Understanding Stochastic Hill Climber

Question

I've been trying to understand the stochastic hill climber for a while, but not having any luck with it. I've looked through a book on heuristics and got a pseudo code. I don't understand what the probability function should look like. I understand that the new solution is piked randomly and accepted based on some probability, what I don't get is how to program this probability. Thanks

PSUEDO-CODE - from How to Solve it: Modern Heuristics - Zbugniew Michalewicz, David Fogel

procedure stochastic hill-climber
begin
     t <- 0
     select a current string vc at random
     evaluate vc
     repeat
          select the string vn from the neighbourhood of vc
          select vn with probability 1/(1+(e^(evaluation(vc) - evaluation(vn))/T))
          t <- t + 1
     until t=MAX
end

Can you add the pseudocode to your question? – Jason Plank Mar 26 '11 at 13:14 — Jason Plank, Mar 26 '11 at 13:14
Hi, I edited my question to include psuedo code, Thanks – smMavrik Mar 26 '11 at 13:22 — smMavrik, Mar 26 '11 at 13:22

score 1 · Accepted Answer · answered Mar 26 '11 at 13:33

1

This is a form of Genetic algorithm which has a fitness function called evaluation. It chooses a neighbor with a large positive difference between the current and neighbor. It has a sigmoid activation function 1/(1 + e^(something)) which means that it will map to the interval (0,1). I believe that the T is to reduce the size of the differences over time to allow the answer to eventually converge to a limit. t is just a counter which represents a generation in the algorithm. The algorithm will end as soon as t reaches the max generation. Hope this helps.

answered Mar 26 '11 at 13:33

Jeremy E

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Thanks, although i don't understand how i would select a specific neighbour. Would i have to check the probability of all the neighbours and the accept the one with the highest probability? – smMavrik Mar 26 '11 at 13:41
You just need to check the probability of "a" neighbor not all. You will need to generate a random number between 0.0 and 1.00 and transition if it is less than the probability of the difference of the evaluations of vc and vn. The missing piece was the random number that they assume you generate to determine if you should transition. If your random number is >= to the caculated probability move on to the next neighbor. – Jeremy E Mar 28 '11 at 13:24

Understanding Stochastic Hill Climber

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