The definition is general to many optimization applications. The objective function (OF) is the procedure used to determine the response value that you are seeking to minimize or maximize, and the decision variable (DV) is the independent variable that you are changing to optimize the OF-value. A deterministic OF returns the same, identical OF-value each time it is given the same DV-value input. By contrast, some OF-values are calculated with a procedure that contains random influences that would represent possible realizations of diverse uncontrolled influences, termed Monte Carlo simulations. In this case, an identical design input, an identical DV-value, will return a distribution of OF-values.

I'm not exactly sure what your transportation network represents. But, I'll suppose it is a road, to provide specific examples. A DV could be the number of parallel lanes in a road. A deterministic OF could be the cost of the road. The more lanes, the more paving and the more land, the more cost. If you repeat the calculation tomorrow, with the same road plan, and landowners, you get the same OF-value.

A stochastic OF might represent the number of accidents. A 10-lane road would provide plenty of space. A 2-lane road (one lane in each direction) will have some people passing others in the on-coming lane. You could simulate traffic patterns (slow cars, and fast cars) and human patience (willing to go slow, wanting to pass immediately) over a year and count the number of cars that will have near misses with oncoming traffic. Depending on the random number sequence, the number might be 80 near misses. But, if you repeat the simulation, it might return 90 or 60 near misses. Each run of the simulator provides a different OF-value.

Stochastic OFs confound an optimizer search for the best DV value. Near the minimum the stochastic variability might be larger than the DV impact, and the superficial trend might make the optimizer move the DV in the wrong direction.

Dear Russell,

Thank you for your response.

For me, every comment is very useful.

At this moment I want to have some overview in what directions it is possible to be viewed this type of optimization.

In your reply I realized that I have to take care of the problem setting in each subsequent iteration.

For me, it would be desirable to examine some simple examples, at this moment, because I do not have experience with this.

I am interested for all type of transportation networks: road, rail and combination of both - intermodal.

Alejandro,

thank yuo.

Here is a list of 2D optimization examples that I use for my course. Nearly all are based on a physical situation. Nearly all are fairly simple to implement (and I include the VBA code). About a third represent stochastic responses.

Dear Russell,

thank you.