Improving Performance on 'Easy' Problems

Answered

Nate MacFadden

• March 25, 2023 15:34

I am new to Gurobi, so please excuse any naive mistakes.

In my research, I must solve a collection of 'easy' feasibility problems: given a (non-pointed, convex) cone defined by m~=1500 (sparse) hyperplanes in 680 dimensions, I must find a point strictly in the interior of this cone. Each hyperplane has either 3 or 4 non-zero values (all values are either 1,-1,2, or -2). This must be done for many similar cones, so I am trying to optimize performance as much as possible.

One can organize these problems in a graph, such that each node refers to a cone feasibility problem. In this organization, if two nodes are connected by an edge, then they differ by at most 4 hyperplanes. I have used Gurobi to solve this problem using the (potentially dual? I'm not sure) simplex method and warm starts. Explicitly, I

1. impose an arbitrary lower bound, eps (canonically chosen eps=1), on how close the found point can be from each hyperplane (so as to get a point in the strict interior) and
2. (arbitrarily) setting an objective of minimizing the sum of the distances to each hyperplane.

With an LP defined as above, it takes ~1000 iterations (~0.065s on my laptop) to solve the first feasibility problem, including model definition. For subsequent feasibility problems, it takes ~10 iterations (~0.014s).

While I am pleased with the decrease in iterations for subsequent problems, I was hoping for a larger decrease in run-time. It seems like I am taking silly run-time hits like ~0.004s to simply update the constraints. Normally, these would be negligible, but the 'easiness' of the problem means that such hits are quite significant.

Are there recommended ways to speed up this problem? I may be able to 'concatenate' dimensions for each feasibility problem, solving two at once (i.e., first 680 dimensions refer to one problem, latter 680 dimensions refer to another; There'd be ~3000 constraints). If the cost in 'warm-starting' is nonlinear, then maybe this would help, but I'd want to have a good suspicion of that before I implement it (as it would take a bit of time to organize the problem in this way).

It makes sense to give an impression of scale. I have more problems then I could ever hope to solve (~10^400). I won't get into details why so as not to go on a tangent about my research, but it'd be great if I could get >millions of solutions per hour. This would mean reducing run-times to <~0.004s. Given the previously quoted time to modify constraints, this goal may be impossible, but I'd like to speed things up as much as possible regardless.

 

Thanks!

Related to

• Performance
• Warm Start
• Tuner

0

• 

  Jaromił Najman

  Gurobi Staff

  • March 27, 2023 07:44

  Hi Nate,

  It seems like I am taking silly run-time hits like ~0.004s to simply update the constraints. Normally, these would be negligible, but the 'easiness' of the problem means that such hits are quite significant.

  How exactly are you updating your constraints in between two solves? Could you please post a code snippet? In best case even a minimal reproducible example?

  Are there recommended ways to speed up this problem?

  You should definitely try Gurobi's automatic parameter tuning tool (an older video can be found here). This way, you can let Gurobi find parameters to decrease running time for your base model which then hopefully would apply to the modified models as well. Since your LP can be solved very quickly, it should be enought to let the parameter tool run for a couple of hours to hopefully find parameters which improve performance of your LP. Also experimenting with the LPWarmStart parameter might be useful.

  Impose an arbitrary lower bound, eps (canonically chosen eps=1), on how close the found point can be from each hyperplane (so as to get a point in the strict interior) and

  Did you try experimenting with different values of eps?

  (arbitrarily) setting an objective of minimizing the sum of the distances to each hyperplane.

  A different objective function might improve or hurt performance. Did you try solving without any objective function?

  Best regards, 
  Jaromił

  0
• 

  Nate MacFadden

  • March 31, 2023 15:44
  • Edited

  

  

  

  Hello Jaromił,
  Unfortunately, I lost my drafted response. I will recreate it here.

  First, please note an error in my previous message: the hyperplane constraints can have other integer values, but said values will be rare. It will predominantly be made of +/-1 and +/-2.

  Thank you for all of the help! I will respond point-by-point:

  1. I have attached a code snippet at the end of this message. The nature of constraints in this problem are quite important, so I unfortunately have to include long lists of constraints. My apologies for the bulk. In the future, is there a way to upload this as a file?
  2. I have not heard of either the parameter tuning tool or LPWarmStart. I imagine that the default value of 1 would be a good choice, but I should experiment with setting LPWarmStart=2. Thank you very much for those references!
  3. Theoretically, any (positive) eps should be allowed. Due to this, I had tried a range of eps, from very small values, to values as large as ~10. I observed no difference in timing. Given that the value of 1 has a nice meaning in my research, and that integers are likely easier for Gurobi, I left it as eps=1.
  4. I tried removing the objective with no noticeable changes to the runtime on my computer.

  Below I attach my code. Given that my reports were based off of my local computer, your timings will likely differ. Even just running this code on my computer at different times (e.g., right after a restart, right before a restart, etc.), I observe different runtimes. Thus the previously quoted times are just meant to be representative. Further, given the small run-times, my method of profiling non-negligibly skews up the run-times.

