * x1 + x2 * x2) * transport_fee_per_m;
}
// 本例子的目标是为了找到最小成本的仓库建造和运输方案
int main(void) {
MDOenv *env = NULL;
MDOemptyenv(&env);
MDOstartenv(env);
// 建立模型
MDOmodel *m = NULL;
// 有两个商场，商场的位置已经确定,分别是(0, 1.7)和(1.4, 2.9)， 所需要的货物重量为100单位和200单位
double market_location[MARKET_NUM][2] = {
{0.0, 1.7},
{1.4, 2.9}};
int market_demand[MARKET_NUM] = {100, 200};
// 仓库位置和建造成本
double facility_location[FACILITY_NUM][2] = {
{0, 1},
{0, 2},
{1, 0},
{1, 1},
{1, 2},
{2, 0},
{2, 1},
{2, 2}};
double facility_expense[FACILITY_NUM] = {3.0, 1.0, 1.5, 1.3, 1.8, 1.6, 1.1, 1.9};
const double transport_fee_per_m = 1.23;
int *cbeg, *cind, *cbeg2, *cind2, idx, col, i, j, status;
double *cval, *cval2, *rhs, *rhs2, obj, x;
char *sense, *sense2, var_name[25];
// 初始化模型同时添加决策变量
CHECK_RESULT(MDOnewmodel(env, &m, MODEL_NAME, FACILITY_NUM * (1 + MARKET_NUM), NULL, NULL, NULL, NULL, NULL));
// 初始化决策变量
// x代表是否在该地建仓库
for (i = 0; i < FACILITY_NUM; ++i) {
CHECK_RESULT(MDOsetcharattrelement(m, VAR_TYPE, i, MDO_BINARY));
CHECK_RESULT(MDOsetdblattrelement(m, OBJ, i, facility_expense[i] +
calculate_transportation_fee(market_location[0], facility_location[i], transport_fee_per_m) +
calculate_transportation_fee(market_location[1], facility_location[i], transport_fee_per_m)));
sprintf(var_name, "Position%d", i);
CHECK_RESULT(MDOsetstrattrelement(m, VAR_NAME, i, var_name));
}
// y代表从j仓库运向i商场的货物量，值的类型为CONTINUOUS类型，下限为0代表不能从j仓库运送小于0单位的货物到i商场
for (i = 0; i < FACILITY_NUM; ++i) {
for (j = 0; j < MARKET_NUM; j++) {
sprintf(var_name, "Transportation_%d_to_%d", i, j);
CHECK_RESULT(MDOsetstrattrelement(m, VAR_NAME, FACILITY_NUM * (1 + j) + i, var_name));
}
}
// 增加约束
cbeg = (int *)malloc(sizeof(int) * FACILITY_NUM * MARKET_NUM);
cind = (int *)malloc(sizeof(int) * (FACILITY_NUM * MARKET_NUM * 2));
cval = (double *)malloc(sizeof(double) * (FACILITY_NUM * MARKET_NUM * 2));
rhs = (double *)malloc(sizeof(double) * FACILITY_NUM * MARKET_NUM);
sense = (char *)malloc(sizeof(char) * FACILITY_NUM * MARKET_NUM);
printf("%d \n", FACILITY_NUM * MARKET_NUM);
idx = 0;
// 约束1 已经决定建造的仓库必须满足所有商场的货物需求
for (i = 0; i < FACILITY_NUM; i++) {
for (j = 0; j < MARKET_NUM; ++j) {
col = i * MARKET_NUM + j;
cbeg[col] = idx;
rhs[col] = 0;
sense[col] = MDO_LESS_EQUAL;
cind[idx] = FACILITY_NUM * (1 + j) + i;
cval[idx++] = 1;
cind[idx] = i;
cval[idx++] = -market_demand[j];
}
}
CHECK_RESULT(MDOaddconstrs(m, FACILITY_NUM*MARKET_NUM, idx, cbeg, cind, cval, sense, rhs, NULL));
// 约束2 如果不建仓库，则此仓库位置运送给所有商场的货物为0
cbeg2 = (int *)malloc(sizeof(int) * MARKET_NUM);
cind2 = (int *)malloc(sizeof(int) * MARKET_NUM * FACILITY_NUM);
cval2 = (double *)malloc(sizeof(double) * MARKET_NUM * FACILITY_NUM);
rhs2 = (double *)malloc(sizeof(double) * MARKET_NUM);
sense2 = (char *)malloc(sizeof(char) * MARKET_NUM);
idx = 0;
for (j = 0; j < MARKET_NUM; ++j) {
cbeg2[j] = idx;
rhs2[j] = market_demand[j];
sense2[j] = MDO_EQUAL;
for (i = 0; i < FACILITY_NUM; i++) {
cind2[idx] = FACILITY_NUM * (1 + j) + i;
cval2[idx++] = 1;
}
}
CHECK_RESULT(MDOaddconstrs(m, MARKET_NUM, idx, cbeg2, cind2, cval2, sense2, rhs2, NULL));
// 开始优化
CHECK_RESULT(MDOsetintattr(m, MODEL_SENSE, MDO_MINIMIZE));
CHECK_RESULT(MDOwrite(m, "test_c.mps"));
CHECK_RESULT(MDOoptimize(m));
CHECK_RESULT(MDOgetintattr(m, STATUS, &status));
// 打印结果
if (status == MDO_OPTIMAL) {
CHECK_RESULT(MDOgetdblattr(m, OBJ_VAL, &obj));
printf("The total cost is %f \n", obj);
