motion-planning

Heuristics and algorithms for the Travelling Salesman Problem (TSP) and Vehicle Routing Problem.

Insertion Heuristics

• Cheapest Insertion
• Nearest Insertion
• Farthest Insertion

Local Optimizers

• 2-opt
• 3-opt

Greedy Heuristics

• Nearest Neighbour

TSP Approximation Heuristics

• Christophedes Algorithm

  • (A factor of 3/2 of the optimal solution length)

  Steps of algorithm:

  1. Find a minimum spanning tree (T)
  2. Find vertexes in T with odd degree (O)
  3. Find minimum weight matching (M) edges to T
  4. Build an Eulerian circuit using the edges of M and T
  5. Make a Hamiltonian circuit by skipping repeated vertexes

MinMax VRP Heuristics

• Fredericksons approximations