vvs
107 lines
3.9 KiB
Python
107 lines
3.9 KiB
Python
"""Demo 3 - Multi-criteria candidate selection.
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You have 100 candidates evaluated on 4 independent criteria
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(quality, cost-efficiency, robustness, compatibility - or whatever
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your domain calls them). You want to pick the ones worth a deeper
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look.
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Naive ranking by total score finds the high-mean candidates - which
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are often single-criterion peaks that compensate with weakness on
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the rest.
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SEM's two-stage filter
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1) best-tradeoff filter ('Pareto core')
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2) cross-criterion filter ('non-redundant witnesses')
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finds the genuine all-rounders: candidates that are not strictly
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worse than another on every axis AND that contribute meaningfully on
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multiple axes (not just one).
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Run:
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python 03_multicriteria_selection.py
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"""
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from __future__ import annotations
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import numpy as np
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from sem_cython12 import wrapper as cy
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def main() -> int:
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if not cy.available():
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print("ERROR: sem_cython12 compiled extension did not load.")
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return 1
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rng = np.random.default_rng(7)
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N, K = 100, 4
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criteria_names = ["Quality", "Cost-efficiency", "Robustness", "Compatibility"]
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# Most candidates: noisy uniform draws across the criteria
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S = rng.uniform(0.30, 0.95, size=(N, K))
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# Inject 5 hidden 'all-rounders' that score moderately well on EVERY
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# criterion - none top any single axis, but they're well-balanced.
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S[0:5] = rng.uniform(0.65, 0.85, size=(5, K))
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# ---- Naive ranking by sum of scores ---------------------------------
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naive_order = np.argsort(S.sum(axis=1))[::-1]
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naive_top10 = naive_order[:10]
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# ---- SEM ranking ----------------------------------------------------
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pareto_mask = cy.pareto_core_mask(S)
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pareto_idx = np.where(pareto_mask == 1)[0]
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nrw = cy.non_redundant_witnesses(S)
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# ---- Reporting ------------------------------------------------------
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print(f"Candidates : {N}")
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print(f"Criteria : {K} ({', '.join(criteria_names)})")
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print()
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print(f"Best-tradeoff frontier size : {len(pareto_idx)}")
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print(f"Cross-criterion winners (NRW) : {len(nrw)}")
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print(f"Hidden all-rounders we injected : 5 (indices 0-4)")
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print()
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overlap_with_hidden = set(nrw.tolist()) & set(range(5))
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naive_overlap_with_hidden = set(naive_top10.tolist()) & set(range(5))
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print(f"NRW recovered hidden all-rounders : "
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f"{len(overlap_with_hidden)}/5 {sorted(overlap_with_hidden)}")
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print(f"Naive top-10 found hidden all-rounders: "
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f"{len(naive_overlap_with_hidden)}/5 {sorted(naive_overlap_with_hidden)}")
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print()
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# Profile of NRW candidates
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print("Cross-criterion winners (NRW) - score profiles:")
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print(f" {'idx':>4} " + " ".join(f"{n[:8]:>9}" for n in criteria_names) +
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f" {'min':>5} {'mean':>5}")
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for i in nrw:
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scores = S[i]
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print(f" {int(i):>4} " +
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" ".join(f"{v:9.3f}" for v in scores) +
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f" {scores.min():5.2f} {scores.mean():5.2f}")
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print()
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print("Naive top-3 (by total score) - score profiles for comparison:")
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print(f" {'idx':>4} " + " ".join(f"{n[:8]:>9}" for n in criteria_names) +
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f" {'min':>5} {'mean':>5}")
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for i in naive_top10[:3]:
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scores = S[i]
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print(f" {int(i):>4} " +
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" ".join(f"{v:9.3f}" for v in scores) +
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f" {scores.min():5.2f} {scores.mean():5.2f}")
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print()
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# Wow line - honest comparison
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n_nrw_hits = len(overlap_with_hidden)
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n_naive_hits = len(naive_overlap_with_hidden)
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print(f"*** SEM's NRW filter recovered {n_nrw_hits}/5 hidden all-rounders. ***")
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print(f"*** Naive sum-of-scores top-10 found only {n_naive_hits}/5. ***")
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if n_nrw_hits > n_naive_hits:
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print(f"*** SEM surfaces {n_nrw_hits - n_naive_hits} candidates the naive ranking misses ***")
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print(f"*** because they don't peak on any single criterion. ***")
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return 0
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if __name__ == "__main__":
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raise SystemExit(main())
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