python - 实现 LHS 不是二进制的蕴涵？

Question

尝试在 Python + Gurobi 中实现指标约束，其中指标(LHS)是二元决策变量的总和。

嗨，我想在 Python + Gurobi 中实现以下功能:

Y_i_d and U_d are binary decision variables:
Y_i_d = model.addVars(passengers, drivers, vtype=grb.GRB.BINARY, name = "Y")
U0_d = model.addVars( drivers, vtype=grb.GRB.BINARY, name = "U0")
U1_d = model.addVars( drivers, vtype=grb.GRB.BINARY, name = "U1")
U2_d = model.addVars( drivers, vtype=grb.GRB.BINARY, name = "U2")
U3_d = model.addVars( drivers, vtype=grb.GRB.BINARY, name = "U3")

我想以某种方式得到以下暗示:

model.addConstr((U0_d[d]+U1_d[d]+U2_d[d]+U3_d[d])==1)
model.addConstr( (grb.quicksum(Y_i_d[ i, d] for i in passengers) == 0) >>     (U0_d[d] == 1))
model.addConstr( (grb.quicksum(Y_i_d[ i, d] for i in passengers) == 1) >>     (U1_d[d] == 1))
model.addConstr( (grb.quicksum(Y_i_d[ i, d] for i in passengers) == 2) >>     (U2_d[d] == 1))
model.addConstr( (grb.quicksum(Y_i_d[ i, d] for i in passengers) == 3) >>     (U3_d[d] == 1))

但是，这不起作用，因为指示符约束将指示符变量声明为二进制类型。有解决方法吗？稍后我必须使用 U_d 变量来定义析取约束。

提前谢谢您!

Answer 1

尝试向后写约束:

model.addConstr((U0_d[d] == 1) >> (grb.quicksum(Y_i_d[ i, d] for i in passengers) == 0))
model.addConstr((U1_d[d] == 1) >> (grb.quicksum(Y_i_d[ i, d] for i in passengers) == 1))
model.addConstr((U2_d[d] == 1) >> (grb.quicksum(Y_i_d[ i, d] for i in passengers) == 2))
model.addConstr((U3_d[d] == 1) >> (grb.quicksum(Y_i_d[ i, d] for i in passengers) == 3))