ILP for pathfinding/routing

[makslevental]

This PR implements routing/path-finding using ILP (using Gurobi/or-tools) through the python pass registration mechanism landed in #710.

Background literature on the (static) Traffic Assignment problem can be found here and here. Brief summary of the model follows; define:

• $(i,j) \in A$ : edges/wires between switchboxes;
• $\mathbf{h}$ : all possible flows, indexed by possible paths $\pi \in \Pi(r, s)$ from path-endpoint (source) $r$ to path-endpoint (target) $s$;
• $d^{rs}$ : number of flows we need to route from $r$ to $s$;
• $x_{ij}$ : amount of flow across an edge/link/wire;
• $t_{ij}(x_{ij})$ : the link performance/penalty functions.

Then the optimization problems is

$$\begin{align} \min_{\mathbf{x}, \mathbf{h}} & & \sum_{\mathbf{h}} t_{ij}(x_{ij})\cdot x_{ij} && (1) \\\ \text{s.t.} & & x_{ij} = \sum_{\pi \in \Pi} \delta_{ij}^\pi h^\pi && (2) \\\ && d^{rs} = \sum_{\pi \in \Pi(r ,s)} h^\pi && (2) \\\ && x_{ij} \in \{0, \dots, c_{ij} \} && (3) \end{align}$$

where

1. the objective to minimze, is the Total System Sime (TST), i.e., can be read as "minimize distance $\times$ time for all flows";
2. flow constraints - flow across each edge is the sum of contributions from all flows with paths passing through that edge;
3. all requested flows must be routed;
4. each edge must not exceed its capacity.

The above model is (roughly) encoded in two modeling languages (Gurobi and or-tools), in utils.py, and tested in CI (only or-tools). Furthermore, in the or-tools formulation, another objective is implemented (minimum number of global edges) in order to compare/constrast with the existing AIEPathfinder.

I am still iterating on the pieces/parts/places but the core (the modeling) is done (I believe) and it would be good to get feedback on the design ASAP.