Two sided constraint is infeasible when the equivalent version using two one sided constraints is not

[jnh277]

Describe the bug
Two sided constraint is infeasible when the equivalent version using two one sided constraints is not.

When I define the below two sided constraint the problem is infeasible

In this problem,
ramp_rate_delta is a positive parameter
meter_power_current and meter_power_previous are continuous variables
slack_below and slack_above are continuous non negative variables

model.addCons(
         -ramp_rate_delta
         <= ((
             meter_power_current
             - meter_power_previous
             + slack_below
             - slack_above)
             <= ramp_rate_delta
         ),
         name=f"ramp_rate_cons_{step}",
     )

However, when I formulate this using two single sided constraints the problem is feasible

    below_cons = model.addCons(
        -ramp_rate_delta
        <=
        meter_power_current
        - meter_power_previous
        + slack_below
    )

    above_cons = model.addCons(
        meter_power_current
        - meter_power_previous
        - slack_above
        <= ramp_rate_delta
    )

To Reproduce
Unsure if this helps, but I have saved the model file for both formulations and attached in zip file

formulations.zip

Expected behavior
The two seemingly equivalent formulations to both be feasible

System

• OS: macOS tahoe
• Version 26
• SCIP version
• installed using uv add pyscipopt

[abb-omidi]

@jnh277,
Hi,

I think your model suffers from numerical issues. This is the solver output I can take by solving both your .cip format:

SCIP> read
*******************************************************
enter filename: "...\formulations\feasible_model.cip"
*******************************************************
read problem <...\formulations\feasible_model.cip>
============

original problem has 80 variables (20 bin, 0 int, 0 impl, 60 cont) and 75 constraints
SCIP> opt

presolving:
problem infeasible or unbounded: variable <t_meter_positive> with objective -1000 can be made infinitely large
presolving (1 rounds: 1 fast, 0 medium, 0 exhaustive):
 3 deleted vars, 0 deleted constraints, 0 added constraints, 0 tightened bounds, 0 added holes, 0 changed sides, 0 changed coefficients
 0 implications, 0 cliques
********************************************************
presolving detected unboundedness (or infeasibility)
********************************************************
Presolving Time: 0.00

SCIP Status        : problem is solved [infeasible or unbounded]
Solving Time (sec) : 0.00
Solving Nodes      : 0
Primal Bound       : +1.00000000000000e+20 (0 solutions)
Dual Bound         : -1.00000000000000e+20
Gap                : infinite

SCIP> read
enter filename: "...\formulations\infeasible_model.cip"

read problem <...\formulations\infeasible_model.cip>
============

WARNING: left hand side of linear constraint greater than right hand side
WARNING:  -> lhs=-0.0736793, rhs=-3.99229
original problem has 80 variables (20 bin, 0 int, 0 impl, 60 cont) and 70 constraints
SCIP>

[jnh277]

Thanks for the response @abb-omidi , I've taken another look at this and I don't a message about unboundedness in the "feasible" version. The output I get is below. However, when I save and load the model I do get the output you show. I am saving the model using model.writeProblem() is there an alternate way or some other way I am meant to save the model?

