Innovative Production Machines and Systems Conference

Hi

Thanks for your interest, the presentation is there now. Looking forward to see your comments.

Afshin

Dear Vlado,

Hi and thanks for your nice question.

The number of selected sites is chosen empirically, but it does not have major influence on the results as we repeat the algorithm enough number of iterations. In the multi-objective Bees Algorithm, the Pareto optimal set will be constructed and updated in each iteration gradually, so the number of selected sites or patches is not a critical parameter.

The Pareto optimal set will be created during the running of algorithm and in the end of each run of the program, the Pareto optimal set is constructed (it is not needed to run the program many times to find non-dominated solutions one by one).

Hope this answer clear more the way of working of the multi-objective Bees Algorithm. Please do not hesitate to ask any other possible question.

Many thanks,

Afshin

I'm not sure I understand your reply.

Can you be more precise in what you mean by iterations in each case. Do you mean iterations/generations of one run of the algorithm, or do you mean multiple iterative runs.

It makes a difference, since the former means that the number of non-dominated points is lower or equal to the number of patches, which in terms means that the number of patches is actually important.

Or alternatively do you mean that you run the program a number of times and accumulate somewhere the results.

Hi

Let me explain it in this way.

In each iteration/generation, the non-dominated solutions are candidate to be added to the Pareto optimal solution. Each of these new non-dominated solution which is not dominated by old member of the Pareto optimal set, will be added to the Pareto optimal set. Also, the old members of the Pareto optimal will be checked, if any of them is dominated be the new member, the dominated ones will be removed from the set.

As program is running, the Pareto optima set will grow ( add and remove from it) and in the end of the run the constructed set will be the answer and this way the Pareto optimal set will be created during the running of program.

So, we do not need to run program many times to create the Pareto optimal set, just one run and get the Pareto optimal set.

Regards,

Afshin

Hi and Thanks Sameh,

In the multi-objective version of the Bees Algorithm, all the selected sites for neighbourhood search are in the same level of attention, so we do not need to devide them to elits and other selected sites and hence the recruited bees for all the selected sites will be equal. This theory helped us to decrease the parameters in the Bees Algorithm by 2.

At the moment, this theory is suitable for multi-objective verion but it is a good point to see how can we implement to the single function optimisation version too.

Regards,

Afshin

are they e and nep?

Sameh Otri
PhD Research Student

They are 'e' and 'nsp', as all selected sites are like elits so we do not have other selected sites and hense 'nsp'.

Regards

Afshin

Hi Ng,

Thanks for your hint. The mistake has been corrected and the corrected paper is re-uploaded.

Many thanks,

Afshin

Hi Afshin,

You're welcome. Now your pdf file cannot be opened.
Error message "File does not begin with %pdf." Is it because
of transition process?

Thank you.

K.W.Ng

Your paper isn't recognised as a pdf file, you didn't by any chance upload the word version of the file?

Anthony

Hi Anthony,

As far as I remember, I re-uploaded the pdf one, but will upload it again.

Regards,

Afshin

Seems everything is back to normal !!!!

Afshin

So, to clarify if I understand well

You are using the bees to generate solutions with the tendency towards improvement and use a meta-heuristic to seed out dominated solutions. It makes sense.

Do you have any guidance about the choice of parameters to improve the quality of the Pareto optimal set found?

Does the number of Pareto optimal points found correlate to the number of sites maintained?

Hi Vlado,

The parameters are chosen imperically, but it is not like that the certain parameter values will give the acceptable answers, if they are chosen in a normal range we will get acceptable answers but maybe in more iterations.

The number of Pareto optimal points is corelated to the number of selected sites and number of iterations, for example if we decrease the number of selected sites but increase the number of iterations, we will find roughly the same number of Pareto optimal points.

Hope I am giving the answer.

Afshin

Dear Capt. Shahriar

Thanks for your comments and interest in the Bees Algorithm.

