Evaluate priority weightings for cycling profiles

[aoles]

Investigate the difference in routing between original GraphHopper's PriorityWeighting and ours OptimizedPriorityWeighting in the context of reducing the number of preparations needed for running CALT with bike profiles.

The original GH weight scaling function based on priorities:

ORS OptimizedPriorityWeighting:

What currently happens is that the penalties of WORST (0), AVOID_AT_ALL_COSTS (1) and REACH_DEST (2) are bumped up by multiplying the weights by 1.25. However, the weight of AVOID_IF_POSSIBLE (3) is multiplied by 2.0 increasing it beyond AVOID_AT_ALL_COSTS. Effectively this means rearranging the priorities by stating that AVOID_IF_POSSIBLE is worse than AVOID_AT_ALL_COSTS. The factor for AVOID_IF_POSSIBLE was changed 3 years ago from 1.1 to 2.0 for no apparent reason.

Evaluate the impact of the following alternatives of altering OptimizedPriorityWeighting:

• reduce the factor for priority AVOID_IF_POSSIBLE (3) from 2.0 to 1.25
• scale all "bad" priorities 0-3 equally by 2.0 (increase steepness of the curve)
• shift all "bad" priorities 0-3 upwards by 2.0 (S-shape type of curve)

An example where the fastest route makes more sense than the recommended one.

[aoles]

R script for visualizing the weight scaling functions

PRIORITY_CODE = c(
  WORST = 0,
  AVOID_AT_ALL_COSTS = 1,
  REACH_DEST = 2,
  AVOID_IF_POSSIBLE = 3,
  UNCHANGED = 4,
  PREFER = 5, 
  VERY_NICE = 6,
  BEST = 7
)

## priority values returned by the priority encoder
priority <- function(code) code / unname(PRIORITY_CODE["BEST"])

sapply(PRIORITY_CODE, priority)
#>              WORST AVOID_AT_ALL_COSTS         REACH_DEST  AVOID_IF_POSSIBLE 
#>          0.0000000          0.1428571          0.2857143          0.4285714 
#>          UNCHANGED             PREFER          VERY_NICE               BEST 
#>          0.5714286          0.7142857          0.8571429          1.0000000

## original weight scaling function
priorityWeighting <- function(x) 1 / (0.5 + priority(x)) 

## current recommendend weighting
optimizedPriorityWeighting <- function(x) {
  w = 1
  if (x <= PRIORITY_CODE["REACH_DEST"])
    w = w * 1.25
  else if (x <= PRIORITY_CODE["AVOID_IF_POSSIBLE"])
    w = w * 2
  
  w / (0.5 + priority(x)) 
}

## reduce the factor for priority AVOID_IF_POSSIBLE (3) from 2.0 to 1.25
optimizedPriorityWeightingReduce <- function(x) {
  w = 1
  if (x <= PRIORITY_CODE["AVOID_IF_POSSIBLE"])
    w = w * 1.25
  
  w / (0.5 + priority(x)) 
}

## scale all "bad" priorities 0-3 equally by 2.0 (increase steepness of the curve)
optimizedPriorityWeightingScale <- function(x) {
  w = 1
  if (x <= PRIORITY_CODE["AVOID_IF_POSSIBLE"])
    w = w * 2
  
  w / (0.5 + priority(x)) 
}

## plots
plot(PRIORITY_CODE, sapply(PRIORITY_CODE, priorityWeighting), ylim = c(0.5, 4), pch = 16, ylab = "weight scaling")
points(PRIORITY_CODE, sapply(PRIORITY_CODE, optimizedPriorityWeighting), col = "red")
points(PRIORITY_CODE, sapply(PRIORITY_CODE, optimizedPriorityWeightingReduce), col = "green", pch = 3)
points(PRIORITY_CODE, sapply(PRIORITY_CODE, optimizedPriorityWeightingScale), col = "blue", pch = 4)

^{Created on 2020-04-20 by the reprex package (v0.3.0)}

[aoles]

Proposed new priority scaling function for recommended (blue) vs. the GH's default priorityWeighting (black) and current recommended (red).

newPriorityWeighting <- function(x) {
  best = PRIORITY_CODE["BEST"]
  val = priority(x) * best - ceiling(best/2)
  2^(-val/3) 
}

[aoles]

Evaluation results of recommended weighting alternatives:

• Interactive visualisation of 100 random cycling routes across Bayern (source)
• Systematic analysis based on 1000 random routes with uniform length distribution (source)

The results were obtained with 63b3313.