Iterative equations with dependence of Gurobi variables
回答済みHello!
I have a problem in which I want to calculate the value of R. R is calculated with an iterative equation (see figure), that stops at convergence (Rn+1 = Rn). In the summatory, only the tasks j with higher priority (hp) than i are considered. If a task has higher priority or not than other, is evaluated in a Gurobi binary variable. My question is:
How could I implement an iterative process that depends on a Gurobi variable?
I can't find any information or hint.
Many thanks in advance.
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Gurobi Staff
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Hi Ana,
To introduce an iterative algorithm within an optimization model, you have to introduce an optimization variable for each iterative step \(R_{i}^{n}\). Thus, the maximum number of iterations has to be finite and known a priori. Then, you have to introduce each step of the iterative process as an equality constraint. Please note that it is important to set a valid lower and upper bound for each iteration optimization variable \(R_{i}^{n}\).
Best regards,
Jaromił0 -
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Many thanks for your answer, Jaromil.
To know valid bounds for each iteration variable is not a problem. I think I can estimate the maximum number of iterations too.
Do you know where can I find documentation or examples of similar problems?
Many thanks again.
Best,
Ana
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Hi Ana,
I am not aware of any specific examples targeting Gurobi. However, I know a nonlinear example of such an application. Section 5 of Mitsos et al. (2009) describes two similar applications. Therein, the iterative algorithms modeled in an optimization manner are integration algorithms using the central-difference formula and the explicit Euler method. I hope this helps.
Best regards,
Jaromił0 -
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Many thanks again.
Best,
Ana.
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