presolving:
(round 1, fast)       15 del vars, 10 del conss, 0 add conss, 5 chg bounds, 0 chg sides, 0 chg coeffs, 0 upgd conss, 20 impls, 0 clqs
(round 2, fast)       15 del vars, 10 del conss, 0 add conss, 5 chg bounds, 5 chg sides, 0 chg coeffs, 0 upgd conss, 20 impls, 0 clqs
(round 3, fast)       15 del vars, 10 del conss, 0 add conss, 15 chg bounds, 5 chg sides, 0 chg coeffs, 0 upgd conss, 20 impls, 0 clqs
   (0.0s) symmetry computation started: requiring (bin +, int +, cont +), (fixed: bin -, int -, cont -)
   (0.0s) no symmetry present (symcode time: 0.00)
presolving (4 rounds: 4 fast, 1 medium, 1 exhaustive):
 15 deleted vars, 10 deleted constraints, 0 added constraints, 15 tightened bounds, 0 added holes, 5 changed sides, 0 changed coefficients
 20 implications, 0 cliques
presolved problem has 60 variables (10 bin, 0 int, 0 impl, 50 cont) and 65 constraints
     45 constraints of type <linear>
     20 constraints of type <indicator>
Presolving Time: 0.00
 time | node  | left  |LP iter|LP it/n|mem/heur|mdpt |vars |cons |rows |cuts |sepa|confs|strbr|  dualbound   | primalbound  |  gap   | compl. 
p 0.0s|     1 |     0 |     9 |     - |shiftand|   0 |  60 |  65 |  55 |   0 |  0 |   0 |   0 |      --      | 2.220949e+05 |    Inf | unknown
  0.0s|     1 |     0 |    48 |     - |  1189k |   0 |  60 |  65 |  55 |   0 |  0 |   0 |   0 | 2.220949e+05 | 2.220949e+05 |   0.00%| unknown
SCIP Status        : problem is solved [optimal solution found]
Solving Time (sec) : 0.00

[jnh277]

Hey @abb-omidi , I've discovered that the model was not saving correctly (I think because I was wrongly using the .cip format). I have resaved both versions using the .mps format. I have checked that when I load them I get the same outcomes I experience when I solve without saving and loading.

formulations.zip

[abb-omidi]

@jnh277,

As far as I know, the best way to write the problem via PySCIPOpt is to use model.writeProblem(), and the best format to investigate the model is .cip. Actually, there should be no conflict between the different formats in the solving process. I think you need to take a closer look at your math model and its parameters. I tried to solve both new files you provided, and in both cases, the problem was solved to optimality!!!

The output log for the feasible file:

read problem <...\feasible.mps>
============

original problem has 75 variables (20 bin, 0 int, 0 impl, 55 cont) and 75 constraints
SCIP> opt

presolving:
(round 1, fast)       15 del vars, 10 del conss, 0 add conss, 5 chg bounds, 0 chg sides, 0 chg coeffs, 0 upgd conss, 20 impls, 0 clqs
(round 2, fast)       15 del vars, 10 del conss, 0 add conss, 5 chg bounds, 5 chg sides, 0 chg coeffs, 0 upgd conss, 20 impls, 0 clqs
(round 3, fast)       15 del vars, 10 del conss, 0 add conss, 15 chg bounds, 5 chg sides, 0 chg coeffs, 0 upgd conss, 20 impls, 0 clqs
   (0.0s) probing cycle finished: starting next cycle
(round 4, exhaustive) 22 del vars, 10 del conss, 0 add conss, 47 chg bounds, 5 chg sides, 0 chg coeffs, 0 upgd conss, 68 impls, 4 clqs
(round 5, fast)       26 del vars, 21 del conss, 0 add conss, 47 chg bounds, 5 chg sides, 0 chg coeffs, 0 upgd conss, 68 impls, 4 clqs
(round 6, fast)       31 del vars, 26 del conss, 0 add conss, 47 chg bounds, 5 chg sides, 0 chg coeffs, 0 upgd conss, 68 impls, 4 clqs
(round 7, fast)       32 del vars, 27 del conss, 0 add conss, 47 chg bounds, 5 chg sides, 0 chg coeffs, 0 upgd conss, 68 impls, 4 clqs
(round 8, fast)       32 del vars, 27 del conss, 0 add conss, 52 chg bounds, 5 chg sides, 0 chg coeffs, 0 upgd conss, 68 impls, 4 clqs
   (0.0s) probing cycle finished: starting next cycle
   (0.0s) symmetry computation started: requiring (bin +, int +, cont +), (fixed: bin -, int -, cont -)
   (0.0s) no symmetry present (symcode time: 0.00)
presolving (9 rounds: 9 fast, 2 medium, 2 exhaustive):
 32 deleted vars, 27 deleted constraints, 0 added constraints, 52 tightened bounds, 0 added holes, 5 changed sides, 0 changed coefficients
 82 implications, 4 cliques
presolved problem has 43 variables (7 bin, 0 int, 0 impl, 36 cont) and 46 constraints
     32 constraints of type <linear>
     14 constraints of type <indicator>
Presolving Time: 0.00

