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Fix #167: Add TravelingSalesman to QUBO reduction #605

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Merged
GiggleLiu merged 7 commits into from
Mar 13, 2026
Merged

Fix #167: Add TravelingSalesman to QUBO reduction #605

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33de860
Add plan for #167: TravelingSalesman to QUBO reduction
hmyuuu Mar 12, 2026
9852947
Implement TravelingSalesman to QUBO reduction (#167)
hmyuuu Mar 12, 2026
b32942a
chore: remove plan file after implementation
hmyuuu Mar 12, 2026
4fe109f
Merge upstream/main to pick up clippy fix
hmyuuu Mar 12, 2026
40be2ff
style: rustfmt after upstream merge
hmyuuu Mar 12, 2026
99335c2
Merge remote-tracking branch 'origin/main' into issue-167-tsp-to-qubo
GiggleLiu Mar 13, 2026
749f818
fix: address Copilot review — store num_edges instead of edges Vec, c…
GiggleLiu Mar 13, 2026
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139 changes: 139 additions & 0 deletions docs/paper/examples/travelingsalesman_to_qubo.json
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{
"source": {
"problem": "TravelingSalesman",
"variant": {
"weight": "i32",
"graph": "SimpleGraph"
},
"instance": {
"num_edges": 3,
"num_vertices": 3
}
},
"target": {
"problem": "QUBO",
"variant": {
"weight": "f64"
},
"instance": {
"matrix": [
[
-14.0,
14.0,
14.0,
14.0,
1.0,
1.0,
14.0,
2.0,
2.0
],
[
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1.0,
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1.0,
2.0,
14.0,
2.0
],
[
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-14.0,
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1.0,
14.0,
2.0,
2.0,
14.0
],
[
0.0,
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-14.0,
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14.0,
3.0,
3.0
],
[
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-14.0,
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3.0,
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3.0
],
[
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[
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[
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-14.0
]
],
"num_vars": 9
}
},
"overhead": [
{
"field": "num_vars",
"expr": {
"Pow": [
{
"Var": "num_vertices"
},
{
"Const": 2.0
}
]
},
"formula": "num_vertices^2"
}
]
}
112 changes: 112 additions & 0 deletions docs/paper/examples/travelingsalesman_to_qubo.result.json
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{
"solutions": [
{
"source_config": [
1,
1,
1
],
"target_config": [
0,
0,
1,
0,
1,
0,
1,
0,
0
]
},
{
"source_config": [
1,
1,
1
],
"target_config": [
0,
0,
1,
1,
0,
0,
0,
1,
0
]
},
{
"source_config": [
1,
1,
1
],
"target_config": [
0,
1,
0,
0,
0,
1,
1,
0,
0
]
},
{
"source_config": [
1,
1,
1
],
"target_config": [
0,
1,
0,
1,
0,
0,
0,
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1
]
},
{
"source_config": [
1,
1,
1
],
"target_config": [
1,
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1,
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]
},
{
"source_config": [
1,
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],
"target_config": [
1,
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0,
1
]
}
]
}
142 changes: 142 additions & 0 deletions examples/reduction_travelingsalesman_to_qubo.rs
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// # Traveling Salesman to QUBO Reduction (Penalty Method)
//
// ## Mathematical Relationship
// The TSP on a graph G = (V, E) with edge weights is mapped to QUBO using
// position-based encoding. Each vertex v and position k has a binary variable
// x_{v,k}, with penalties enforcing:
//
// 1. Assignment constraint: each vertex appears exactly once in the tour
// 2. Position constraint: each position has exactly one vertex
// 3. Edge constraint: consecutive positions use valid edges
// 4. Objective: total edge weight of the tour
//
// The QUBO has n^2 variables (n vertices x n positions).
//
// ## This Example
// - Instance: K3 complete graph with edge weights [1, 2, 3]
// (w01=1, w02=2, w12=3)
// - Source: TravelingSalesman on 3 vertices, 3 edges
// - QUBO variables: 9 (3^2 = 9, position encoding)
// - Optimal tour cost = 6 (all edges used: 1 + 2 + 3)
//
// ## Outputs
// - `docs/paper/examples/travelingsalesman_to_qubo.json` — reduction structure
// - `docs/paper/examples/travelingsalesman_to_qubo.result.json` — solutions
//
// ## Usage
// ```bash
// cargo run --example reduction_travelingsalesman_to_qubo
// ```

use problemreductions::export::*;
use problemreductions::prelude::*;
use problemreductions::topology::{Graph, SimpleGraph};

pub fn run() {
println!("=== TravelingSalesman -> QUBO Reduction ===\n");

