Someone expert for network analysts!

[NaoyaAKITA]

Hello, I am a student trying to do a Vehicle Routing Problem with ArcGIS Pro Network Analyst.For the first, I tried some simple problems and got answers.However, I have some troubles.

This is the 4 patterns I set up.

Pattern1：Fixed Cost=0, Cost Per Unit Time=1, Cost Per Unit Distance=0

Pattern2：Fixed Cost=1, Cost Per Unit Time=1, Cost Per Unit Distance=0

Pattern3：Fixed Cost=0, Cost Per Unit Time=1, Cost Per Unit Distance=1

Pattern4：Fixed Cost=1, Cost Per Unit Time=1, Cost Per Unit Distance=1

*Every pattern has one route(Capacity=160, no time window).

*16 visit places and 1 depot are the same in every pattern.

*Visit Places：Service time=0, Delivery_1=10, no time window

*Depot：Service time=0

Then, I got the answers.

In Pattern1 and Pattern2, total travel time is 329.109977.

In Pattern and Pattern4, total travel time is 328.119617.

Why is the answer of Pattern1 and Pattern2 longer than that of Pattern and Pattern4?

Please help me.

[HeatherMoe]

The VRP solver uses a heuristic meaning it does not find an exact (best) solution every time but instead follows a series of steps to get a good answer. Those series of steps change based on the parameters that are set in the problem and can result in the solver finding a different good (local optimal) solution. By changing the cost of the distance it affects the total overall cost the solver is trying to minimize and so it might (and in your case does) find a different local optimal solution then when the solve is run without the distance cost because it is solving a different problem.

If you look at the output from those four solves you might also see that the total distance traveled is shorter for patterns 3 and 4 and that the shorter distance cost offsets the slightly longer travel time.

[NaoyaAKITA]

Thank you for your kindness.

Can I ask you some more questions?

I got the output about total distance and time from four solves.
In Pattern1 and Pattern2, total travel time is 329.109977 and total distance is 269818.52764.
In Pattern 3 and Pattern4, total travel time is 328.119617 and total distance is 266143.493321.
Pattern3 and 4 are shorter than Pattern1 and 2 in both total travel time and total distance.
So, it contradicts that the total distance traveled is shorter for patterns 3 and 4 and that the shorter distance cost offsets the slightly longer travel time.
Why?

In addition, I want to understand when the algorithm converges.
Could you tell me when the algorithm reaches convergence in VRP?

[HeatherMoe]

With both the travel time and distance slightly shorter, this seems like it is just a product of the solver being a heuristic and by passing in different parameters it is going through a slightly different set of steps.