- I looked up linear programming in AIMA and found very little contents.

I'm not familiar with the LP solvers, however I looked it up on

wikipedia and found the "Simplex" algorithm... but I was unable to see

the connection with load-optimization. Perhaps you could shed some

more light on this?

Thanks for the reply.

Regards,

John.

--- In aima-talk@yahoogroups.com, "Robin" <rhewitt@...> wrote:

>

> This is a classic Operations Research problem that

> I'd think would be straightforward to solve by linear

> programming. Have you looked into using an LP solver?

>

> -- Robin

>

> --- In aima-talk@yahoogroups.com, "zappbrann" <john@> wrote:

> >

> > Hello,

> >

> > I'm trying to build an application that optimizes the way packages

> > (cargo) are loaded into a 3D space (truck). The goal is to fit as

many

> > packages as possible.

> >

> > I've looked at using a standard search algorithm (from chapter 3)

> > However, the branching factor is definitely too big to make it

> > feasible. I also thought about using a planning algorithm (from

> > chapter 11) but I don't know if that is the right approach.

> >

> > Does anybody have any ideas on what types of algorithms I should

look

> > at?

> >

> > Regards,

> >

> > John.

> >

> - Hello John,

It might have helped had I mentioned the problem name. It's "bin

packing." You might try searching for that directly, or for that and

"programming."

Bin packing would actually be an integer programming problem, but one

method for tackling these is to solve first by linear programming,

ignoring the integer constraint, then find the integer solution that's

closest and is within the constraints. Better integer-programming

methods you might consider for this are Branch and Bound and Cutting

Plane:

http://mat.gsia.cmu.edu/orclass/integer/integer.html

Bin packing is NP hard, but it sounds like your particular problem

might be small. That's why I thought it would make sense to at least

look at using a direct method from OR.

There are also special-purpose methods for bin packing, however, since

it's such a classic problem and an NP-hard one. Here are some links:

http://mathworld.wolfram.com/Bin-PackingProblem.html

http://en.wikipedia.org/wiki/Bin_packing_problem

A 1D bin-packing solver:

http://www.cs.arizona.edu/icon/oddsends/bpack/bpack.htm

I did a quick search and find that people have used genetic algorithms

to solve, and to optimize solutions for, bin packing problems. That

might be more along the lines of what you were originally looking for.

The idea would be to use a heuristic (such as sorting by size) with a

greedy algorithm to solve non-optimally, then use a GA to optimize

the solution.

Finally, the resource I've found most helpful for understanding the

principles of LP is the classic text by George Dantzig: Linear

Programming and Extensions:

http://www.amazon.com/gp/product/0691059136/102-0117124-8181715?v=glance&n=283155

-- Robin

--- In aima-talk@yahoogroups.com, "zappbrann" <john@...> wrote:

>

> I looked up linear programming in AIMA and found very little contents.

> I'm not familiar with the LP solvers, however I looked it up on

> wikipedia and found the "Simplex" algorithm... but I was unable to see

> the connection with load-optimization. Perhaps you could shed some

> more light on this?

>

> Thanks for the reply.

>

> Regards,

> John.

>

> --- In aima-talk@yahoogroups.com, "Robin" <rhewitt@> wrote:

> >

> > This is a classic Operations Research problem that

> > I'd think would be straightforward to solve by linear

> > programming. Have you looked into using an LP solver?

> >

> > -- Robin

> >

> > --- In aima-talk@yahoogroups.com, "zappbrann" <john@> wrote:

> > >

> > > Hello,

> > >

> > > I'm trying to build an application that optimizes the way packages

> > > (cargo) are loaded into a 3D space (truck). The goal is to fit as

> many

> > > packages as possible.

> > >

> > > I've looked at using a standard search algorithm (from chapter 3)

> > > However, the branching factor is definitely too big to make it

> > > feasible. I also thought about using a planning algorithm (from

> > > chapter 11) but I don't know if that is the right approach.

> > >

> > > Does anybody have any ideas on what types of algorithms I should

> look

> > > at?

> > >

> > > Regards,

> > >

> > > John.

> > >

> >

> - On Wed, Jun 14, 2006 12:22:56PM -0000, zappbrann wrote:
> Hello,

It is a very interesting problem. Please post the solutions, links, etc you find

>

> I'm trying to build an application that optimizes the way packages

> (cargo) are loaded into a 3D space (truck). The goal is to fit as many

> packages as possible.

to solve it.

--

Ivan F. Villanueva B.

A.I. library: http://www.artificialidea.com

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