Excel 求解器样式约束优化/约束编程 R

Question

I'm trying to write some R code to perform constrained optimisation, where the constraints are not of the usual (g(x) < c) type.

An example of the type of problem I am trying to solve is the following:

A company is trying to determine how much to produce each year for the next 5 years, given an assumed price for each year. It can produce upto X per year, but over any given 3 year window can produce no more than 2X. In addition, in any given year, it cannot produce less than 0.5X unless it produces 0X. Other constraints may be equally impossible to write as a set equation (eg if X > a, Y < c).

I'm very comfortable solving this type of thing in Excel Solver, as it's relatively easy to be very flexible with these sort of restrictions (eg each year have an if statement that looks at the quantity produced in current, past, and next year, and returns 0 if less than 2X, sum the if statements in a cell, and set the constraint of that variable equal to 0).

It's just gotten too large to realistically do in excel. I'm pretty comfortable in R but haven't done this sort of thing. If anyone can point me to a useful package or a good way of managing a lot of dynamic constraints rely on If statements etc, I would be super appreciative

Answer 1

You can use IF statements in optimization problems. This will make the problem nonlinear, so you need a nonlinear solver (Excel solver contains GRG2 which is quite a good NLP solver). However, IFs may make the problem discontinuous or non-differentiable. This can cause problems. Eg, the solver may get stuck and report a local optimum, instead of a global one.

It may be better to reformulate the model using binary variables. Often this will make the model otherwise linear. Disadvantage: it often requires some skill and experience to come up with and implement these reformulations. The exact form of these reformulations is often solver-dependent (eg it may depend on whether the solver supports indicator constraints or SOS sets) and very problem-dependent.