Counterfactual Routing Using Integer Programming with Constraint Generation
cs.AI · cs.DS
Quick verdict
Exact IP with constraint generation solves no-slack routing counterfactuals provably optimally; fastest by far (9.0s vs 118.8s) but ranked only 4th in quality.
Summary
This competition paper describes the authors' submission to the IJCAI 2025 Counterfactual Routing Competition, which asks for minimal modifications to a road network (edge type, minimum width, maximum curb height) that make a user's 'foil' route the shortest path under a weighted-Dijkstra planner. The authors formulate the task as an integer linear program with three binary variables per edge (change cost, disable, enable), a big-M constraint requiring the foil path to be strictly lighter than every alternative simple path, and a constraint-generation loop: solver callbacks apply the proposed edits, rerun Dijkstra on the modified graph, and add a violated-path cut until the foil route is optimal. Because enumerating all simple paths is exponential, this cutting-plane scheme keeps the formulation tractable; the method solves the problem exactly, deliberately disallowing the competition's 0.05 route-distance slack, which makes solutions valid but not necessarily minimal under the official metric. On the 25 public training instances (5 maps × 5 routes) all instances solve within 10 seconds on a laptop-class i7-1365U. In the held-out final evaluation the method ranked fourth in solution quality but was fastest on every instance, averaging 9.0 seconds versus 118.8 seconds for the next-fastest submission. Main limitations: the no-slack restriction explains the fourth-place quality, and the proposed fix — enumerating near-foil target routes with warm starts — is sketched as future work rather than evaluated.
Review complete
Assessment at a glance
4
risk flags identified
● high 0
● medium 2
● low 2
5 strengths · 5 weaknesses · 5 author questions
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Key claims under review
- The counterfactual routing problem — minimal map edits making a user's foil route shortest — can be solved exactly by an integer program made tractable via constraint generation, avoiding exponential enumeration of simple paths.
- All 25 competition training instances are solved to proven optimality within 10 seconds on a consumer laptop (i7-1365U, 16 GB RAM).
- In the CRC 25 final held-out evaluation, the method was fastest on every instance with an average runtime of 9.0 s versus 118.8 s for the next-fastest submission.
- The method ranked fourth in solution quality, which the authors attribute to deliberately disallowing the competition's 0.05 route-distance slack; extending to slack via target-route enumeration is left as future work.
Strengths
Exact, certifiably optimal solutions
The constraint-generation loop (Section 3.1, Figure 1) terminates only when rerunning Dijkstra on the modified graph returns the foil route as the shortest path, so every reported solution carries an optimality certificate for the solved restriction — no heuristic approximation.
Dominant runtime
Fastest on every held-out test instance in the CRC 25 final evaluation, averaging 9.0 s versus 118.8 s for the next-fastest submission (Abstract, Section 1); all 25 training instances solved within 10 s on consumer hardware (Section 4, Table 1).
Scalable formulation
Honest scoping of the contribution
Numerical care in big-M selection
Weaknesses
Quality ranking reported without numbers
Solves a restriction; remedy untested
Near-absent related work
Specification gaps
Limited evaluation breadth
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Scope & Claims
This is a short competition-submission paper describing the authors' entry to the IJCAI 2025 Counterfactual Routing Competition (CRC 25). The task: given an Amsterdam road multi-graph with edge attributes (length, width, curb height, path type) and a user's 'foil' route, find the minimal set of edge operations (change type, change minimum width, change maximum curb height) that makes the foil route the shortest A→B path under a weighted-Dijkstra planner, with edge weights length × 1.4 per crossing × 0.6 preferred-type bonus (Equation 1, Section 2.1). The competition permits the counterfactual's shortest path to sit within route-distance dr ≤ 0.05 of the foil; the authors deliberately solve the zero-slack restriction. Central claims: (i) the problem admits an exact ILP made tractable by constraint generation; (ii) all 25 training instances solve within 10 s on a laptop (Table 1); (iii) in the final held-out evaluation the method ranked fourth in solution quality but was fastest on every instance — 9.0 s average versus 118.8 s for the next-fastest submission.
The remaining sections cover Methodology Assessment, Statistical Evidence, Results & Reproducibility, Limitations & Risks, and Verdict & Recommendations.
- All 5 strengths & 5 weaknesses, analyzed in detail
- 4 risk flags with severity, section & reviewer questions
- Methods & statistical evidence assessment
- 5 questions a peer reviewer would ask
- Full six-dimension evaluation report & recommendations
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Frequently asked questions
What is counterfactual routing?
Given a road network and a route a user actually took (the 'foil' route), counterfactual routing finds the smallest set of changes to network attributes — road type, minimum width, maximum curb height — that would have made that route the optimal shortest path. It answers questions like 'your route would have been best if road X were not a bicycle path'.
How does this paper solve the counterfactual routing problem?
It formulates the task as an integer program: binary variables decide, for each road edge, whether to change its cost or enable/disable it, and big-M constraints force the foil route to be strictly shorter than every alternative path. Since there are exponentially many alternatives, constraints are added lazily: the solver's callbacks rerun Dijkstra on the modified map and each shorter path found adds one more constraint, until the foil route is provably optimal.
How well did this method do in the IJCAI 2025 Counterfactual Routing Competition?
It placed fourth out of the competing submissions in solution quality, but was the fastest on every held-out test instance: an average runtime of 9.0 seconds versus 118.8 seconds for the next-fastest team. On the 25 public training instances it solved everything within 10 seconds on a laptop-class CPU.
Why did it only rank fourth in solution quality?
The competition allowed the counterfactual's shortest path to be within 0.05 route-distance of the user's route, but the authors deliberately require an exact match. Their answers are therefore provably minimal for this stricter problem yet can use more edits than necessary under the official scoring. The proposed remedy — enumerating near-foil target routes and solving each — is described as future work and was not evaluated.
About this review
This is an AI-generated preliminary review by Evolve.Pub, produced from the openly available text of the paper. It is not peer review and does not represent the authors' views. The canonical record of the paper is at the publisher link above.
- Inline mathematical notation is mangled by PDF extraction (subscripts collapse, e.g. the δ-constraint in Section 2 and summation symbols render as 'P'), though all sections, the full Table 1 data, and both references are present — no truncation detected at the end of the text.
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