 time | node  | left  |LP iter|LP it/n|mem/heur|mdpt |vars |cons |rows |cuts |sepa|confs|strbr|  dualbound   | primalbound  |  gap   | compl.
p 0.0s|     1 |     0 |    16 |     - |  clique|   0 |  43 |  46 |  46 |   0 |  0 |   0 |   0 | 2.199324e+05 | 6.305983e+05 | 186.72%| unknown
  0.0s|     1 |     0 |    37 |     - |  1150k |   0 |  43 |  46 |  46 |   0 |  0 |   4 |   0 | 2.220949e+05 | 6.305983e+05 | 183.93%| unknown
r 0.0s|     1 |     0 |    37 |     - |randroun|   0 |  43 |  46 |  46 |   0 |  0 |   4 |   0 | 2.220949e+05 | 2.220949e+05 |   0.00%| unknown
  0.0s|     1 |     0 |    37 |     - |  1150k |   0 |  43 |  46 |  46 |   0 |  0 |   4 |   0 | 2.220949e+05 | 2.220949e+05 |   0.00%| unknown

SCIP Status        : problem is solved [optimal solution found]
Solving Time (sec) : 0.00
Solving Nodes      : 1
Primal Bound       : +2.22094898483744e+05 (3 solutions)
Dual Bound         : +2.22094898483744e+05
Gap                : 0.00 %

The output log for the infeasible one:

read problem <...\infeasible.mps>
============

original problem has 80 variables (20 bin, 0 int, 0 impl, 60 cont) and 70 constraints
SCIP> opt

presolving:
(round 1, fast)       15 del vars, 10 del conss, 0 add conss, 5 chg bounds, 0 chg sides, 0 chg coeffs, 0 upgd conss, 20 impls, 0 clqs
(round 2, fast)       15 del vars, 10 del conss, 0 add conss, 5 chg bounds, 5 chg sides, 0 chg coeffs, 0 upgd conss, 20 impls, 0 clqs
(round 3, fast)       15 del vars, 10 del conss, 0 add conss, 15 chg bounds, 5 chg sides, 0 chg coeffs, 0 upgd conss, 20 impls, 0 clqs
   (0.0s) probing cycle finished: starting next cycle
(round 4, exhaustive) 22 del vars, 10 del conss, 0 add conss, 47 chg bounds, 5 chg sides, 0 chg coeffs, 0 upgd conss, 68 impls, 4 clqs
(round 5, fast)       26 del vars, 20 del conss, 0 add conss, 47 chg bounds, 5 chg sides, 0 chg coeffs, 0 upgd conss, 68 impls, 4 clqs
(round 6, fast)       30 del vars, 24 del conss, 0 add conss, 47 chg bounds, 5 chg sides, 0 chg coeffs, 0 upgd conss, 68 impls, 4 clqs
(round 7, fast)       31 del vars, 25 del conss, 0 add conss, 47 chg bounds, 5 chg sides, 0 chg coeffs, 0 upgd conss, 68 impls, 4 clqs
(round 8, fast)       31 del vars, 25 del conss, 0 add conss, 48 chg bounds, 5 chg sides, 0 chg coeffs, 0 upgd conss, 68 impls, 4 clqs
   (0.0s) probing cycle finished: starting next cycle
   (0.0s) symmetry computation started: requiring (bin +, int +, cont +), (fixed: bin -, int -, cont -)
   (0.0s) no symmetry present (symcode time: 0.00)
presolving (9 rounds: 9 fast, 2 medium, 2 exhaustive):
 31 deleted vars, 25 deleted constraints, 0 added constraints, 48 tightened bounds, 0 added holes, 5 changed sides, 0 changed coefficients
 82 implications, 4 cliques
presolved problem has 49 variables (7 bin, 0 int, 0 impl, 42 cont) and 43 constraints
     29 constraints of type <linear>
     14 constraints of type <indicator>
Presolving Time: 0.00