This paper is about multi objective function in continious domain, but the bee team are working on the combinatorial problems too and the specific problem you mention is one of the problems they have in their hand. As you have valuable experiences in this field, I am sure my colleagues looking forward to consult about these kind of problems with you.

Regrards,

Ashin

Dear Captain Shahriar,

Thanks again for your nice comments and question. I beleive the Bees Algorithm could be used to optimise the location of the containers in the cargo ship in order to have minimum difference between real C.G. and desired C.G. It would be a very intersting area and I think the next paper will be in this area !!!!

It might be interesting as well to optimise the location of C.G. and broken stowage, using the multi objective Bees Algorithm.

Regards,

Afshin

Does this mean that the sites don't get stuck at a local optimum? Or you refer to the effect what the scouts have on the whole process

Dear Shahriar,

Optimisations of the cargo loading in containers and calculating the centre of gravity of cargo seem an interesting application and a promising area of research for the bees Algorithm.
As my bee-college Afshin mentioned earlier it is a similar to some of the applications we are dealing with at the moment.
If you have any matrail to read and data sets to run our algorithm on, please email them to me at otris1@cf.ac.uk

Thanks again for your interest and
good luck, captain, in your journey among the bees world!

King-Bee
Sameh
Sameh Otri
PhD Research Student

Hi Vlado,

You are absolutely right, the algorithm will not stuck in local minimum. In the basic version, this problem was existing and when the algorithm reaches a local optimum, it was stucking there till finding better solution from random search. But, in the new version, when there is no new information to discover in a patch (means bee is located in the local or global optimum), the algorithm records that position and move the bee to other positions as it does not help to keep searching in the neighbourhood of that site.

Regards,

Afshin

Hi Ahmed,

Theoritically, there is no resteriction about the number of objective functions but the more the number of objective function, the more number of population and selected sites and iteration needed. This means, increasing the number of objective functions, increases the computation to get Pareto optimal set.

Regards,

Afshin

Dear Masoud,

Thanks for your comment. There are some packages which include optimisatio toolbox like Matlab. In these packages you can find toolboxes for optimisation with algorithms like Genetic Algorithm, Simulated Anealing, and ... . But not the Bees Algorithm at the moment maybe they have not discovered how good is the Bees Algorithm !!!. I am sure they will include the Bees Algorithm in their packages very soon, meantime you are so welcome the software provided in Cardiff Bay Bees to optimise single and multi objective functions.

Regarding the second question, the Bees Algorithm does not need any specific information about the problem unless the objective function. But in the end the algorithm will come up with some values for the parameters which withoes parameter value we will recieve the optimum objective function. If some there is a resteriction about the parameters values, these limitations can be stated as constraints in the algorithm and algorithm avoids to choose a value in unfeasiable regions.

Hope could give you some explanations and please do not hesitate to contact if there is any other issues.

Regards,

Afshin

How do you judge if there is new information or not?

What criteria do u use?

Sameh Otri
PhD Research Student

Dear Sameh,

In the new version of the Bees Algorithm two parts have been added (detals are in the Lapmamap 2007 paper titled Preliminary Design using the Bees Algorithm) shrinking and abondonment. If after some iterations, the representative bee in a site is not changing, it means that the neighbourhood search can not find any other better solution in that specific patch size, so we shrink the neighbourhood size to do more detal searching and if after some shrinkings still the representative bee is unchanged, it is assumed that the bee is located on a peak ( which can bee local or global optimum ).

Regards,

Afshin

What if these criteria (number of shrinking and the shrinking step) were not right? [i.e. you stopped shrinking after 20 times but if u made the shrink number 21st you may find better results or when you select the shrinking step it was slightly greater the position of the optimum]

In these cases, the Bees Algorithm may miss the global optimum as well (if we consider the patch as a search space and zoom in it) as you will stop search around that patch?

So is there a real guarantee that the Bees Algorithm will not stuck in local optimum?

Thanks again

Sameh Otri
PhD Research Student

Thanks Sameh for your detailed questions.

