Combinatorial Auction WDP Solver

Experiments on engineering faster exact solvers for the Winner Determination Problem (WDP) in combinatorial auctions. Investigates how preprocessing and heuristic branching guidance affect Gurobi's branch-and-bound performance across random and CATS-inspired instance families.

Repository layout

src/
  data_types.py          # Bid and AuctionInstance dataclasses
  generate.py            # Random XOR auction generator
  generate_cats.py       # CATS Arbitrary / Paths / Regions generators
  model.py               # Gurobi MIP model builder (XOR-WDP formulation)
  preprocess.py          # Bid deduplication, dominance removal, decomposition
  solve.py               # solve_instance, solve_lp_relaxation, solve_by_decomposition
  heuristics.py          # bundle_size and conflict_degree priority scorers
  mip_start.py           # Greedy warm-start builder
  features.py            # Conflict graph construction and statistics
  experiment.py          # run_heuristic_comparison (dispatches to all generators)
  analysis.py            # Figure and table generation (importable library)

run_density_sweep.py     # Main branching heuristic sweep (20–60 items, 3 methods)
run_preprocessing_sweep.py  # Preprocessing / MIP-start / decomposition comparison
run_cats_sweep.py        # CATS Arbitrary sweep (40–100 items, 3 methods)
run_analysis.py          # Regenerate all figures and summary tables

results/
  density_sweep_raw.csv
  preprocessing_experiment_raw.csv
  cats_raw.csv
  figures/               # Generated figures (PDFs) and summary tables (CSVs)

report.tex / report.pdf  # Final report
refs.bib                 # BibTeX references

Requirements

• Python 3.10+
• Gurobi 13.x with a valid licence (gurobipy)
• pandas, matplotlib, numpy

pip install pandas matplotlib numpy gurobipy

Reproducing experiments

Run scripts from the repository root. Each script saves results to results/.

# Main branching heuristic sweep (~5 min)
python run_density_sweep.py

# Preprocessing / MIP-start / decomposition comparison (~2 min)
python run_preprocessing_sweep.py

# CATS Arbitrary sweep (~10 min)
python run_cats_sweep.py

# Regenerate all figures and summary tables
python run_analysis.py

Figures are written to results/figures/. Pre-computed CSVs are included so run_analysis.py can be run without re-solving.

Methods

Method	Description
default	Gurobi defaults, no preprocessing
bundle_size	Branch priorities proportional to bundle size
conflict_degree	Branch priorities proportional to conflict-graph degree
default_mip_start_bundle	Default + greedy warm start (sorted by bundle size)
decomposition_default	Solve each conflict-graph component independently

Key results

• Bundle-size priority achieves up to 11× speedup on medium-difficulty random XOR instances (50 items, 40 bidders, 20 bids each)
• At the hardest tested configuration (60 items, 40 bidders, 20 bids), heuristics regress slightly — static priority orderings are insufficient when all bids are maximally conflicted
• CATS Arbitrary instances show consistent but modest gains (1.1–1.3×); CATS Paths and Regions have near-integral LP relaxations and are solved trivially at the root node regardless of method