 time | node  | left  |LP iter|LP it/n|mem/heur|mdpt |vars |cons |rows |cuts |sepa|confs|strbr|  dualbound   | primalbound  |  gap   | compl.
p 0.0s|     1 |     0 |     7 |     - |  clique|   0 |  49 |  43 |  43 |   0 |  0 |   0 |   0 | 2.177949e+05 | 6.284607e+05 | 188.56%| unknown
  0.0s|     1 |     0 |    28 |     - |  3344k |   0 |  49 |  43 |  43 |   0 |  0 |  10 |   0 | 2.199574e+05 | 6.284607e+05 | 185.72%| unknown
r 0.0s|     1 |     0 |    28 |     - |randroun|   0 |  49 |  43 |  43 |   0 |  0 |  10 |   0 | 2.199574e+05 | 2.199574e+05 |   0.00%| unknown
  0.0s|     1 |     0 |    28 |     - |  3344k |   0 |  49 |  43 |  43 |   0 |  0 |  10 |   0 | 2.199574e+05 | 2.199574e+05 |   0.00%| unknown

SCIP Status        : problem is solved [optimal solution found]
Solving Time (sec) : 0.00
Solving Nodes      : 1
Primal Bound       : +2.19957367335726e+05 (2 solutions)
Dual Bound         : +2.19957367335726e+05
Gap                : 0.00 %

As you can already see, the primal bound in this case is different from the feasible one, and I guess there is a numerical issue in your problem. Is it possible to write the whole compact formulation and the minimum required data to see what's happened in the solving process?

[Joao-Dionisio]

@jnh277 can you also show the output of model.printVersion() and model.printExternalCodeVersions()?

[jnh277]

Really weirdly, I am getting a different result when I optimize directly vs when I save and load the "infeasible" formulation. Because this seems counter intuitive, i've done a quick recording and explanation showing this https://www.loom.com/share/13ebaf4f00d34a0e85838bca7ace6dd6

Outputs from version checks

self._model.printVersion()
SCIP version 10.0.0 [precision: 8 byte] [memory: block] [mode: optimized] [LP solver: SoPlex 8.0.0] [GitHash: NoGitInfo]
Copyright (c) 2002-2025 Zuse Institute Berlin (ZIB)

self._model.printExternalCodeVersions()
External libraries: 
  SoPlex 8.0.0         Linear programming solver developed at Zuse Institute Berlin (soplex.zib.de) [GitHash: NoGitInf]
  CppAD 20180000.0     Algorithmic Differentiation of C++ algorithms developed by B. Bell (github.com/coin-or/CppAD)
  ZLIB 1.2.12          General purpose compression library by J. Gailly and M. Adler (zlib.net)
  TinyCThread 1.2      small portable implementation of the C11 threads API (tinycthread.github.io)
  AMPL/MP 4.0.3        AMPL .nl file reader library (github.com/ampl/mp)
  Nauty 2.8.8          Computing Graph Automorphism Groups by Brendan D. McKay (users.cecs.anu.edu.au/~bdm/nauty)
  sassy 2.0            Symmetry preprocessor by Markus Anders (github.com/markusa4/sassy)
  Ipopt 3.14.19        Interior Point Optimizer developed by A. Waechter et.al. (github.com/coin-or/Ipopt)

[Joao-Dionisio]

I think that's a first in doing a video answer, but I quite enjoyed it, thank you! ahah
I have sometimes experienced this as well, and in my case, the reason was often that some decimals got truncated when writing the problem. But the person to ask regarding this is definitely @DominikKamp : Do you have any additional insight on what might cause a different solving path when optimizing vs writing + reading + optimizing, Dominik?

[DominikKamp]

If there is no difference in the problem before writing and after reading, then the difference might be after the written decimals as you said.