If we do not choose the parameters, defenitaly we will not get good results but the range of parameters which are acceptable or give good results are very wide. In the case of number iteration before abondonment, it should have a good chance to find a better solution in neighbourhood if there is any by trying enough number of iterations. If the optimum is outside the patch size, when algorithm finds a better solution and choose that one as representative, in the next attempt, the patch will be shifted as the new representative be in the centre so the patch will move without changing the size of course. In this case, as algorithm runs, the representative will be more close to the optimum (local or global) and after some iterations, the optimum will be in the patch.

Please let me know if you need more explanation or it raised another question.

Regards,

Afshin

Thanks for your comment Mr Uraz.

There is a comparison with GA (the only result could be found in the litrature).The GA and the Bees Algorithm results are illustrated and can be seen that the Bees Algorithm will give longer Pareto front and more Pareto optimal points.

Regards,

Afshin

Dear Afshin
Thanks very much for prompt answer and the compliments for software use.
Just with few more Qs:

Is the accuracy of algorithm's output a function of sample size? What about the measurement erros?

thanks again,
Masoud

Thanks again for your comments.

About the accuracy, I would like to refer you to the Bees paper in IPROMS 2006, which you can find a very good comparison about the accuracy and speed of the algorithm with other optimisation algorithms. But here the comparison can only made by visuality as unfortunately the results we from GA are only shown in the graph. Accordings the graphs illustrated in the paper for results obtained from the GA and the Bees Algorithm, it can be seen that the Bees Algorithm can give slightly more accurate answers (the answers are closer to 0,0).

Regards,

Afshin

Thanks for your comments. Maximising f(x) is equal to minimising -f(x) and vice versa. So we can change any maximising problem to another minimising problem and vice versa.

Actually, in the Bees Algorithm maximising problems will be solved. so if we have minimising problem, first we change them to maximising problem then solve them.

There is acomparison with GA and can bee seen that the Bees Algorithm can find longer Pareto front than GA.

This problem is an optimisation problem and there are other techniques and algorithms for solving multi-objective function optimisation problems (Multi-Objective Optimization using Evolutionary Algorithms, by Deb). Here the authors are introducing a new algorithm for solving multi-objective function problems called the Bees Algorithm for multi-objective function.

Regards,

Afshin

You are right, the reults are compared with results reported in Deb[12] and we did not test the NSGA and NSGAII.

Regrads,

Afshin

Thanks for your comments. In multi-objective problems, there are two stages; first optimisation which will come up with Pareto optimal set or set of non-dominated solutions, and second, decision making or finding the most suitable solution among the Pareto optimal set. In the paper, the first stage was explained and Multi-objective Bees Algorithm is developed to generate the Pareto optimal set. Actually, decision making stage is not optimisation problem any more and in this stage according the specification of the problem and other factors like availabilty of materials, one of the non-dominated solutions will be chosen.

In the specified problem, the goal is to produced as much as possible more non-dominated solutions and of course the Pareto front to be as long as possible.

There is another paper about the same problem but with only onr objective function, and in that case the algorithm came up with one solution rather than a set. This paper is submitted to publish in IMCHE, and has a very good numerical comparison with GA and other techniques.

Regards,

Afshin

Dear Afshin,

Currently I have no access to the paper of Deb[12]. But I believe you have the paper, so I have a number of questions here:
Do you know what is the population size being used in their test using NSGA and NSGAII?
Do they use the similar technique like the one you use where you collect pareto-front solutions and update them whenever there's a better one?

Thanks

Ang

Hi Ang,

The refernce number 12 is a Technical Report and you can find it online with this address: http://www.iitk.ac.in/kangal/reports.shtml#2000
Technical Report No. 200002

As you can see in the report, unfortunately there is no information about the population size and other parameters used in thd GAs. The technique for creating the Pareto optimal set is also a bit different as the technique we used in the Multi-Objective Bees Algorithm is based on the carasteristics of the Bees Algorithm.

Regards,

Afshin