title: Hill Climbing search algorithm Applied to travelling salesman
body: <p>Let's say we are given 7 cities A,B,C,D,E,F,G and we have a start state ABCDEFGA with some cost 'x' , I don't understand what the children of this node would be.Meaning how would the second iteration of the hill climbing algorithm proceed?</p>
  
  <p>Would the node ABCDEFGA which is the start state have 6 children? As in would the </p>
  
  <p><strong>second iteration</strong> be ACBDEFGA, <strong>ADCBEFGA</strong>, AECDBFGA, AFCDEBGA, AGCDEFBA?</p>
  
  <p><strong>Third Iteration:</strong> Let's say  ADCBEFGA is selected in the second iteration, then would the third iteration be exchanging city 'C' with all other cities and so forth? </p>
  
  <p>I would just like to know if my understanding of the algorithm is right.</p>