Why does it take a long time to establish this matrix constraint?

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Jie Zhu

2024年10月17日 08:50

I would like to know why it takes a long time to establish the second-order cone constraint shown in the following code. Here, a_x has dimensions (1, 33), DRCC_cov_load[t] is a (33×33) positive semi-definite matrix, and a_x_T is the transpose of a_x. What puzzles me is that establishing other second-order cone constraints of this form (with different a_x and b_x) takes almost negligible time, but establishing this particular constraint takes about 20 seconds. I am using an i9-14900HX CPU. I wonder if the modeling speed is related to the sparsity of the matrix? Is there any way to reduce the time required to establish this constraint?

a_x , a_x_T, b_x = B_INV_P_V[i:i+1,:] @ delta_p_t[t], delta_p_t[t].T @ B_INV_P_V[i:i+1,:].T, V_MAX - Bus_V[t,i]   # affine function of uncertainty
lhs = model.addVar()
model.addConstr(lhs == b_x - a_x @ DRCC_mean_load[t])
model.addConstr(DRCC_cof*(a_x @ DRCC_cov_load[t] @ a_x_T) <= lhs * lhs)

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Riley Clement
Gurobi Staff

2024年10月20日 04:38
Hi Jie,

Any chance of creating a reproducible example using numpy.save to write the data to file?

- Riley
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Jie Zhu

2024年10月20日 08:13
https://1drv.ms/u/c/f3004033f0c5eb61/EXSrJgerUQZCiy6dAO7zcyIBtaTUnggCXcqKpQBBHTWteA?e=yrF9Jt

Thank you so much for your response. I've uploaded the part of my code that takes a long time to run, along with the data used (saved in .npy format), to this OneDrive link. I'd really appreciate it if you could take a look and suggest any ways to improve the code's execution speed. Thanks again!
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Riley Clement
Gurobi Staff

2024年10月20日 23:00
When I run the constraint I get the following warning:
```
Chained matrix multiplications of MVars is inefficient, collect numeric terms first when building expressions
```
Do you see this warning with your version of Gurobi?

What puzzles me is that establishing other second-order cone constraints of this form (with different a_x and b_x) takes almost negligible time

Were the a_x and b_x in this case MVars? In your current code they are MLinExpr, which is why the warning is being issued.
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Jie Zhu

2024年10月21日 00:46
Thank you for your reply, when I define a_x and b_x as Mvar the speed of the computation is greatly improved!

In my complete code, I used the warning library, which prevented this warning from appearing. However, when I uploaded a simplified version of the code, I encountered the warning. I referred to the link https://support.gurobi.com/hc/en-us/articles/9191776582801-What-should-I-do-upon-RuntimeWarning-Chained-matrix-multiplications-of-MVars, but the chained matrix multiplication only contains a single numeric term, so the suggested method from that link did not work.

I updated the code in the new OneDrive link to include faster computation for comparison. I defined a_x and b_x as MVar and found that the warning disappeared and the computation speed improved.

https://onedrive.live.com/?redeem=aHR0cHM6Ly8xZHJ2Lm1zL3UvYy9mMzAwNDAzM2YwYzVlYjYxL0VjdFgxWUZKOUdGQ2dFT0FDREMtRTFNQjN1aWFsQ1Z2MGQ1bmxhUWh5V2JHVGc%5FZT1jTGgzc0k&cid=F3004033F0C5EB61&id=F3004033F0C5EB61%21s81d557cbf44942618043800830be1353&parId=root&o=OneUp

Hopefully, the Gurobi team can optimize this further so that different programming styles can have the same computation speed, thanks again!
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