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

From: Andrzej Lewandowski <lewando_at_...28...>
Date: Thu, 29 Apr 2010 07:51:06 -0500
```"However, it is impossible to obtain points on non-convex portions of the
Pareto front"

OP said that single element of Pareto Point would be enough. For non-convex
Pareto sets and "smooth" traversing Pareto sets see, for example

A.L.

-----Original Message-----
From: Marco Zimmerling [mailto:marco_at_...260...]
Sent: Thursday, April 29, 2010 3:38 AM
To: eclipse-clp-users_at_lists.sourceforge.net
Subject: Re: [eclipse-clp-users] Pareto Optimality + Branch and Bound?

Hi Philipp,

I'm not aware of any ECLiPSe framework for Pareto front
generation/approximation.

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:
http://www.tik.ee.ethz.ch/sop/publicationListFiles/zlb2004a.pdf

Marco

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: eclipse-clp-users_at_lists.sourceforge.net
> 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 - 12:51:14 CEST

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