# Question:How can I estimate the minimum distance travelled in the x-y plane when my travel path is restricted?

## Question:How can I estimate the minimum distance travelled in the x-y plane when my travel path is restricted?

Maple

Good day all.

My particular question concerns a Traveling Salesman-type problem.

Suppose I wish to move along the x-y plane and visit specific nodes (see the attached worksheet).

Starting at the origin, A, I intend to visit four locations, B to E, and finally return to the origin point. These nodes may be visited in any order - but, my total distance travelled must be a minimum.
However, my direction of travel is restricted; namely:

1. Movement is limited to the x and y-directions only (up and down as well as left and right)
2. Horizontal (left or right) movement is permitten only at y=1 and y=10

This second rule restricts me from turning left or right in between y= 1 and 10.
The Traveling Salesman routine (attached) is constructed to select a tour that is confined to orthogonal movement but it does not observe the second restriction (i.e. move left or right when you reach y=1 or y=10).

Is there any way in which I can build this condition into the routine so that the movement along the circuit observes the restrictions?

If so - is it possible to graphically illustrate the order of travel (using arrows from point-to-point) on a point plot?

I appreciate you taking the time to read this.

MaplePrimes_May_6.mw

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