Re: [eclipse-clp-users] Pareto Optimality + Branch and Bound?

From: Marco Zimmerling <marco_at_...260...>
Date: Thu, 29 Apr 2010 10:38:20 +0200
Hi Philipp,

I'm not aware of any ECLiPSe framework for Pareto front 

As Andrzej suggested, one of the most common methods is the weighted sum 
approach. Assuming two objective functions f1(X) and f2(X), with X being 
the vector of decision variables, the single criteria problem becomes

   f(X) = w1*f1(X) + w2*f2(X),

where w1 and w2 are weights that *should* reflect the importance of each 
objective. Typically, one assumes w1 + w2 = 1. By solving this problem 
for different combinations of w1 and w2, you can generate different 
Pareto optimal points. However, it is impossible to obtain points on 
non-convex portions of the Pareto front, and it is often difficult to 
generate a smooth Pareto front (i.e., without holes). So it is 
worthwhile to look into other approach as well. The article "Survey of 
multi-objective optimization methods for engineering" by Marler and 
Arora (Struct Multidics Optim 26, pp. 369-395, 2004) provides a good 
overview of multiobjective optimization methods, including a discussion 
of pros and cons.

Another branch of research uses evolutionary methods to find good 
approximations of the Pareto front. The optimization problem is treated 
as a black box; the focus lies on efficient stochastic search methods. 
If you want to get a feeling:


Andrzej Lewandowski wrote:
> Convert to standard optimization problem (i.e. single criteria) using
> weighted sum of individual criteria
> A.L.
> -----Original Message-----
> From: Philipp Marcus [mailto:marcus_at_...247...] 
> Sent: Wednesday, April 28, 2010 4:13 PM
> To:
> Subject: [eclipse-clp-users] Pareto Optimality + Branch and Bound?
> Hi,
> I have a COP with two cost variables and I'm searching for a pareto 
> optimal solution. Though it would be nice to get the complete pareto 
> front, I'd already be happy with *one* pareto optimal value. Is there a 
> framework I could use? If not so, do you have any suggestions how this 
> could be implemented?
> Best regards,
> Philipp
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Received on Thu Apr 29 2010 - 08:56:12 CEST

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