I need to implement a load scheduling algorithm that involves solving an online optimisation problem from a research paper for my Real time systems course.
This convex optimisation problem is setup through Model predictive control or receding horizon control. This problem involves under 100 decision variables. I am just googling about solvers and it would be great if you can give me more accurate suggestions about specific numerical solvers available in python for solving these kinds of cost functions (quadratic + one norm + infinity norm) and constraints (both equality and inequality). I think its convex (single minimum) because the author says so.
*If you are an expert you dont have to read the contents below just click and look at the first attachment and suggest to me a solver or links to a solver in python, Thanks :)*
Full paper at this link: https://github.com/JosePeeterson/pdf_hosting/blob/master/paper_2_RTS.pdf
Please see the cost function and constraints in the attachment.
**Brief description of the problem:**
We want to schedule tasks (i.e. power allocation) that maximises power allocation from renewable sources, W to Electric vehicle (EV) loads, E that have some timing deadlines, di (due to running out of charge). We should minimize the use of grid energy sources, G and only use it in the worst case when EV load demand cannot be satisfied using renewable sources.
In the objective function the matrix W represents renewable energy/power allocation for task i at time step k. we look into N time steps into the future from the current time step, t.
Say we have a renewable energy forecast chart that predicts the maximum output power at future times like in renewable energy generation forecast graph attached. Matrix G is grid generated power/energy also indexed similarly to W and is available at all times. Total power/energy supplied to load E is W + G. phi (flexibility factor) is the term that implicitly brings W into the cost fucntion. we try to keep phi large so that we can always defer load scheduling to future times if renewable power/energy is not sufficiently available for the time being and maybe available in the future. Note: the size/dimension (MXN) of matrix W and G is decreasing as we approach end of active tasks list in the time horizon N. As tasks in active tasks get completed and as we approach the last deadline in active task list M and N are decreasing.
In constraint 7, we put a cap on the maximum renewable energy available for all the M tasks up to N time steps using the renewable energy generation forcast graph attached.
constraint 8 is a conservation equation W and G power/energy supplied equals load energy required, E for the M tasks.
In constriant 9 mi is maximum power that can be supplied to the load due to loads physical limitation.
In contraint 10 and 11, di is the deadline of task i, delta t is time step for within which the optimisation must be solved. ei(k) is the remanining energy required for the task to complete.
From this description please suggest solvers or links to solvers that can be used in python.
Thank you!!
Thanks for your reply, Aparna Sathya Murthy.
I do not have time and do not know how to convert the cost function into a linear program. So I am not sure if I can use the first two links. The third link maybe too generic also.
I have attached some comments from others forums where I posted this question.
https://stackoverflow.com/questions/66137844/recommended-python-solver-for-an-online-optimization-problem
https://realpython.com/linear-programming-python/
check these links may help:-
https://realpython.com/linear-programming-python/
http://www.optimization-online.org/DB_FILE/2008/09/2095.pdf
https://towardsdatascience.com/a-simple-way-to-optimize-something-in-python-740cda7fd3e0
https://apmonitor.com/pdc/index.php/Main/NonlinearProgramming
https://developers.google.com/optimization/introduction/python
https://realpython.com/python-scipy-cluster-optimize/
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