Convergence error

Replies to This Discussion

Permalink Reply by Robert Vier on August 26, 2014 at 3:09

if you could explain yourself a bit more i could eventually give an answer

Permalink Reply by Dan Hou on August 26, 2014 at 5:31

Hi Robert,

The objectives are about daylight and energy consumption. The convergence graphs change a lot in early generation but little in later generations. How do the convergence graphs reflect the objective values? Is there any function representing the relation between them?

Bests,

Dan

Permalink Reply by Robert Vier on September 3, 2014 at 1:31

Convergence Graphs are built simply like the following:

- One graph per goal dimension Di

- Take the last X generations (depending on the 'history' slider in the top left of the viewport)

- Get the upper and lower bound of Di for each generations elite (light grey) and pareto front (dark grey)

- Take all the bounds of Di out of X and scale them to [0;1]

- Draw the bounds over the generations

.. this is the only 'function' they have got.

Regarding their change over generations, you might want to check on the formulation of your fitness functions. It's impossible to tell you what goes wrong without having a look at your setup.

David Rutten has elaborated fitness functions quite a bit on his blog, and recently also in a paper:

http://ieatbugsforbreakfast.wordpress.com/2014/08/22/icgg2014-paper/

http://ieatbugsforbreakfast.wordpress.com/2011/03/

http://ieatbugsforbreakfast.wordpress.com/2011/03/04/fitness-functi...

if you open up galapagos, you find the links.

Best

Robert

Permalink Reply by Robert Vier on September 3, 2014 at 1:35

.. So a Convergence Graph which is just dark grey means that the algorithm found as many pareto-non-dominant solutions (forming the pareto front) such that all the elite consists of them.

from a certain point on, the pareto-front has to be truncated to fit the elite size - which is done either by the hypervolume contribution or after the SPEA2 archiving strategy.

Permalink Reply by Dan Hou on August 26, 2014 at 5:53

And I find the result graph is also strange:

1. Most values of one objective (uniformity performance) are centralizing around one value (0). I think this is related to the objective features. Because my variable is discrete, the values of objectives may distribute unevenly. In other words, many individules may share a very closed value of one objective. Does this condition influence the optimization results?

2. And from the two-dimensional plane by other two objectives (total energy consumption and UDI100-2000), all the solution seem to be around a monotonous curve？ What reasons lead to this condition?

3. If the generation is adequate, is it possible to solve those problems?

Thank you for your help.

Dan

Permalink Reply by Robert Vier on September 3, 2014 at 1:50

the yellow solutions are the history of the run. only the red ones represent the current state of the search - where you can set different opacities for the pareto-front and the rest of the elite in the top left corner of the viewport.

1) yes this probably has an effect, since the algorithm potentially cannot make as good decisions on where to go when an objective remains the same for a set of different parameters. but it does not necessarily mean that it suffers badly.

2) the monotonous curve is the history. your solutions are quite sparsely distributed in the objective space which can mean an overconstrained problem (discontinuous pareto front) or that your search parameters have to be adjusted - respectively it found some niches to converge to.

3) what do you mean with adequate and solve..?! nobody knows your generation, problem, or how to solve it.

Permalink Reply by Dan Hou on September 1, 2014 at 20:22

Hi Robert,

What is meaning of this condition that the convergence graphs rebound in the last few generations?

Bests,

Dan

Permalink Reply by Robert Vier on September 3, 2014 at 2:13

aparently the elite / pareto front had a reason to grow in its extents again. 

option

1) the algorithm is still in the elite filling phase. means all the pareto-non-dominant solutions are contained in the elite. either the remaining space in the elite is filled with the best non-front-solutions according to SPEA2-fitness, or according to their hypervolume contribution (the hightest ones are added)

2) the algorithm is in the pareto-front-truncation phase if there are more non-dominant solutions than the elite can take. so either the front is truncated by the SPEA2-strategy based on euclidean multi-dimensional distances or, again, the least hypervolume contribution.

it can always happen that the algotihm discovers new solutions which make those filling / truncation schemes select a different set.

Permalink Reply by Dan Hou on September 3, 2014 at 5:41

Hi Robert,

Thank you for your patient reply. Indeedly, I need to make some adjustion on my variables. And what about above problem? Why do the three convergence graphs rebound at the same time in the last few generations?

Bests,

Dan