Add single machine scheduling separator by Opt-Mucca · Pull Request #2990 · ERGO-Code/HiGHS

Opt-Mucca · 2026-04-23T10:02:35Z

This PR implements identification of natural-date single-machine scheduling subproblems and derives valid inequalities. See the description of highs/mip/HighsMachineSchedSeparator.h for the exact description.

Motivation: The instance neos-3046615-murg from MIPLIB 2017 benchmark now solves well within time limit, and neos-3046601-motu from MIPLIB 2017 collection now solves in a second or two (both were previously unsolvable within a few hours). This change should introduce some tiny epsilon and very positively affect some instances.

Changes:

Add highs/mip/HighsMachineSchedSeparator.h and highs/mip/HighsMachineSchedSeparator.cpp. Currently the separator is only called once, and the cuts are only added to the pool. This is efficient, and I noticed no real change by trying to separate more frequently.
I have removed some presolve code that shifts integer columns to have a lower bound of zero. Such a shift completely destroys any structure of this subproblem and makes it impossible to efficiently find. I've tested this change in isolation locally, and there was only some (positive) performance noise. I don't believe it is done for any purpose other than cosmetics + potentially making it easier to transform the LP when generating cuts, so it should be fine to remove. @fwesselm I may be missing something obvious there....

Potential improvements that I don't think need to be made:

Someone could model jobs from [-inf, 0] instead of [0, inf]. I'd currently not spot these. I'd also not spot a row where both binary columns share the same coefficient value (different signs), although I think presolve is going to scale these rows most of the time already.
Computing these inequalities requires finding a clique. I implemented the most naive greedy approach possible. I don't think we have any max-clique code outside of HighsCliqueTable, which I don't think was efficient to use in this case (could be wrong). There's likely going to be some instances that this code could improve but fails to because of this naive approach, however it ensures near-zero overhead is added to all other instances. An example: I suspect supportcase26 could be improved with some better detection.

This should not be merged until a more thorough performance check has been made! @fwesselm This is a way lower priority than the MIP Worker Refactor to review / test.

codecov · 2026-04-23T10:11:24Z

Codecov Report

❌ Patch coverage is 56.12245% with 86 lines in your changes missing coverage. Please review.
✅ Project coverage is 72.89%. Comparing base (187c624) to head (7f1b433).
⚠️ Report is 127 commits behind head on latest.

Files with missing lines	Patch %	Lines
highs/mip/HighsMachineSchedSeparator.cpp	54.25%	85 Missing and 1 partial ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           latest    #2990      +/-   ##
==========================================
- Coverage   72.92%   72.89%   -0.04%     
==========================================
  Files         436      438       +2     
  Lines      106038   106283     +245     
  Branches    17071    17118      +47     
==========================================
+ Hits        77329    77470     +141     
- Misses      28433    28536     +103     
- Partials      276      277       +1

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Opt-Mucca · 2026-05-13T12:56:43Z

I've added some basic clique extraction (was the largest TODO). It now solves the benchmark instance neos-5107597-kakapo within time limit reliably.
That instance had overlapping binary variables, e.g.,

x = 1 -> y_0 - y_1 >= b_0
x = 0 -> y_1 - y_0 >= b_1
y = 1 -> y_0 - y_1 >= b_2
y = 0 -> y_1 - y_0 >= b_3
b_i >= 0

From this you can conclude that x=y. I'm not sure how to efficiently store a multi-graph and find these overlaps though, so I only find one half of it at a time, i.e., x + ~y <= 1.

…ine-schedule-sepa

…HiGHS into machine-schedule-sepa

BenChampion

Thanks for asking me to review this change! It was very educational. (The quantity of comments reflects that: I added the comments as I worked through it.)

To summarize my feedback, some parts of this were much harder to understand than others. It might help to delineate as much as possible

code that identifies the single machine scheduling structure, ensuring we don't try to build the cuts where they won't be helpful
code that computes the data we need once we've identified the structure
the complete preconditions for the valid inequalities
ideas for each step, intents behind data structures, and your algorithmic strategy

In due course, testing results would also be good to see.

Once you've had a chance to digest my feedback I'd be happy to chat. (It would certainly help me to fill any gaps in my understanding.)

BenChampion · 2026-07-14T16:18:46Z

    HPRESOLVE_CHECKED_CALL(static_cast<Result>(convertImpliedInteger(col)));

-    // shift integral variables to have a lower bound of zero
+    // shift "binary" variables to have a lower bound of zero


I see you have an outstanding comment to @fwesselm about this; I don't think I know enough yet to evaluate the implications of changing this.

It is in general nice to have variables have a lower bound of zero. I don't see this making any mathematical difference though, and it completely changes the structure. I don't believe it's done in other solvers. The advantage would be that there's less changes needed to be done in stuff like cut transformation as they already have a lb of 0.
Consider that HiGHS has proven that one job has to start at at-least time 5. It will shift this 0. The job variable no longer represents the start time though, it now represents the start time + 5, which is impossible to recover easily. It can no longer be used to make the inequality.

BenChampion · 2026-07-30T12:45:47Z

+  std::vector<double> processingTimes;
+  processingTimes.resize(largestDegree + 1, kHighsInf);
+  // Iterate over potential neighbours and check validity
+  for (HighsInt col : potentialNeighbours) {


Worth explaining in more detail your strategy here? (In particular, you are enlarging neighbors with every iteration.) I had to backtrack multiple times to figure out what this loop was doing.

