Automated generation of concentric circles metro maps using mixed-integer optimization
Bibliographic record
Abstract
The concentric circles (CC) map design is an alternative approach for schematically representing metro systems. Compared with traditional octo-linear maps, CC maps can effectively simplify the perception of a network by visually accenting circular line patterns. This design offers new insights into the schematic drawing of metro systems that can improve map readability and engagement. Automated mapping studies in the literature have mostly applied the traditional octo-linear design using optimization methods, where design criteria are modeled as constraints and/or objective functions in a constrained mixed-integer optimization program, whereas the automated CC map drawing approach has received less attention. In this article, we develop an automatic CC map drawing method by adopting map design criteria as a mixed-integer programming problem. Numerical experiments are conducted using (a) a simple network to illustrate the model procedure in detail, (b) two real-world metro networks in Vienna and Montréal to analyze the effects of the selected map center and parameter settings and (c) the Beijing subway to analyze the applicability of the proposed approach to large-scale metro networks.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".