🌿 TSP Branch & Bound
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# 🌿 TSP Branch & Bound ## 1. 🎯 Learning Objectives - Compute lower bounds using reduced cost matrix - Trace B&B search tree for TSP - Apply permanent exclusion rules ## 2.
🌿 TSP Branch & Bound
1. 🎯 Learning Objectives
- Compute lower bounds using reduced cost matrix
- Trace B&B search tree for TSP
- Apply permanent exclusion rules
2. 📖 Core Content
3.1 Reduced Cost Matrix
Step 1: Subtract row minima from each row Step 2: Subtract column minima from each column Lower bound = sum of all reductions
3.2 Example
Matrix: [∞,20,30,10,11][15,∞,16,4,2][3,5,∞,2,4][19,6,18,∞,3][16,4,7,16,∞] Row reductions: row0-10, row1-2, row2-2, row3-3, row4-4 → sum=21 After row reduction + column reduction → LB ≈ 30-40.
3.3 B&B Search Tree
Root (LB=30) → Branch on edges from city 0: (0,1)=20, (0,2)=30, (0,3)=10, (0,4)=11 Choose smallest edge cost (0,3)=10. Recurse with reduced matrix, exclude row0/col3. Continue until complete tour found. Prune branches with LB ≥ current best.
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