I am using networkx to work on shortest path problems. I am mostly using shortest_path. I was wondering if, with the current version of networkx, it is possible to constrain the shortest path calculation?

The example below generated these two shortest paths between A and G:

The picture on the left shows the best route when minimizing a 'length' attribute and the one on the right, when minimizing a 'height' attribute.

If we compute the stats for these routes we got:

Best route by length: ['A', 'B', 'E', 'F', 'D', 'G']
Best route by height: ['A', 'C', 'E', 'G']
Stats best routes: {
                   'by_length': {'length': 13.7, 'height': 373.0}, 
                   'by_height': {'length': 24.8, 'height': 115.0}
                   }

Is there a way to add a constrain when calculating the shortest path? (e.g. calculate the shortest path by minimizing the length attribute but also keeping height<300

Code to compute the graph network:

import matplotlib.pyplot as plt
from itertools import combinations, groupby
import os
import numpy as np
import networkx as nx
import random


# 1. Define test network 
MG = nx.MultiDiGraph()
MG.add_edges_from([("B", "A", {"length": 0.8}), ("A", "B", {"length": 1.}), ("D", "G", {"length": 3.5}),
                   ("B", "D", {"length": 20.8}), ("A", "C", {"length": 9.7}), ("D", "C", {"length": 0.3}),
                   ("B", "E", {"length": 4.8}), ("D", "E", {"length": 0.05}), ("C", "E", {"length": 0.1}),          
                   ("E", "C", {"length": 0.7}), ("E", "F", {"length": 0.4}), ("E", "G", {"length": 15.}),           
                   ("F", "C", {"length": 0.9}), ("F", "D", {"length": 4.}),                       
                  ])
attrs = {'B': {"x": -20., "y": 60.}, 'A': {"x": 28., "y":55.},
         'C': {"x": -12., "y": 40.}, 'D': {"x": 40., "y":45.},
         'E': {"x": 8., "y": 35.}, 'F': {"x": -8., "y":15.},    
         'G': {"x": 21., "y":5.},    
        }

for num, (k,v) in enumerate(attrs.items()):
    attrs[k]={**v,
             }  
nx.set_node_attributes(MG, attrs)

rng = np.random.default_rng(seed=42)
random_height = list(rng.uniform(low=0, high=100, size=len(MG.edges)).round(0))
attrs={}
for num, edge in enumerate(MG.edges):
    attrs[edge]={'height': random_height[num]}
nx.set_edge_attributes(MG, attrs)


# 2. Calculate shortest route
best_route_by_length = nx.shortest_path(MG, "A", "G",weight="length")
print(f"Best route by length: {best_route_by_length}")

best_route_by_height = nx.shortest_path(MG, "A", "G",weight="height")
print(f"Best route by height: {best_route_by_height}")

# 3. Get stats for each route

def get_route_edge_attributes(
    G, route, attribute=None, minimize_key="length", retrieve_default=None
):
    """
    """
    attribute_values = []
    for u, v in zip(route[:-1], route[1:]):
        # if there are parallel edges between two nodes, select the one with the
        # lowest value of minimize_key
        data = min(G.get_edge_data(u, v).values(), key=lambda x: x[minimize_key])
        if attribute is None:
            attribute_value = data
        elif retrieve_default is not None:
            attribute_value = data.get(attribute, retrieve_default(u, v))
        else:
            attribute_value = data[attribute]
        attribute_values.append(attribute_value)
    return attribute_values


stats_best_route={}
stats_best_route['by_length']={'length': sum(get_route_edge_attributes(MG,
                                                                   best_route_by_length,
                                                                  'length')),
                              'height': sum(get_route_edge_attributes(MG,
                                                                   best_route_by_length,
                                                                  'height'))}
stats_best_route['by_height']={'length': sum(get_route_edge_attributes(MG,
                                                                   best_route_by_height,
                                                                  'length')),
                              'height': sum(get_route_edge_attributes(MG,
                                                                   best_route_by_height,
                                                                  'height'))}

print(f"Stats best routes: {stats_best_route}")

Edit 07/06/21

My problem is potentially too large to be able to use a brute force solution.

I also opened a post in the networkx discussion page, it seems possible to implement a special class that acts numerical in single_source_dijkstra. However, this solution is not perfect: if there are two admissible short paths (in height), the algorithm will find the shorter one regardless of its height. This can make it look impossible to reach a destination node, when an admissable path exists... (more details here: https://github.com/networkx/networkx/discussions/4832#discussioncomment-778358)