目录背景完整代码输出背景一般来说通过pip install gurobipy安装的免费gurobi限制了1000个变量要突破1000个变量限制需要或者证书下面代码可以测试你是不是获取了证书。你可以修改下面代码的num_vars将其设为3000试试。完整代码 3000约束量的规划求解以验证证书是否为免费限制证书 免费限制证书: 约束量1000 importgurobipyasgpfromgurobipyimportGRB# 创建模型modelgp.Model(3000_constraints)# 添加变量num_vars1000# 约束量varsmodel.addVars(num_vars,vtypeGRB.CONTINUOUS,namex)# 添加约束约束量3000foriinrange(num_vars):# 示例每个约束为x_i 1model.addConstr(vars[i]1,namefconstraint_{i})# 添加目标函数最大化总和model.setObjective(sum(vars),GRB.MAXIMIZE)# 求解model.optimize()# 输出结果ifmodel.statusGRB.OPTIMAL:print(最优解,model.objVal)输出Restricted license-fornon-production use only-expires2027-11-29Gurobi Optimizer version13.0.1build v13.0.1rc0(win64-Windows11.0(22631.2))CPU model:11th Gen Intel(R)Core(TM)i5-1135G7 2.40GHz,instructionset[SSE2|AVX|AVX2|AVX512]Thread count:4physical cores,8logical processors,using up to8threads Optimize a modelwith1000rows,1000columnsand1000nonzeros(Max)Model fingerprint:0x837464c6Model has0linear objective coefficientsandan objective constant of-499500Coefficient statistics:Matrixrange[1e00,1e00]Objectiverange[0e00,0e00]Boundsrange[0e00,0e00]RHSrange[1e00,1e00]Presolve removed1000rowsand1000columns Presolve time:0.01s Presolve:All rowsandcolumns removed Iteration Objective Primal Inf.Dual Inf.Time04.9950000e050.000000e000.000000e000s Solvedin0iterationsand0.01seconds(0.00work units)Optimal objective4.995000000e05最优解499500.0