Thank you for nice question. This algorithm is inspired from food foraging behaviour of honey bees and we are testing and tuning the parameters of the Bees Algorithm to solve the TSP. The result will be published on the coming papers.

Thank you for your comments and questions.

In Table 1, "Reference" refers to the name of the test function. The mathematical model of the functions are given in the column "Test Function".

The number of evaluations has been calculated exactly following the pseudo code. As you mentioned in your question; in each iteration both step 5 and step 7 have been used for calculating the number of function evaluations.

Table 2, presents the result obtained by the Bees Algorithm and other algorithms available in the literature review.

All the parameters required for the algorithm are stated in section 3.2.

Recruitment, fittest bees' selection and other related parameters are part of the learning mechanism in the Bees Algorithm.

All the given sets of parameters are found empirically. Different set of parameters will give different results.

In your paper, you have classed the swarm-based optimization algorithms into Ant Colony Optimization, Genetic Algorithm and Particle Swarm Optimisation algorithm, my question: are there other evolutionary algorithm techniques that being excluded and why?

I do know that there is a technique called evolutionary programming (pioneered by Lawrence J. Fogel) and how do you class this technique?

Can you comment on agent-based approach, and differentiate between agent-based approach and swarm-based approach?

Hope you can clarify my queries and give your views.

Thanks.

We believe that EP and ES are in the same family as the GA.

In an earlier draft of our paper, we called the GA a population-based optimisation algorithm.

Such a categorisation is probably more appropriate than that of "swarm-based algorithm" and of course also describes EP better.

Thank you for your interest in our paper.

Dear Prof Pham,
Thanks for your reply. It is very interesting to see advances in using bio-inspired techniques to solve research problems. Your paper shows the performance of the new approach (bees algorithm) is better than the previous approaches. If evolutionary algorithms are global search methods, correct me if I am wrong, I would say the bees algorithm and ants algorithm are global + local search methods and both methods eliminate unnecessary evaluations and thus are more efficient. One step further, can you explain, in what way, the bees algorithm and ants algorithm are different that enable the bees algorithm to out-perform the ants algorithm?

Thanks

Dear Dr Ang,

Thank you for your interest in our algorithm and very relevant questions/comments.

You are entirely correct that our algorithm performs both local and global search.

As for the comparison with the Ant Algorithm, I must note that the results given in our paper pertain only to the test cases presented.

We cannot claim that the Bees Algorithm is better than the Ant Algorithm or any other algorithm in all cases. I think the 'No Free Lunch' theorem is quite correct.

Best wishes.

DTP.

PS: I hope you will hear directly from the 'Bees' also.

Hi Vlado: How did you discover that chink in our work??? You must have too much spare time!!! Seriously, thanks for your interest. The No-Free-Lunch problem, I am afraid, is my answer to your question. The Bees might have a better explanation. See you.

The Bees Algorithm addresses the central question of stochastic global optimisation, namely the balance between local exploitation and global exploration.

The Bees Algorithm consists of neighbourhood search plus global search which enable the algorithm to perform better than Ant Colony Optimisation which need another local search algorithm to improve its performance.

Thank you for your comment, I think you have showed us a very important and essential point...

Hi Mark,
Many thanks for your contribution and for coming to the defence of the Bees.
I am sure they will want to buy you lunch some time. And it will be free to you!
Cheers.
DTP.

Dear Gonzalo: Many thanks for your comment. We agree completely with you! Muchas gracias! DTP.

I absolutely agree. Having a sound understanding of the processes at work, preferrably rooted in maths is key to answering the Why does it perform one way or another questions. The added benefit is understanding the behaviour of the algorithm or the family in dynamic environments. In an off-line chat with Mark we seem to agree that this kind of "foraging" algorithms are probably best suited for situations where the space changes.

Thank you for you interest and comments/questions.

The Bees Algorithm is in its general format and is able to solve the problems it faces with no need for any major changes in its structure or performance

We hope it will continue solving all problems in future as well

Please stay with us for further comments and questions

Sameh Otri
PhD Research Student

Thanks for your comments, the Bees Algorithm is new and developed in MEC, The authors are sure it will be used in some applications or packages by MEC or others in the near future. Just keep searching for Bees Algorithm to see new out comings.

including the previous answer, an explanation for the first comment... you might be right about the table but we thought that its good to show all the algorithms on the same benchmarking table, even there are some unavailable data...

Thanks for your comments, the success criteria was measured as success runs out of 100 independent runs, which for all the test functions were 100%. In algorithm like the Bees Algorithm, GA and …, the best solution which the algorithm can find, after a number of iterations, will be presented, in table 2 the benchmark has been shown to see how this answer for the Bees Algorithm and other algorithm matches the global optimum (success column).

Please do not hesitate to ask if you need more information or any other question.