   

  Also, thank you again, very much, for the help.,

  Nate

  import gurobipy as gp
  import time
  
  # Define hyperplanes
  # ------------------
  H0_sparse = [{148: -1, 193: -1, 282: 1, 24: 1}, {148: -1, 282: -1, 193: 1, 53: 1}, {193: -1, 282: -1, 148: 1, 363: 1}, {148: -1, 24: -1, 193: 1, 14: 1}, {193: -1, 24: -1, 148: 1, 35: 1}, {148: -1, 53: -1, 282: 1, 28: 1}, {282: -1, 53: -1, 148: 1, 3: 1}, {148: -1, 14: -1, 24: 1, 28: 1}, {148: -1, 28: -1, 14: 1, 53: 1}, {14: -1, 28: -1, 148: 1, 1: 1}, {193: -1, 256: -1, 363: 1, 35: 1}, {193: -1, 363: -1, 256: 1, 282: 1}, {256: -2, 193: 1, 334: 1}, {193: -1, 35: -1, 256: 1, 24: 1}, {256: -1, 35: -1, 193: 1, 46: 1}, {282: -2, 193: 1, 3: 1}, {256: -2, 363: 1, 46: 1}, {334: -3, 363: 1, 256: 1, 2: 1}, {256: -1, 46: -1, 334: 1, 35: 1}, {334: -1, 46: -1, 256: 1, 57: 1}, {334: -2, 363: 1, 67: 1}, {363: -2, 334: 1, 3: 1}, {67: -2, 2: 1, 57: 1}, {57: -2, 46: 1, 67: 1}, {282: -2, 363: 1, 53: 1}, {363: -4, 3: 2, 282: 1, 2: 1}, {122: -1, 125: -1, 219: 1, 7: 1}, {122: -1, 219: -1, 125: 1, 53: 1}, {125: -1, 219: -1, 122: 1, 226: 1}, {122: -1, 7: -1, 125: 1, 6: 1}, {125: -1, 7: -1, 122: 1, 8: 1}, {122: -1, 53: -1, 219: 1, 28: 1}, {219: -1, 53: -1, 122: 1, 3: 1}, {122: -1, 6: -1, 7: 1, 28: 1}, {122: -1, 28: -1, 6: 1, 53: 1}, {6: -1, 28: -1, 122: 1, 1: 1}, {125: -1, 128: -1, 226: 1, 8: 1}, {125: -1, 226: -1, 128: 1, 219: 1}, {128: -1, 226: -1, 125: 1, 233: 1}, {125: -1, 8: -1, 128: 1, 7: 1}, {128: -1, 8: -1, 125: 1, 9: 1}, {219: -2, 125: 1, 3: 1}, {128: -1, 131: -1, 233: 1, 9: 1}, {128: -1, 233: -1, 131: 1, 226: 1}, {131: -1, 233: -1, 128: 1, 241: 1}, {128: -1, 9: -1, 131: 1, 8: 1}, {131: -1, 9: -1, 128: 1, 10: 1}, {226: -3, 233: 1, 128: 1, 3: 1}, {131: -1, 134: -1, 241: 1, 10: 1}, {131: -1, 241: -1, 134: 1, 233: 1}, {134: -1, 241: -1, 131: 1, 249: 1}, {131: -1, 10: -1, 134: 1, 9: 1}, {134: -1, 10: -1, 131: 1, 11: 1}, {233: -4, 241: 2, 131: 1, 3: 1}, {134: -1, 137: -1, 249: 1, 11: 1}, {134: -1, 249: -1, 137: 1, 241: 1}, {137: -1, 249: -1, 134: 1, 258: 1}, {134: -1, 11: -1, 137: 1, 10: 1}, {137: -1, 11: -1, 134: 1, 12: 1}, {241: -5, 249: 3, 134: 1, 3: 1}, {137: -1, 141: -1, 258: 1, 12: 1}, {137: -1, 258: -1, 141: 1, 249: 1}, {141: -1, 258: -1, 137: 1, 266: 1}, {137: -1, 12: -1, 141: 1, 11: 1}, {141: -1, 12: -1, 137: 1, 13: 1}, {249: -6, 258: 4, 137: 1, 3: 1}, {141: -1, 145: -1, 266: 1, 13: 1}, {141: -1, 266: -1, 145: 1, 258: 1}, {145: -1, 266: -1, 141: 1, 275: 1}, {141: -1, 13: -1, 145: 1, 12: 1}, {145: -1, 13: -1, 141: 1, 15: 1}, {258: -7, 266: 5, 141: 1, 3: 1}, {145: -1, 150: -1, 275: 1, 15: 1}, {145: -1, 275: -1, 150: 1, 266: 1}, {150: -1, 275: -1, 145: 1, 284: 1}, {145: -1, 15: -1, 150: 1, 13: 1}, {150: -1, 15: -1, 145: 1, 16: 1}, {266: -8, 275: 6, 145: 1, 3: 1}, {150: -1, 154: -1, 284: 1, 16: 1}, {150: -1, 284: -1, 154: 1, 275: 1}, {154: -1, 284: -1, 150: 1, 292: 1}, {150: -1, 16: -1, 154: 1, 15: 1}, {154: -1, 16: -1, 150: 1, 17: 1}, {275: -9, 284: 7, 