for (i = 0; i < FACILITY_NUM; ++i) {
CHECK_RESULT(MDOgetdblattrelement(m, "X", i, &x));
if (x) {
printf("The No.%d warehouse should be built. \n", i);
}
}
} else {
printf("No feasible solution exists \n");
}
free(cbeg);
free(cind);
free(cval);
free(rhs);
free(sense);
free(cbeg2);
free(cind2);
free(cval2);
free(rhs2);
free(sense2);
MDOfreemodel(m);
MDOfreeenv(env);
return 0;
}
8.3.6.3. 人力分配¶
#include <stdio.h>
#include "Mindopt.h"
#include <stdlib.h>
#define CHECK_RESULT(code) { int res = code; if (res != 0) { fprintf(stderr, "Bad code: %d \n", res); exit(res); } }
#define MODEL_NAME "workforce"
#define MODEL_SENSE "ModelSense"
#define STATUS "Status"
#define OBJ_VAL "ObjVal"
#define X "X"
#define WORKERS_NUM 7
#define DAY_NUM 7
int main(void) {
MDOenv *env = NULL;
MDOemptyenv(&env);
MDOstartenv(env);
MDOmodel *m = NULL;
int id = 0;
char var_name[20];
int i, j;
// 每天需要的人力数
const char *day_name[] = {"Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday", "Sunday"};
double workers_per_day[] = {3, 1, 4, 2, 1, 3, 3};
// 每个工人一天的工资
char *workers_name[] = {"Xiaoming", "Huahua", "HongHong", "Dahua", "Lihua", "Niuniu", "Gouzi"};
double workers_pay[] = {13, 10, 11, 8, 9, 14, 14};
// 每个工人可以出勤的时间
int availability[WORKERS_NUM][DAY_NUM];
int non_zero_num = 32;
int non_zero_col[] = {0, 0, 0, 0, 1, 1, 1, 1, 2,2, 2,
2, 3, 3, 3, 3, 4,4, 4, 4, 4,
4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6};
int non_zero_row[] = {1, 2, 4, 6, 0, 1, 4, 5, 2, 3, 4,
6, 1, 2, 4, 5, 0, 1, 2, 3, 4,
6, 0, 1, 2, 5, 0, 1, 2, 4, 5, 6};
for (j = 0; j < non_zero_num; ++j) {
availability[non_zero_col[j]][non_zero_row[j]] = 1;
}
int *cbeg, *cind, idx, status;
double *cval, *rhs, obj, x;
char *sense;
// 初始化模型同时添加决策变量
CHECK_RESULT(MDOnewmodel(env, &m, MODEL_NAME, 0, NULL, NULL, NULL, NULL, NULL));
// 初始化决策变量，并设置其在目标函数中的系数
for (j = 0; j < DAY_NUM; ++j) {
for (i = 0; i < WORKERS_NUM; ++i) {
if (availability[i][j]) {
sprintf(var_name, "%s.%s", workers_name[i], day_name[j]);
CHECK_RESULT(MDOaddvar(m, 0, NULL, NULL, workers_pay[i], 0, 1, MDO_BINARY, (const char*)var_name));
id++;
}
}
}
// 增加约束
// 约束： 满足每天的人力需求
cbeg = (int *)malloc(sizeof(int) * DAY_NUM);
cind = (int *)malloc(sizeof(int) * id);
cval = (double *)malloc(sizeof(double) * id);
rhs = (double *)malloc(sizeof(double) * DAY_NUM);
sense = (char *)malloc(sizeof(char) * DAY_NUM);
idx = 0;
id = 0;
for (i = 0; i < DAY_NUM; ++i) {
cbeg[i] = idx;
rhs[i] = workers_per_day[i];
sense[i] = MDO_EQUAL;
for (j = 0; j < WORKERS_NUM; ++j) {
if (availability[j][i]) {
cind[idx] = id;
cval[idx++] = 1;
id++;
}
}
}
CHECK_RESULT(MDOaddconstrs(m, DAY_NUM, idx, cbeg, cind, cval, sense, rhs, day_name));
// 开始优化
CHECK_RESULT(MDOsetintattr(m, MODEL_SENSE, MDO_MINIMIZE));
CHECK_RESULT(MDOoptimize(m));
CHECK_RESULT(MDOwrite(m, "test_c.mps"));
CHECK_RESULT(MDOgetintattr(m, STATUS, &status));
// 打印结果
if (status == MDO_OPTIMAL) {
CHECK_RESULT(MDOgetdblattr(m, OBJ_VAL, &obj));
printf("The total cost is %f \n", obj);
for (j = 0; j < WORKERS_NUM; ++j) {
char *worker_name = workers_name[j];
for (i = 0; i < DAY_NUM; ++i) {
CHECK_RESULT(MDOgetdblattrelement(m, X, i, &x));
if (x == 1) {
printf("%s should work at %s \n", worker_name, day_name[i]);
}
}
}
} else {
printf("No feasible solution exists \n");
}
// 释放被分配的内存
free(cbeg);
free(cind);
free(cval);
free(rhs);
free(sense);
MDOfreemodel(m);
MDOfreeenv(env);
return 0;
}