Grasshopper

algorithmic modeling for Rhino

# Structural Optimization

Good Evening to everyone,

I'm writing here because I'm trying to optimize a girder bridge for my thesis.

I'm trying to achieve the less expensive construction material, with the problem of satisfy structural verifications (1 fitness for any of these, like stress in the beam must not exceed the elastic value, ecc..). Now, my problem is that, since I know that a solution with 3 beam of specific dimension and another solution of 4 beam with smaller dimension of the other, can be the same in terms of cost and tension, I obtain a huge pareto front solution.

At this point I don't really know how to proceed because, I need to find the "best" solution in terms of cost that minimize every subtraction verification simultaneously.

Any idea?

Thank you in advance.

Leonardo

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### Replies to This Discussion

Hi Leonardo,

From the standpoint of multi-objective optimization, all solutions on the Pareto front are equally good, in the sense that improvement in terms of one criterion implies losses in one or more other criteria. The idea is that the shape of the Pareto front will help you to make decisions about which objectives are more important than others by visualizing the trade-offs involved.

In your case, you probably have too many objectives for this understanding of trade-offs to occur, because it's difficult to visually understand a Pareto front with more than two or three objectives.

So I would recommend having less objectives, for example by replacing some objectives with penalties.(Btw, having that many objectives also makes the optimization very difficult. To be precise, for multi-objective optimization, the difficulty increases exponentially with each objective (!)).

Let me know if that helps, and if you have more questions!

Cheers,

Thomas

Hi Thomas and thank you for your help. My english is not so good, and I excuse for this, but I try to express myself as best as I can.

As you suggested, I've tried to reduce the fitness function to only one (Cost of the structural material in my case) and penalize the individuals that not satisfy the structural verification by multipliyng the cost for that iteration for a factor 10. This seem to work really good, infact I obtained a convergence of the results in a specific area and number of beams.

Now, I've to modify something because the thickness of the insole, tend to minimum of the range (only because it's the most expensive material in my case), despite the validation of structural verification that is satisfied with the maximum height of the beams.

I'm expecting a insole thickness about 20-30 cm and beams height less that the maximum. I increase the range of the thickness insole to a minimum of 20 cm, but I hope the solution tend to a larger value.

Do you have some suggestion in this case?

Your post was really helpful, thank you so much again for the perfect explanation!

Leonardo

Hi Leonardo,

I not sure what you mean with "insole", but assume you're talking about the flanges (i.e., the horizontal elements) of the beams.

I'm not a structural engineer, but to me it makes sense to prefer taller beams with less material, when the goal is to save material, because, in that way, you get the geometric benefit of a larger cross section.

If you prefer the beams less tall, I'd limit their maximum height, rather than specify a minimum material thickness (unless you have other reasons for it).

Cheers, Thomas

PS: Are you still using Octopus for the single-objective optimization?

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