150: 1, 3: 1}, {154: -1, 158: -1, 292: 1, 17: 1}, {154: -1, 292: -1, 158: 1, 284: 1}, {158: -1, 292: -1, 154: 1, 301: 1}, {154: -1, 17: -1, 158: 1, 16: 1}, {158: -1, 17: -1, 154: 1, 18: 1}, {284: -10, 292: 8, 154: 1, 3: 1}, {158: -1, 163: -1, 301: 1, 18: 1}, {158: -1, 301: -1, 163: 1, 292: 1}, {163: -1, 301: -1, 158: 1, 309: 1}, {158: -1, 18: -1, 163: 1, 17: 1}, {163: -1, 18: -1, 158: 1, 19: 1}, {292: -11, 301: 9, 158: 1, 3: 1}, {163: -1, 168: -1, 309: 1, 19: 1}, {163: -1, 309: -1, 168: 1, 301: 1}, {168: -1, 309: -1, 163: 1, 318: 1}, {163: -1, 19: -1, 168: 1, 18: 1}, {168: -1, 19: -1, 163: 1, 20: 1}, {301: -12, 309: 10, 163: 1, 3: 1}, {168: -1, 173: -1, 318: 1, 20: 1}, {168: -1, 318: -1, 173: 1, 309: 1}, {173: -1, 318: -1, 168: 1, 327: 1}, {168: -1, 20: -1, 173: 1, 19: 1}, {173: -1, 20: -1, 168: 1, 21: 1}, {309: -13, 318: 11, 168: 1, 3: 1}, {173: -1, 178: -1, 327: 1, 21: 1}, {173: -1, 327: -1, 178: 1, 318: 1}, {178: -1, 327: -1, 173: 1, 337: 1}, {173: -1, 21: -1, 178: 1, 20: 1}, {178: -1, 21: -1, 173: 1, 22: 1}, {318: -14, 327: 12, 173: 1, 3: 1}, {178: -1, 184: -1, 337: 1, 22: 1}, {178: -1, 337: -1, 184: 1, 327: 1}, {184: -1, 337: -1, 178: 1, 346: 1}, {178: -1, 22: -1, 184: 1, 21: 1}, {184: -1, 22: -1, 178: 1, 23: 1}, {327: -15, 337: 13, 178: 1, 3: 1}, {184: -1, 190: -1, 346: 1, 23: 1}, {184: -1, 346: -1, 190: 1, 337: 1}, {190: -1, 346: -1, 184: 1, 356: 1}, {184: -1, 23: -1, 190: 1, 22: 1}, {190: -1, 23: -1, 184: 1, 25: 1}, {337: -16, 346: 14, 184: 1, 3: 1}, {190: -1, 197: -1, 356: 1, 25: 1}, {190: -1, 356: -1, 197: 1, 346: 1}, {197: -1, 356: -1, 190: 1, 366: 1}, {190: -1, 25: -1, 197: 1, 23: 1}, {197: -1, 25: -1, 190: 1, 26: 1}, {346: -17, 356: 15, 190: 1, 3: 1}, {197: -1, 203: -1, 366: 1, 26: 1}, {197: -1, 366: -1, 203: 1, 356: 1}, {203: -1, 366: -1, 197: 1, 375: 1}, {197: -1, 26: -1, 203: 1, 25: 1}, {203: -1, 26: -1, 197: 1, 27: 1}, {356: -18, 366: 16, 197: 1, 3: 1}, {203: -1, 210: -1, 375: 1, 27: 1}, {203: -1, 375: -1, 210: 1, 366: 1}, {210: -1, 375: -1, 203: 1, 384: 1}, {203: -1, 27: -1, 210: 1, 26: 1}, {210: -1, 27: -1, 203: 1, 29: 1}, {366: -19, 375: 17, 203: 1, 3: 1}, {210: -1, 216: -1, 384: 1, 29: 1}, {210: -1, 384: -1, 216: 1, 375: 1}, {216: -1, 384: -1, 210: 1, 393: 1}, {210: -1, 29: -1, 216: 1, 27: 1}, {216: -1, 29: -1, 210: 1, 30: 1}, {375: -20, 384: 18, 210: 1, 3: 1}, {216: -1, 223: -1, 393: 1, 30: 1}, {216: -1, 393: -1, 223: 1, 384: 1}, {223: -1, 393: -1, 216: 1, 403: 1}, {216: -1, 30: -1, 223: 1, 29: 1}, {223: -1, 30: -1, 216: 1, 31: 1}, {384: -21, 393: 19, 216: 1, 3: 1}, {223: -1, 230: -1, 403: 1, 31: 1}, {223: -1, 403: -1, 230: 1, 393: 1}, {230: -1, 403: -1, 223: 1, 414: 1}, {223: -1, 31: -1, 230: 1, 30: 1}, {230: -1, 31: -1, 223: 1, 32: 1}, {393: -22, 403: 20, 223: 1, 3: 1}, {230: -1, 237: -1, 414: 1, 32: 1}, {230: -1, 414: -1, 237: 1, 403: 1}, {237: -1, 414: -1, 230: 1, 422: 1}, {230: -1, 32: -1, 237: 1, 31: 1}, {237: -1, 32: -1, 230: 1, 33: 1}, {403: -23, 414: 21, 