This is an implementation of the paper Jabrayilov and Mutzel (2023), which compares the MILP formulations of the vertex coloring problem, namely, the Assignment model, the POP (partial-ordering based) model, and the POPH (POP hybrid) model.
All models are the strengthened versions, along with some preprocessing tricks (e.g., an upper bound derived by a heuristic) mentioned in the paper.
Run the main.py in the root directory. It will read instances defined in config_local.yaml (downloaded from https://mat.tepper.cmu.edu/COLOR/instances.html, standard graph coloring instances) and solve them via the Assign, POP, POPH models.
This project depends on the Gurobi solver and Networkx package.
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Implement a max clique heuristic to find the initial lower bound of a graph (and add an associated constraint into the models).
- It turns out that a greedy method performs poorly and I just use the method in
Networkx.
- It turns out that a greedy method performs poorly and I just use the method in
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Automatically analyze the Gurobi logs (via implementing a parser) and output the stat file. The official package
grblogtoolsis not available for Anaconda Python 3.6. -
Add functionality to draw the convergence plot (based on Gurobi log).
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Use the initial solution of the heuristic coloring method as a warm start of MILP models.
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If the upper bound equals the lower bound, turn off the preprocessing to save the solution time.
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Avoid defining redundant variables (i.e., g_{v, H}) in the POP and POPH models.
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Restructure and refactor (WIP).
Jabrayilov, A., Mutzel, P. 2023. Strengthened partial-ordering based ILP models for the vertex coloring problem. Working Paper.