I've added a small comment

BenChampion

Thanks for addressing my comments. This looks good to me now modulo some new comments/continuing discussions, and proper testing.

That just leaves the clique size at least three thing: why can't we form the inequality for two jobs? Is it just not useful? Or is it something else? (EDIT: this is only for my understanding)

BenChampion · 2026-07-31T08:41:11Z

+  // 1 -> (i,j) y = 0, 2 -> (i,j) y = 1, 4 -> (j,i) y = 0, 8 -> (j,i) y = 1
+  HighsHashTable<std::tuple<HighsInt, HighsInt, HighsInt>, uint8_t> jobOrder;
+
+  auto addEntry = [&](HighsInt posCol, HighsInt negCol, HighsInt binCol,


It's much harder to reason about what a function is doing if it can modify any value in scope rather than just three specific things.

BenChampion · 2026-07-31T08:51:52Z

+          continue;
+        }
+        // Add cliques x1 + ~x2 <= 1 and ~x1 + x2 <= 1 which together imply x1
+        // == x2 (depending on signs may also have x1 == ~x2)


This last addition is a little confusing but I think I know what you mean (that the original variables may already be complemented with respect to each other)

BenChampion · 2026-07-31T09:25:59Z

+    // My_ji + s_i - s_j >= p_ji, p_ji >= 0
+    // y_ji = 1 -> s_i >= s_j + p_jj - M


Suggested change

// My_ji + s_i - s_j >= p_ji, p_ji >= 0

// y_ji = 1 -> s_i >= s_j + p_jj - M

// My_ji + s_i - s_j >= p_ji, p_ji >= 0

// y_ji = 1 -> s_i >= s_j + p_ji - M

Also, don't you want M(1-y_ji)?

It's just re-arranging and setting y_ji = 1 so that it becomes M. Edit: Fixed the p_jj error

…HiGHS into machine-schedule-sepa

…ine-schedule-sepa

fwesselm

Looks good, @Opt-Mucca!

Opt-Mucca · 2026-08-04T12:28:19Z

This improves performance by 1% or so on the test set of @fwesselm I'm now going to merge it

Opt-Mucca added 3 commits April 22, 2026 17:30

Implement single machine schedule sepa

4b55a3c

Don't handle infinite lower bounds

856e4d7

Sort potential neighbours greedily

85406e5

Opt-Mucca requested a review from fwesselm April 23, 2026 10:02

Opt-Mucca added 5 commits April 24, 2026 10:37

Add back restricted version of integer variable shifting

8a4caca

Add it back to the correct spot....

b1b8bb5

Make std::min not look at different types

c1eed97

Make formatter happy

27e9cd5

Add clique detection

8f6de97

Remove releasedate as parameter

202fb62

jajhall assigned Opt-Mucca May 21, 2026

Merge latest into branch

d24cd51

Opt-Mucca marked this pull request as draft June 21, 2026 08:49

Opt-Mucca added 4 commits June 22, 2026 12:49

Use HighsHashTree instead of unordered_map. Remove incorrect cliques

ea4ee18

Add clique extraction

7bd1589

Skip dupplicate baseBinCol entries

0e10e49

Merge latest into branch"

2bb6401

Opt-Mucca marked this pull request as ready for review June 26, 2026 12:21

Opt-Mucca mentioned this pull request Jun 26, 2026

Implement strongly connected component analysis on the clique table #3097

Closed

fwesselm and others added 4 commits June 30, 2026 16:11

Merge branch 'latest' of https://github.com/ERGO-Code/HiGHS into mach…

9ada144

…ine-schedule-sepa

Merge branch 'latest' of https://github.com/ERGO-Code/HiGHS into mach…

8c4cbb9

…ine-schedule-sepa

Add comments from Franz

4953df6

Merge branch 'machine-schedule-sepa' of https://github.com/ERGO-Code/…

e2b1319

…HiGHS into machine-schedule-sepa

jajhall added the MIP label Jul 2, 2026

BenChampion requested changes Jul 30, 2026

View reviewed changes

Add most comments from Ben

0ebbf1a

BenChampion approved these changes Jul 31, 2026

View reviewed changes

Clean up loop

e0e8bd5

fwesselm added 2 commits August 3, 2026 12:04

Merge branch 'machine-schedule-sepa' of https://github.com/ERGO-Code/…

5ba06a2

…HiGHS into machine-schedule-sepa

Merge branch 'latest' of https://github.com/ERGO-Code/HiGHS into mach…

d5febde

…ine-schedule-sepa

fwesselm approved these changes Aug 4, 2026

View reviewed changes

Comment thread highs/mip/HighsMachineSchedSeparator.cpp

Comment thread highs/mip/HighsMachineSchedSeparator.cpp

Comment thread highs/mip/HighsMachineSchedSeparator.cpp

Comment thread highs/mip/HighsMachineSchedSeparator.cpp

Comment thread highs/mip/MipTimer.h

Add lambda suggestion from Franz

7f1b433

Opt-Mucca merged commit dc83470 into latest Aug 4, 2026
534 of 536 checks passed

		// My_ji + s_i - s_j >= p_ji, p_ji >= 0
		// y_ji = 1 -> s_i >= s_j + p_jj - M

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