230: 1, 3: 1}, {237: -1, 245: -1, 422: 1, 33: 1}, {237: -1, 422: -1, 245: 1, 414: 1}, {245: -1, 422: -1, 237: 1, 432: 1}, {237: -1, 33: -1, 245: 1, 32: 1}, {245: -1, 33: -1, 237: 1, 34: 1}, {414: -24, 422: 22, 237: 1, 3: 1}, {245: -1, 253: -1, 432: 1, 34: 1}, {245: -1, 432: -1, 253: 1, 422: 1}, {253: -1, 432: -1, 245: 1, 442: 1}, {245: -1, 34: -1, 253: 1, 33: 1}, {253: -1, 34: -1, 245: 1, 36: 1}, {422: -25, 432: 23, 245: 1, 3: 1}, {253: -1, 262: -1, 442: 1, 36: 1}, {253: -1, 442: -1, 262: 1, 432: 1}, {262: -1, 442: -1, 253: 1, 449: 1}, {253: -1, 36: -1, 262: 1, 34: 1}, {262: -1, 36: -1, 253: 1, 37: 1}, {432: -26, 442: 24, 253: 1, 3: 1}, {262: -1, 270: -1, 449: 1, 37: 1}, {262: -1, 449: -1, 270: 1, 442: 1}, {270: -1, 449: -1, 262: 1, 86: 1}, {262: -1, 37: -1, 270: 1, 36: 1}, {270: -1, 37: -1, 262: 1, 38: 1}, {442: -27, 449: 25, 262: 1, 3: 1}, {270: -1, 279: -1, 38: 1, 86: 1}, {270: -1, 38: -1, 279: 1, 37: 1}, {279: -1, 38: -1, 270: 1, 39: 1}, {270: -1, 86: -1, 279: 1, 449: 1}, {279: -2, 270: 1, 288: 1}, {449: -28, 86: 26, 270: 1, 3: 1}, {279: -2, 39: 1, 86: 1}, {279: -1, 39: -1, 288: 1, 38: 1}, {288: -1, 39: -1, 279: 1, 40: 1}, {288: -2, 279: 1, 296: 1}, {288: -3, 296: 1, 40: 1, 86: 1}, {288: -1, 40: -1, 296: 1, 39: 1}, {296: -1, 40: -1, 288: 1, 42: 1}, {296: -2, 288: 1, 305: 1}, {296: -4, 305: 2, 42: 1, 86: 1}, {296: -1, 42: -1, 305: 1, 40: 1}, {305: -1, 42: -1, 296: 1, 43: 1}, {305: -2, 296: 1, 313: 1}, {305: -5, 313: 3, 43: 1, 86: 1}, {305: -1, 43: -1, 313: 1, 42: 1}, {313: -1, 43: -1, 305: 1, 44: 1}, {313: -2, 305: 1, 322: 1}, {313: -6, 322: 4, 44: 1, 86: 1}, {313: -1, 44: -1, 322: 1, 43: 1}, {322: -1, 44: -1, 313: 1, 45: 1}, {322: -2, 313: 1, 331: 1}, {322: -7, 331: 5, 45: 1, 86: 1}, {322: -1, 45: -1, 331: 1, 44: 1}, {331: -1, 45: -1, 322: 1, 47: 1}, {331: -2, 322: 1, 341: 1}, {331: -8, 341: 6, 47: 1, 86: 1}, {331: -1, 47: -1, 341: 1, 45: 1}, {341: -1, 47: -1, 331: 1, 48: 1}, {341: -2, 331: 1, 350: 1}, {341: -9, 350: 7, 48: 1, 86: 1}, {341: -1, 48: -1, 350: 1, 47: 1}, {350: -1, 48: -1, 341: 1, 49: 1}, {350: -2, 341: 1, 360: 1}, {350: -10, 360: 8, 49: 1, 86: 1}, {350: -1, 49: -1, 360: 1, 48: 1}, {360: -1, 49: -1, 350: 1, 50: 1}, {360: -2, 350: 1, 370: 1}, {360: -11, 370: 9, 50: 1, 86: 1}, {360: -1, 50: -1, 370: 1, 49: 1}, {370: -1, 50: -1, 360: 1, 51: 1}, {370: -2, 360: 1, 379: 1}, {370: -12, 379: 10, 51: 1, 86: 1}, {370: -1, 51: -1, 379: 1, 50: 1}, {379: -1, 51: -1, 370: 1, 52: 1}, {379: -2, 370: 1, 388: 1}, {379: -13, 388: 11, 52: 1, 86: 1}, {379: -1, 52: -1, 388: 1, 51: 1}, {388: -1, 52: -1, 379: 1, 54: 1}, {388: -2, 379: 1, 397: 1}, {388: -14, 397: 12, 54: 1, 86: 1}, {388: -1, 54: -1, 397: 1, 52: 1}, {397: -1, 54: -1, 388: 1, 55: 1}, {397: -2, 388: 1, 407: 1}, {397: -15, 407: 13, 55: 1, 86: 1}, {397: -1, 55: -1, 407: 1, 54: 1}, {407: -1, 55: -1, 397: 1, 56: 1}, {407: -2, 397: 1, 418: 1}, {407: -16, 418: 14, 56: 1, 86: 1}, {407: -1, 56: -1, 418: 1, 55: 1}, {418: -1, 56: -1, 407: 1, 