The Travelling Salesperson Problem (AQA A-Level Further Maths): Flashcards

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The Travelling Salesperson Problem
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TSP objective

Shortest route visiting all vertices & returning to start

Hamiltonian cycle

Closed path visiting each vertex exactly once, then returns

Classical TSP seeks

Minimum weight Hamiltonian cycle

Tours in nn-vertex network

12(n1)!\frac{1}{2}(n-1)!

Heuristic algorithm

Finds good solution that may not be optimal

Nearest neighbour: at each step, choose

Minimum weight arc to unvisited vertex

Nearest neighbour strategy

Repeat from each vertex, select best tour

Upper bound from known tour

Length of that tour

Lower bound: delete VV, calculate

Two smallest arcs from VV + MST of rest

Best bounds to find

Smallest upper bound, largest lower bound

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