perf: scale the absolute gap with the goal energy, and give it to the probe

[andig]

fixes #186

A fixed cent sits below the slack the c_min gate leaves in the LP relaxation whenever a vehicle's minimum power is a sizeable share of a slot. The relaxation charges below c_min on a fractional z, the integer schedule cannot, and CBC has to enumerate to prove the difference. On the three phase request of #186 that is 9 ct of slack and no proof in 110 minutes; a 2.5 ct gap proves the same schedule in 1.5 s. The analysis and the three options tried are on the issue.

Two changes. OPTIMIZER_GAP_SHARE, 0.25 % by default: the absolute gap becomes max(gap_abs, gap_share × goal energy × mean import price), where goal energy is what the batteries still need for their s_goal. A request without a goal keeps the cent. And the probe runs with that gap instead of proving to CBC's own tolerance, which alone turns the #170 request into a joint Optimal in 0.7 s where it splits today.

Measured under the production limits on the requests from #186, #170 and the one phase household of the README:

request	before	after
#186, 221 steps	split, Feasible, 7.9 s	joint, Optimal, 1.5 s, −0.1 ct
#186, 414 steps	split, Feasible, 7.9 s	joint, Optimal, 2.0 s, −0.2 ct
#170	split, Feasible, 5.4 s	joint, Optimal, 1.9 s, same cost
one phase	joint, Optimal, 1.2 s	joint, Optimal, 1.0 s, same cost

A replay of the production slow-request dump, 120 requests with a goal and 120 without, before and after, follows as a comment.

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[andig]

@ekkea if this is ok to do it should dramatically improve performance and reduce "feasible" solutions without giving away much. Wdyt?

[andig]

Replay of the production slow-request dump, 9,691 requests dumped between July and October for exhausting the limit or leaving more than a currency unit unproven. Sample of 240: all 2 October requests with a goal plus 118 random ones with a goal, and 40 October plus 80 random ones without. Each replayed on main (e8f9b2b) and on this branch under the production limits, 10 s and one thread, same machine, same CBC.

group		Optimal	joint path	mean solve	median solve
with a goal, 120	main	41	27	5.97 s	7.67 s
	branch	51	39	5.39 s	7.65 s
without, 120	main	40	26	6.06 s	7.64 s
	branch	53	40	5.40 s	7.36 s

Money, on the requests whose cost is money and not penalty units, 102 and 99 of the two groups: 186 identical to the cent, 7 worse, worst by 0.27 ct, 8 better. The requests without a goal keep the 1 ct gap, so their change is the probe alone: 14 more joint proofs out of 120.

Two of the better ones are not cents. On main the cost stage hit its 3 s cap on them with 27.9 € and 15.4 € still between schedule and bound and the split went on with that incumbent; the branch proves the joint objective in 1.0 and 2.0 s and returns a schedule better by that amount. One of the two is reported Optimal on main, which it is not: the label comes from the tie break MILP proving the preferences over a cost schedule that was never proven. Separate issue, noted here because the replay surfaced it.

The one request that got slower by more than a second, and the 0.21 ct it lost, is a joint solve on both sides whose continuity stage found a different equal-cost schedule; the gap did not change its path.

Nothing hit the limit on either side. Scripts and samples are in this session's scratchpad, the outputs fit a comment: bench_gap.py replays a sample against a source tree, bench_compare.py joins the two.

🤖 Generated with Claude Code