58: 1}, {418: -2, 407: 1, 426: 1}, {418: -17, 426: 15, 58: 1, 86: 1}, {418: -1, 58: -1, 426: 1, 56: 1}, {426: -1, 58: -1, 418: 1, 59: 1}, {426: -2, 418: 1, 436: 1}, {426: -18, 436: 16, 59: 1, 86: 1}, {426: -1, 59: -1, 436: 1, 58: 1}, {436: -1, 59: -1, 426: 1, 60: 1}, {436: -2, 426: 1, 446: 1}, {436: -19, 446: 17, 60: 1, 86: 1}, {436: -1, 60: -1, 446: 1, 59: 1}, {446: -1, 60: -1, 436: 1, 61: 1}, {446: -2, 436: 1, 453: 1}, {446: -20, 453: 18, 61: 1, 86: 1}, {446: -1, 61: -1, 453: 1, 60: 1}, {453: -1, 61: -1, 446: 1, 62: 1}, {453: -2, 446: 1, 459: 1}, {453: -21, 459: 19, 62: 1, 86: 1}, {453: -1, 62: -1, 459: 1, 61: 1}, {459: -1, 62: -1, 453: 1, 63: 1}, {459: -2, 453: 1, 467: 1}, {459: -22, 467: 20, 63: 1, 86: 1}, {459: -1, 63: -1, 467: 1, 62: 1}, {467: -1, 63: -1, 459: 1, 64: 1}, {467: -2, 459: 1, 472: 1}, {467: -23, 472: 21, 64: 1, 86: 1}, {467: -1, 64: -1, 472: 1, 63: 1}, {472: -1, 64: -1, 467: 1, 65: 1}, {472: -2, 467: 1, 477: 1}, {472: -24, 477: 22, 65: 1, 86: 1}, {472: -1, 65: -1, 477: 1, 64: 1}, {477: -1, 65: -1, 472: 1, 66: 1}, {477: -2, 472: 1, 482: 1}, {477: -25, 482: 23, 66: 1, 86: 1}, {477: -1, 66: -1, 482: 1, 65: 1}, {482: -1, 66: -1, 477: 1, 68: 1}, {482: -2, 477: 1, 485: 1}, {482: -26, 485: 24, 68: 1, 86: 1}, {482: -1, 68: -1, 485: 1, 66: 1}, {485: -1, 68: -1, 482: 1, 69: 1}, {485: -2, 482: 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{53: -2, 3: 1, 28: 1}, {299: -1, 28: -1, 41: 1, 53: 1}, {41: -1, 28: -1, 299: 1, 1: 1}, {206: -2, 4: 1, 24: 1}, {206: -3, 4: 1, 273: 1, 14: 1}, {273: -2, 206: 1, 353: 1}, {206: -1, 24: -1, 273: 1, 14: 1}, {273: -1, 24: -1, 206: 1, 35: 1}, {4: -1, 14: -1, 206: 1, 41: 1}, {273: -3, 353: 1, 4: 1, 35: 1}, {353: -3, 4: 1, 273: 1, 2: 1}, {273: -1, 35: -1, 353: 1, 24: 1}, {353: -1, 35: -1, 273: 1, 46: 1}, {353: -2, 4: 1, 67: 1}, {67: -2, 2: 1, 57: 1}, {46: -2, 35: 1, 57: 1}, {57: -2, 46: 1, 67: 1}, {41: -2, 1: 1, 4: 1}, {161: -2, 4: 1, 7: 1}, {161: -2, 166: 1, 41: 1}, {166: -2, 161: 1, 171: 1}, {161: -1, 7: -1, 166: 1, 6: 1}, {166: -1, 7: -1, 161: 1, 8: 1}, {161: -1, 41: -1, 4: 1, 6: 1}, {161: -1, 6: -1, 41: 1, 7: 1}, {41: -1, 6: -1, 161: 1, 1: 1}, {166: -3, 171: 1, 4: 1, 8: 1}, {171: -2, 166: 1, 176: 1}, {166: -1, 8: -1, 171: 1, 7: 1}, {171: -1, 8: -1, 166: 1, 9: 1}, {171: -4, 176: 2, 4: 1, 9: 1}, {176: -2, 171: 1, 182: 1}, {171: -1, 9: -1, 176: 1, 8: 1}, {176: -1, 9: -1, 171: 1, 10: 1}, {176: -5, 182: 3, 4: 1, 10: 1}, {182: -2, 176: 1, 188: 1}, {176: -1, 10: -1, 182: 1, 9: 1}, {182: -1, 10: -1, 176: 1, 11: 1}, {182: -6, 188: 4, 4: 1, 11: 1}, {188: -2, 182: 1, 195: 1}, {182: -1, 11: -1, 188: 1, 10: 1}, {188: -1, 11: -1, 182: 1, 12: 1}, {188: -7, 195: 5, 4: 1, 12: 1}, {195: -2, 188: 1, 201: 1}, {188: -1, 12: -1, 195: 1, 11: 1}, {195: -1, 12: -1, 188: 1, 13: 1}, {195: -8, 201: 6, 4: 1, 13: 1}, {201: -2, 195: 1, 208: 1}, {195: -1, 13: -1, 201: 1, 12: 1}, {201: -1, 13: -1, 195: 1, 15: 1}, {201: -9, 208: 7, 4: 1, 15: 1}, {208: -2, 201: 1, 214: 1}, {201: -1, 15: -1, 208: 1, 13: 1}, {208: -1, 15: -1, 201: 1, 16: 1}, {208: -10, 214: 8, 4: 1, 16: 1}, {214: -2, 208: 1, 221: 1}, {208: -1, 16: -1, 214: 1, 15: 1}, {214: -1, 16: -1, 208: 1, 17: 1}, {214: -11, 221: 9, 4: 1, 17: 1}, {221: -2, 214: 1, 228: 1}, {214: -1, 17: -1, 221: 1, 16: 1}, {221: -1, 17: -1, 214: 1, 18: 1}, {221: -12, 228: 10, 4: 1, 18: 1}, {228: -2, 221: 1, 235: 1}, {221: -1, 18: -1, 228: 1, 17: 1}, {228: -1, 18: -1, 221: 1, 19: 1}, {228: -13, 235: 11, 4: 1, 19: 1}, {235: -2, 228: 1, 243: 1}, {228: -1, 19: -1, 235: 1, 18: 1}, {235: -1, 19: -1, 228: 1, 20: 1}, {235: -14, 243: 12, 4: 1, 20: 1}, {243: -2, 235: 1, 251: 1}, {235: -1, 20: -1, 243: 1, 19: 1}, {243: -1, 20: -1, 235: 1, 21: 1}, {243: -15, 251: 13, 4: 1, 21: 1}, {251: -2, 243: 1, 260: 1}, {243: -1, 21: -1, 251: 1, 20: 1}, {251: -1, 21: -1, 243: 1, 22: 1}, {251: -16, 260: 14, 4: 1, 22: 1}, {260: -2, 251: 1, 268: 1}, {251: -1, 22: -1, 260: 1, 21: 1}, {260: -1, 22: -1, 251: 1, 23: 1}, {260: -17, 268: 15, 4: 1, 23: 1}, {268: -2, 260: 1, 277: 1}, {260: -1, 23: -1, 268: 1, 22: 1}, {268: -1, 23: -1, 260: 1, 25: 1}, {268: -18, 277: 16, 4: 1, 25: 1}, {277: -2, 268: 1, 286: 1}, {268: -1, 25: -1, 277: 1, 23: 1}, {277: -1, 25: -1, 268: 1, 26: 1}, {277: -19, 286: 17, 4: 1, 26: 1}, {286: -2, 277: 1, 294: 1}, {277: -1, 26: -1, 286: 1, 25: 1}, {286: -1, 26: -1, 277: 1, 27: 1}, {286: -20, 294: 18, 4: 1, 27: 1}, {294: -2, 286: 1, 303: 1}, {286: -1, 27: -1, 294: 1, 26: 1}, {294: -1, 27: -1, 286: 1, 29: 1}, {294: -21, 303: 19, 4: 1, 29: 1}, {303: -2, 294: 1, 311: 1}, {294: -1, 29: -1, 303: 1, 27: 1}, {303: -1, 29: -1, 294: 1, 30: 1}, {303: -22, 311: 20, 4: 1, 30: 1}, {311: -2, 303: 1, 320: 1}, {303: -1, 30: -1, 311: 1, 29: 1}, {311: -1, 30: -1, 303: 1, 31: 1}, {311: -23, 320: 21, 4: 1, 31: 1}, {320: -2, 311: 1, 329: 1}, {311: -1, 31: -1, 320: 1, 30: 1}, {320: -1, 31: -1, 311: 1, 32: 1}, {320: -24, 329: 22, 4: 1, 32: 1}, {329: -2, 320: 1, 339: 1}, {320: -1, 32: -1, 329: 1, 31: 1}, {329: -1, 32: -1, 320: 1, 33: 1}, {329: -25, 339: 23, 4: 1, 33: 1}, {339: -2, 329: 1, 348: 1}, {329: -1, 33: -1, 339: 1, 32: 1}, {339: -1, 33: -1, 329: 1, 34: 1}, {339: -26, 348: 24, 4: 1, 34: 1}, {348: -2, 339: 1, 358: 1}, {339: -1, 34: -1, 348: 1, 33: 1}, {348: -1, 34: -1, 339: 1, 36: 1}, {348: -27, 358: 25, 4: 1, 36: 1}, {358: -2, 348: 1, 368: 1}, {348: -1, 36: -1, 358: 1, 34: 1}, {358: -1, 36: -1, 348: 1, 37: 1}, {358: -28, 368: 26, 4: 1, 37: 1}, {368: -2, 358: 1, 377: 1}, {358: -1, 37: -1, 368: 1, 36: 1}, {368: -1, 37: -1, 358: 1, 38: 1}, {368: -29, 377: 27, 4: 1, 38: 1}, {377: -2, 368: 1, 386: 1}, {368: -1, 38: -1, 377: 1, 37: 1}, {377: -1, 38: -1, 368: 1, 39: 1}, {377: -30, 386: 28, 4: 1, 39: 1}, {386: -2, 377: 1, 395: 1}, {377: -1, 39: -1, 386: 1, 38: 1}, {386: -1, 39: -1, 377: 1, 40: 1}, {386: -31, 395: 29, 4: 1, 40: 1}, {395: -2, 386: 1, 405: 1}, {386: -1, 40: -1, 395: 1, 39: 1}, {395: -1, 40: -1, 386: 1, 42: 1}, {395: -32, 405: 30, 4: 1, 42: 1}, {405: -2, 395: 1, 416: 1}, {395: -1, 42: -1, 405: 1, 40: 1}, {405: -1, 42: -1, 395: 1, 43: 1}, {405: -33, 416: 31, 4: 1, 43: 1}, {416: -2, 405: 1, 424: 1}, {405: -1, 43: -1, 416: 1, 42: 1}, {416: -1, 43: -1, 405: 1, 44: 1}, {416: -34, 424: 32, 4: 1, 44: 1}, {424: -2, 416: 1, 434: 1}, {416: -1, 44: -1, 424: 1, 43: 1}, {424: -1, 44: -1, 416: 1, 45: 1}, {424: -35, 434: 33, 4: 1, 45: 1}, {434: -2, 424: 1, 444: 1}, {424: -1, 45: -1, 434: 1, 44: 1}, {434: -1, 45: -1, 424: 1, 47: 1}, {434: -36, 444: 34, 4: 1, 47: 1}, {444: -2, 434: 1, 451: 1}, {434: -1, 47: -1, 444: 1, 45: 1}, {444: -1, 47: -1, 434: 1, 48: 1}, {444: -37, 451: 35, 4: 1, 48: 1}, {451: -2, 444: 1, 457: 1}, {444: -1, 48: -1, 451: 1, 47: 1}, {451: -1, 48: -1, 444: 1, 49: 1}, {451: -38, 457: 36, 4: 1, 49: 1}, {457: -2, 451: 1, 465: 1}, {451: -1, 49: -1, 457: 1, 48: 1}, {457: -1, 49: -1, 451: 1, 50: 1}, {457: -39, 465: 37, 4: 1, 50: 1}, {465: -2, 457: 1, 470: 1}, {457: -1, 50: -1, 465: 1, 49: 1}, {465: -1, 50: -1, 457: 1, 51: 1}, {465: -40, 470: 38, 4: 1, 51: 1}, {470: -2, 465: 1, 475: 1}, {465: -1, 51: -1, 470: 1, 50: 1}, {470: -1, 51: -1, 465: 1, 52: 1}, {470: -41, 475: 39, 4: 1, 52: 1}, {475: -2, 470: 1, 92: 1}, {470: -1, 52: -1, 475: 1, 51: 1}, {475: -1, 52: -1, 470: 1, 54: 1}, {475: -42, 92: 40, 4: 1, 54: 1}, {475: -1, 54: -1, 52: 1, 92: 1}, {54: -1, 92: -1, 475: 1, 55: 1}, {106: -2, 5: 1, 105: 1}, {55: -2, 54: 1, 56: 1}, {56: -2, 55: 1, 58: 1}, {58: -2, 56: 1, 59: 1}, {59: -2, 58: 1, 60: 1}, {60: -2, 59: 1, 61: 1}, {61: -2, 60: 1, 62: 1}, {62: -2, 61: 1, 63: 1}, {63: -2, 62: 1, 64: 1}, {64: -2, 63: 1, 65: 1}, {65: -2, 64: 1, 66: 1}, {66: -2, 65: 1, 68: 1}, {68: -2, 66: 1, 69: 1}, {69: -2, 68: 1, 70: 1}, {70: -2, 69: 1, 71: 1}, {71: -2, 70: 1, 72: 1}, {72: -2, 71: 1, 73: 1}, {73: -2, 72: 1, 74: 1}, {74: -2, 73: 1, 75: 1}, {75: -2, 74: 1, 76: 1}, {76: -2, 75: 1, 77: 1}, {77: -2, 76: 1, 78: 1}, {78: -2, 77: 1, 79: 1}, {79: -2, 78: 1, 81: 1}, {81: -2, 79: 1, 82: 1}, {82: -2, 81: 1, 83: 1}, {83: -2, 82: 1, 85: 1}, {85: -2, 83: 1, 87: 1}, {87: -2, 85: 1, 88: 1}, {88: -2, 87: 1, 90: 1}, {90: -2, 88: 1, 91: 1}, {91: -2, 90: 1, 93: 1}, {93: -2, 91: 1, 95: 1}, {95: -2, 93: 1, 96: 1}, {96: -2, 95: 1, 98: 1}, {98: -2, 96: 1, 100: 1}, {100: -2, 98: 1, 101: 1}, {101: -2, 100: 1, 102: 1}, {102: -2, 101: 1, 104: 1}, {104: -2, 102: 1, 105: 1}, {105: -2, 104: 1, 106: 1}, {429: -2, 4: 1, 86: 1}, {429: -3, 4: 1, 3: 1, 92: 1}, {429: -1, 86: -1, 3: 1, 92: 1}, {86: -1, 92: -1, 429: 1, 97: 1}, {97: -2, 5: 1, 86: 1}, {462: 1, 439: -3, 4: 1, 84: 1}, {462: -2, 439: 1, 92: 1}, {439: -2, 462: 1, 410: 1}, {462: -1, 84: -1, 439: 1, 89: 1}, {439: -1, 84: -1, 462: 1, 80: 1}, {462: -4, 92: 2, 4: 1, 89: 1}, {462: -1, 89: -1, 92: 1, 84: 1}, {89: -1, 92: -1, 462: 1, 94: 1}, {410: -2, 4: 1, 80: 1}, {410: -3, 4: 1, 439: 1, 2: 1}, {439: -1, 80: -1, 410: 1, 84: 1}, {410: -1, 80: -1, 439: 1, 2: 1}, {103: -2, 5: 1, 99: 1}, {99: -2, 103: 1, 94: 1}, {94: -2, 99: 1, 89: 1}];
  
