The Next Generation of Activity-Based Travel Demand Modeling with Michel Bierlaire

For most models, it's always the trade-off between the behavioral richness and the computational cost we have.

So from the top of the three dimensions, we relax on this.

And remember while learning the Deuce-Troy model, we're running the multi-logic model, we'll talk about six different mode choice on this.

Later, even we'll talk about destination choice, we may have a 500 traffic zones.

But now with all the three dimensions being relaxed, Give a sense.

What's the dimensionality? What's the scale of magnitude here on the number of possible states? Oh, I'm talking about billions.

So even more.

The idea is that none of this methodology should try to enumerate them.

And there are techniques, especially in the context of the Markov chain Monte Carlo simulation, which are designed to simulate complex distributions actually defined on this combinatorial space.

One of them is called Metropolis Hastings, and this is really designed to actually focus on what matters.

So just to give you an example, even if you have billions of alternatives, Most of them are irrelevant because they are completely off.

They will never be attractive.

So if you are able quite easily or quite fast to identify the alternatives that matter, those who are really competing with the one that you observe, then you can actually reduce the operational size of the problem.

And this is exactly what they do in combinatorial optimization.

They actually slice the problem into pieces and get hit very fast on the irrelevant parts so that we can focus on the smaller part that really matters.

And in the context of choice modeling, this is what you try to do.

Forget about all the dominated alternatives that we don't even need to look at them and focus only on those which are actually competing with the observed alternative to understand why this one was chosen and this one was not chosen.

I have a student right now who has been able to estimate a logit model with the thousands of alternatives using only a binary logit at each iteration.

So two alternatives.

So you need to do it in a specific way.

You cannot take any alternative, but it's actually working quite well and it's promising.

So that's something that we plan to develop even.

You have several technical papers on this.

In this forum, it's hard to go into all the depths there.

Let's try a little bit to give people some intuition.

For most models, it's always the trade-off between the behavioral richness and the computational cost we have.

So from the top of the three dimensions, we relax on this.

And remember while learning the Deuce-Troy model, we're running the multi-logic model, we'll talk about six different mode choice on this.

Later, even we'll talk about destination choice, we may have a 500 traffic zones.

But now with all the three dimensions being relaxed, Give a sense.

What's the dimensionality? What's the scale of magnitude here on the number of possible states? Oh, I'm talking about billions.

So even more.

The idea is that none of this methodology should try to enumerate them.

And there are techniques, especially in the context of the Markov chain Monte Carlo simulation, which are designed to simulate complex distributions actually defined on this combinatorial space.

One of them is called Metropolis Hastings, and this is really designed to actually focus on what matters.

So just to give you an example, even if you have billions of alternatives, Most of them are irrelevant because they are completely off.

They will never be attractive.

So if you are able quite easily or quite fast to identify the alternatives that matter, those who are really competing with the one that you observe, then you can actually reduce the operational size of the problem.

And this is exactly what they do in combinatorial optimization.

They actually slice the problem into pieces and get hit very fast on the irrelevant parts so that we can focus on the smaller part that really matters.

And in the context of choice modeling, this is what you try to do.

Forget about all the dominated alternatives that we don't even need to look at them and focus only on those which are actually competing with the observed alternative to understand why this one was chosen and this one was not chosen.

I have a student right now who has been able to estimate a logit model with the thousands of alternatives using only a binary logit at each iteration.

So two alternatives.

So you need to do it in a specific way.

You cannot take any alternative, but it's actually working quite well and it's promising.

So that's something that we plan to develop even.

You have several technical papers on this.

In this forum, it's hard to go into all the depths there.

Let's try a little bit to give people some intuition.