在Visual Basic .NET中再现Excel Solver GRG非线性优化

Question

I am trying to re-produce the following Excel Solver GRG Nonlinear optimization using the Microsoft Solver Foundation in VB.NET (numbers are simplified for the sake of this example):

1. Objective : Total Gas Rate = 100000
2. Variable : Well 1 Oil Rate
3. Constraints : 0 <= Well 1 Gas Rate <= 1000, Well 2 Gas Rate = 2000

This optimization is subject to the following relationships:

1. Well 1 Gas Rate = Well 1 Oil Rate * 5
2. Total Gas Rate = Well 1 Gas Rate + Well 2 Gas Rate

Is it possible to solve such a problem using Solver Foundation? When trying to implement this, the two things I struggled with are:

1. It appears that Solver Foundation models only have two GoalKind's: minimum and maximum. In my case, I am trying to optimize for a specific value. Is there any way to do this?
2. How do I define the above relationships? I would think the latter would be defined as part of the goal definition (eg, model.AddGoal("total_gas_rate", GoalKind.[not sure what goes here], Well1PGasRate + Well2PGasRate ), but how do I define the other one?

Thanks!

Answer 1

This answer only addresses part 1 of your question and in a conceptual manner, but hopefully it is helpful. If you're trying to optimize for a specific value target and the output of your function is output then you could try something like this pseudocode:

minimize(absolute_value(output/target-1))

Effectively, this will give you a value that reaches zero as the output of your function nears the target value. So you can still use an optimization engine that minimizes the final output of your function.