Afshin

you say in your paper "The results are averages
for 100 independent runs. It can be seen that after
approximately 3,000,000 visits, the Bees Algorithm
was able to find solutions close to the optimum."

i mean the measure of this closeness as success criteria.

you have a termination criteria such as
|f*-f|.less than. e1|f*|+e2

this gives how close the solution(f) to the global solution (f*).

i wonder the values you used for e1 and e2.

Thanks for your comments again, the acceptable error is 0.1% of global optimum or .001 (which one is smaller) and for zero answers, .001.

thanks..

1. For the first question, the variables for some of the functions given below,

De Jong:
n= 15, m= 5, nsp =2, nep =2, e =2, ngh=0.1

Brainin:
n= 30, m= 5, nsp =2, nep =3, e =1, ngh=1

Rosenbrock-(a):
n= 10, m= 3, nsp =2, nep =4, e =1, ngh=0.1

Hyper Sphere:
n= 8, m= 3, nsp =1, nep =2, e =1, ngh=0.1

All these variables found empirically. Regarding other algorithms, all the results and variables can be found in the reference number 6.

2. We had the same question last week and it was answered by Prof. Pham:
“We cannot claim that the Bees Algorithm is better than the Ant Algorithm or any other algorithm in all cases. I think the 'No Free Lunch' theorem is quite correct”.
You can also find more details above, in the posts that we sent last week

Thank you for your interest in our paper. Please do not hesitate to ask, if you need more information.

Best wishes

There is wisdom in the "no free lunch", and it does help on the path to enlightenment. If there is no free lunch, what is the cost for different problems? Or phrasing this differently, why the bee algorithm exhibits the described behaviour/performance in the benchmark cases. I'm particularly interested in functions 1 and 6, since they are "out of trend".

A related request. Do you have the data for the medians and the variance, not just the means for the performance of the bees for each test case? Do you mind publishing this data, please.

Thanks for your interest, for the first part Ebubakir gave some information, I just want to add somthing for the second question.
As you said Hyper sphere is a simple function to get the optimum. But as you wrote functions 5a and 5b (Rosenbrok)are second order and Hyper sphere is 6, as we can see for the Rosenbrok order 4 (function 6) the required evaluations are much more than Hyper sphere.
We can see this trend for Ant Algorithm and GA as they need more evaluations for Hyper sphere order 6 than Rosenbrok order 2.

Thanks for your comment, Anthony.
Although the Bees Algorithm has some similarities with PSO, but there are some major diffrences as:
1- Neighbourhood search is one of them, in PSO we can not see this kind of search as in BA.
2- In PSO, every particle moves from current position to its next position regarding PBest Gbest, as in BA selected bees recruit for neibourhood search about themselves.
3-In PSO, the particles will randomly placed at the first and will move to their next positions in each iteration, but in BA in each iteration we have some randomly placed bees about the search space.
There are some other details which can be said if needed.

Hopy this comment and reply encourage PSO people to come and share their ideas.

A.Ghanbarzadeh

Thanks for your nice comments, Vlado.

I have uploaded some more details about the results for 4 functions. ( Result.pdf )
Please let us know if you need more information.

A.Ghanbarzadeh

Thanks. That makes an interesing food for thought

Well, you do have variations of PSOs with differently structured neigbourhoods, including collaboration. I've stumbled upon a number of papers describing similar ideas.

IMO, the biggest significant difference is that the difference in metaphors should help in optimising the performace using different (maybe slightly different) methods.

There is probably quite a lot of merit in comparing bees to GAs. Not just their performance, but the underlying structure, how can they help to understand the different performance, in different problems.

Indeed Vlado. My current work is focussed on this very issue.

Hi Anthony and Vlado,

I believe the difference is more than just in the metaphors employed.

PSO uses quite different "swarming" rules from those adopted by the Bees.

Let us get the Bees team to have a serious bebate with you some time.

Cheers.

DTP.

Many thanks, Mr Dent!

However, I suspect your cover as a wasp is about to be blown!

May I advise you to buzz off before the Bees, aided and abetted by Mark, swarm onto you!

I suppose it could. The shape of the algorithm defines the main properties of the search.

In order to apply it for clustering, I suppose the trickiest bit would be the encoding of the problem in terms suitable for applying the bee-algorithm shape.

Hi Vlado,
I like the idea of the "shape of an algorithm". What do you suppose the shape for the Bees Algorithm might be?
Cheers.
DTP.

Hi Adi,
Sure can! As you know, the difficulty, as with all distance-based clustering algorithms, is to define "distances"!
Cheers.
DTP.

Hi Adi,

My hypothesis is that, whatever GAs can do, our Bees Algorithm can too! You are cordially invited to test the hypothesis on your problem!

Cheers.

DTP.

Please see the IPROMS 2007... We have a special session.