如何解决Julia JuMP运行报错type VariableIndex has no field head问题

• 顺序错误：代码中@NLconstraint(ALT, f1 <= y)写在了f1的@NLexpression定义之前，Juniper解析约束时f1还未被注册为合法非线性表达式，被识别为无效变量引用，触发类型字段不存在报错。
• 括号缺失：k6和FF表达式中exp(-landa*h)/1-exp(-landa*h)存在运算优先级错误，你实际需要的是exp(-landa*h)/(1-exp(-landa*h))，漏了分母的括号会导致后续计算结果完全不符合预期。

调整代码顺序，补全缺失的括号即可，修正后完整代码如下：

using JuMP,CPUTime, Distributions, Ipopt,Juniper,Gurobi
#-----Model parameters--------------------------------------------------------
sig, C1, c0 = 2, 300, 10;
E, landa, T0, T1, T2, gam1, gam2, a1, a2, a3, ap = 0.05, 0.01, 0, 2, 2, 1, 1, 0.5, 0.1, 50, 25;
f(x) = cdf(Normal(0, 1), x);
#---------------------------------------------------------------------------
ALT= Model(optimizer_with_attributes(Juniper.Optimizer, "nl_solver"=>optimizer_with_attributes(Ipopt.Optimizer, "print_level" => 0),
       "mip_solver"=>optimizer_with_attributes(Gurobi.Optimizer, "logLevel" => 0),"registered_functions" =>[Juniper.register( :f, 1, f; autodiff = true)])
       );
# variables-----------------------------------------------------------------
JuMP.register(ALT, :f, 1, f; autodiff = true);
@variable(ALT, 0.001 <= h <= 40);
@variable(ALT, 0.000001 <= L <= 4);
@variable(ALT, 2 <= n <= 30, Int);
@variable(ALT, y);
#---------------------------------------------------------------------------
@NLexpression(ALT,k1,h/(1-f(L-sig*sqrt(n))+f(-L - sig*sqrt(n)))); # HARL1
@NLexpression(ALT,k2,(1-(1+landa*h)*exp(-landa*h))/(landa*(1-exp(-landa*h)))); #to
@NLexpression(ALT,k3,E*n+T1*gam1+T2*gam2);
@NLexpression(ALT,k4,1/landa+h/(1-f(L-sig*sqrt(n))+f(-L-sig*sqrt(n))));
@NLexpression(ALT,k5,-(1-(1+landa*h)*exp(-landa*h))/(landa*(1-exp(-landa*h)))+E*n+T1*gam1+T2*gam2);
# 补全了分母的括号
@NLexpression(ALT,k6,(exp(-landa*h)/(1-exp(-landa*h)))*(a3/(2*f(-L)))+ap); #SF/ARL0+W F=a3 ap=W
@NLexpression(ALT,k7,1-f(L-sig*sqrt(n))+f(-L-sig*sqrt(n)));
@NLexpression(ALT,F,c0/landa+C1*(k1-k2+k3)+((a1+a2*n)/h)*(k4+k5+k3)+k6);
# 补全了分母的括号
@NLexpression(ALT,FF,k4-k2+E*n+T1+T2+(1-gam1)*((exp(-landa*h)/(1-exp(-landa*h))*T0)/(2*f(-L)))); #ST0/ARL0
# 把f1、f2的定义移到约束之前
f1=@NLexpression(ALT,F/FF);
f2=@NLexpression(ALT,1/k7);
#constraints--------------------------------------------------------
@NLconstraint(ALT, f(-L) <= 1/400);
@NLconstraint(ALT, f1 <=y);
#objectivefunction---------------------------------------------------------
#-------------------------------------------------------------------------
@NLobjective(ALT,Min,y);
optimize!(ALT);
#--------------------------------------------------------------------------
f1min=JuMP.value(y);
LL=JuMP.value(L);
nn=JuMP.value(n);
hh=JuMP.value(h);

修改后运行即可正常求解，不会再触发该报错。

内容的提问来源于stack exchange，提问作者Soma