  # Find the difference between the two sets of inequalities
  H0minus1 = [h for h in H0_sparse if (h not in H1_sparse)];
  H1minus0 = [h for h in H1_sparse if (h not in H0_sparse)];
  
  H0minus1ind = [i for i,h in enumerate(H0_sparse) if (h not in H1_sparse)];
  H1minus0ind = [i for i,h in enumerate(H1_sparse) if (h not in H0_sparse)];
  
  # Init timing
  # -----------
  cumtime, reltime = [], [];
  
  cumtime.append([]);
  reltime.append([]);
  t0 = time.time();
  cumtime[-1].append([0,'start problem 1']);
  
  # Create a new model
  # ------------------
  m = gp.Model();
  cumtime[-1].append([time.time()-t0,'defined model']);
  reltime[-1].append([cumtime[-1][-1][0]-cumtime[-1][-2][0],'defined model']);
  
  # Create variables
  var = [];
  for i in range(680):
      var.append(m.addVar(name=f"x_{i}"));
  cumtime[-1].append([time.time()-t0,'added variables']);
  reltime[-1].append([cumtime[-1][-1][0]-cumtime[-1][-2][0],'added variables']);
  
  # Set objective function
  m.setObjective(sum(var), gp.GRB.MINIMIZE)
  cumtime[-1].append([time.time()-t0,'set objective']);
  reltime[-1].append([cumtime[-1][-1][0]-cumtime[-1][-2][0],'set objective']);
  
  # Add constraints
  eps=1;
  cons = [];
  for h in H0_sparse:
      cons.append(m.addConstr(sum([coeff*var[i] for i,coeff in h.items()])>=eps));
  cumtime[-1].append([time.time()-t0,'added constraints']);
  reltime[-1].append([cumtime[-1][-1][0]-cumtime[-1][-2][0],'added constraints']);
  
  # Solve it!
  m.optimize();
  x_sol = [v.X for v in var];
  cumtime[-1].append([time.time()-t0,'solved 1st problem']);
  reltime[-1].append([cumtime[-1][-1][0]-cumtime[-1][-2][0],'solved 1st problem']);
  t1st_gurobi = cumtime[-1][-1][0];
  
  # Solve related problem
  # ---------------------
  cumtime.append([]);
  reltime.append([]);
  t0 = time.time();
  cumtime[-1].append([0,'start problem 2']);
  
  m.remove([cons[i] for i in H0minus1ind]);
  
  cumtime[-1].append([time.time()-t0,'removed old constraints']);
  reltime[-1].append([cumtime[-1][-1][0]-cumtime[-1][-2][0],'removed old constraints']);
  
  cons.append([m.addConstr(sum([coeff*var[i] for i,coeff in h.items()])>=eps) for h in H1minus0]);
  cumtime[-1].append([time.time()-t0,'added new constraints']);
  reltime[-1].append([cumtime[-1][-1][0]-cumtime[-1][-2][0],'added new constraints']);
  
  # Solve it!
  m.optimize();
  x_sol = [v.X for v in var];
  cumtime[-1].append([time.time()-t0,'solved 2nd problem']);
  reltime[-1].append([cumtime[-1][-1][0]-cumtime[-1][-2][0],'solved 2nd problem']);
  t2nd_gurobi = cumtime[-1][-1][0];
  
  # Print results
  # -------------
  print('\n');
  print('results');
  print('-------');
  print('1st solve:');
  print(cumtime[0]);
  print('\n');
  print('2nd solve:');
  print(cumtime[1]);

  0
• 

  Jaromił Najman

  Gurobi Staff

  • April 03, 2023 09:25

  Hi Nate,

  In the future, is there a way to upload this as a file?

  Uploading files in the Community Forum is not possible but we discuss an alternative in Posting to the Community Forum.

  I have not heard of either the parameter tuning tool or LPWarmStart. I imagine that the default value of 1 would be a good choice, but I should experiment with setting LPWarmStart=2. Thank you very much for those references!

  Given the size of the model you posted, I don't think there is much to get here.

  There are a few slight tweaks that you might want to consider.

  Use the addVars method instead of adding each variable one by one. Use gurobipy.quicksum instead of Python's sum method.

  var = m.addVars(680,name="x")
  
  m.setObjective(gp.quicksum(var), gp.GRB.MINIMIZE)
  
  cons = [];
  for h in H0_sparse:
      cons.append(m.addConstr(gp.quicksum(coeff*var[i] for i,coeff in h.items())>=eps))

  Instead of reading each variable solution value one by one, you can get all at once.

  x_sol = m.getAttr("X",var)

  Regarding the modified model. The good news is that Gurobi already picks up the previous solution as warm start. This is the reason why it only needs 10 iterations, so there should be no need for you to do something here.

  Right now you are removing some constraints and then adding new ones. You could try just changing the coefficients of variables in a given constraints, i.e., instead of removing the constraints, try to re-use them by adjusting the variable coefficients accordingly. It might be possible that you would have to add more constraints than you would have to remove. If you know a priori how many constraints you would have at most, then you could add redundant constraints and only change coefficients on those. However, I don't think that this would give any significant boost, given the already extremely low runtime. It might very likely be that the most significant part of the time is spent from translating from Python to C. Thus, I thin, that if you really want to squeeze out the last little bit of model construction/modification performance, you should switch from Python to C.

  Best regards, 
  Jaromił

  0

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