// K3 complete graph with edge weights: w01=1, w02=2, w12=3
let graph = SimpleGraph::new(3, vec![(0, 1), (0, 2), (1, 2)]);
let tsp = TravelingSalesman::new(graph, vec![1i32, 2, 3]);

// Reduce to QUBO
let reduction = ReduceTo::<QUBO>::reduce_to(&tsp);
let qubo = reduction.target_problem();

println!(
"Source: TravelingSalesman on K3 ({} vertices, {} edges)",
tsp.graph().num_vertices(),
tsp.graph().num_edges()
);
println!(
"Target: QUBO with {} variables (position encoding: 3 vertices x 3 positions)",
qubo.num_variables()
);
println!("Q matrix:");
for row in qubo.matrix() {
let formatted: Vec<String> = row.iter().map(|v| format!("{:8.1}", v)).collect();
println!(" [{}]", formatted.join(", "));
}

// Solve QUBO with brute force
let solver = BruteForce::new();
let qubo_solutions = solver.find_all_best(qubo);

// Extract and verify solutions
println!("\nOptimal QUBO solutions: {}", qubo_solutions.len());
let mut solutions = Vec::new();
for sol in &qubo_solutions {
let extracted = reduction.extract_solution(sol);
let edge_names = ["(0,1)", "(0,2)", "(1,2)"];
let selected: Vec<&str> = extracted
.iter()
.enumerate()
.filter(|(_, &v)| v == 1)
.map(|(i, _)| edge_names[i])
.collect();
println!(" Edges: {}", selected.join(", "));

// Closed-loop verification: check solution is valid in original problem
let metric = tsp.evaluate(&extracted);
assert!(metric.is_valid(), "Tour must be valid in source problem");
println!(" Cost: {:?}", metric);

solutions.push(SolutionPair {
source_config: extracted,
target_config: sol.clone(),
});
}

// Cross-check with brute force on original problem
let bf_solutions = solver.find_all_best(&tsp);
let bf_metric = tsp.evaluate(&bf_solutions[0]);
let qubo_metric = tsp.evaluate(&reduction.extract_solution(&qubo_solutions[0]));
assert_eq!(
bf_metric, qubo_metric,
"QUBO reduction must match brute force optimum"
);

println!(
"\nVerification passed: optimal tour cost matches brute force ({:?})",
bf_metric
);

// Export JSON
let source_variant = variant_to_map(TravelingSalesman::<SimpleGraph, i32>::variant());
let target_variant = variant_to_map(QUBO::<f64>::variant());
let overhead = lookup_overhead(
"TravelingSalesman",
&source_variant,
"QUBO",
&target_variant,
)
.expect("TravelingSalesman -> QUBO overhead not found");

let data = ReductionData {
source: ProblemSide {
problem: TravelingSalesman::<SimpleGraph, i32>::NAME.to_string(),
variant: source_variant,
instance: serde_json::json!({
"num_vertices": tsp.graph().num_vertices(),
"num_edges": tsp.graph().num_edges(),
}),
},
target: ProblemSide {
problem: QUBO::<f64>::NAME.to_string(),
variant: target_variant,
instance: serde_json::json!({
"num_vars": qubo.num_vars(),
"matrix": qubo.matrix(),
}),
},
overhead: overhead_to_json(&overhead),
};

let results = ResultData { solutions };
let name = "travelingsalesman_to_qubo";
write_example(name, &data, &results);
}

fn main() {
run()
}
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