in mathematical modeling of whales encircling prey in (2.2)-(2.3) (paper in Article The Whale Optimization Algorithm
), the search agents update their location accordance to the best agent. That is, the search agents approach the prey by the amount A.D when A>0 or move away by the same amount when A
Because of C (not equal to 1) the algorithm is translation sensitive.
If you consider two functions, say
f1(x)=x^2 on [0,100]
f2(x)=(x-1000)^2 on [1000, 1100]
the landscapes are exactly the same. A stochastic iterative algorithm that is not translation sensitive produces exactly the two same sequences of fitness values (assuming, of course, you use the same seed for the RNG);
But this is not the case for WOA. A serious drawback.
Usually translation sensitivity favours some special positions in the search space (quite often 0* or on a diagonal).
So if the solution precisely is on such a position it is "too easy" to find it, and comparisons with other methods are not fair.
Mr Clerc
thank you for your answer. i have a few questions:
1) I am not good with optimisation problems. so can you explain translation sensitive a bit more?
2) I wrote a mini code in matlab. I assigned the point x* to (0,0). whatever I take the vector X (except for the points on the axis), the new positions are in the coordinate plane in the 1st region (for r0.5). so how do we get to the solution through the points in the 2nd and 4th regions?
3) What if the solution is not on such a position?
I am grateful for your time and reply.
1) If you plot f1 and f2 you can see the curves are exactly the same. Therefore a good iterative algorithm must have the same behaviour on both.
If the sequence of sampled points on f1 is x1, x2, ... then the sequence of sampled point on f2 must be x1+1000, x2+1000, ...
If not, it is biased. WOA is biased for translation.
Just try with a non biased algorithm, even a rudimentary one like, say, gradient descent.
2) It is perfectly possible that WOA has other biases (assuming, or course, your code is correct). There is a simple way to see that by plotting a signature:
f(x)=1 on [0,1]^2 (i.e. a Plateau function)
Run ten times with N sampled points, say N=10,000
Plot the 10*N sampled points. If there is no bias the result should look like the one produced by uniform random search.
I read the paper you quote. According to the formulae of WOA I guess such a signature is not very good and probably contains straight lines starting from (0,0).
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