Traveling Salesman Radu Mariescu Istodor 24 1 2019

Traveling Salesman Radu Mariescu Istodor 24. 1. 2019

Traveling Salesman Problem

Mathematical formulation

O-Mopsi TSP Player 2 Player 1 Optimum ? ?

How good was the order? Optimum order Start Player’s order End Player’s route Mismatch 4

Cycle vs Path

Circuit board

Circuit board Martin Grötschel, 2013

Local search HEURISTIC

Node Swap

2 -optimization

Link Swap T 1 B A 1 2 T 2 3

Random Mix Algorithm Random. Mix Initialize order at random FOR i 1 TO N DO // N is a fixed number of iterations (10, 000) Chose operation randomly Do selected operation at a random location Update solution if improvement was found END FOR

How it works? DEMO

Why mix? Node swap and link swap stops 2 -opt and link swap stops Node swap solves 2 -opt solves Node swap stops Link swap or 2 -opt solves

Local optima Optimum

Recovery strategy: Repeat the process

Improvement rate [PERCENTAG E] Link swap [PERCEN TAGE] 2 opt [PERCENTAGE] Node Swap

1 run 5 rep. 1. 2 Approximation (e) How many iterations? 10 rep. 15 rep. 0. 8 20 rep. 25 rep. 0. 4 0 0. 02 1% 0. 3% 0 1000 1 10 Iterations 10000 0. 9% 0. 01 0% Iterations 10000

How many repetitions? Games solved 150 140 144 145 130 O-Mopsi (145 games) 121 120 110 100 144 107 0 5 10 15 Repetitions 20 25 30

Thank You ! Radu Mariescu-Istodor radum@cs. uef. fi

Only solved by node swap link swap 2 opt node swap link swap 2 opt node swap

TSP tool setup 7 nodes