I wrote the first paper that formally introduced the metro map layout problem in 2004, by presenting aesthetic criteria and the first algorithmic solutions. Previously, all the metro maps were drawn by hand.
Our methods were evaluated using the metro maps of CityRail (Sydney), London, Paris and Tokyo. This paper, the first on the problem, is well cited by Info Vis researchers from UK, Germany, Greece and Tawian, and the solution is still the most practical method.

Seok-Hee Hong, Damian. Merrick and Hugo do Nascimento, The Metro Map Layout Problem, Journal of Visual Language and Computing, 17(3), pp. 203-224, 2006, Elsevier.

We investigate the new problem of automatic metro map layout. In general, a metro map consists of a set of lines which have intersections or overlaps. We define a set of aesthetic criteria for good metro map layouts and present a method to produce such layouts automatically. Our method uses a variation of the spring algorithm with a suitable preprocessing step. The experimental results with real world data sets show that our method produces good metro map layouts quickly.

Seok-Hee Hong, Damian Merrick and Hugo A D do Nascimento, The Metro Map Layout Problem , Proceedings of Graph Drawing 2004, Lecture Notes in Computer Science 3383, Springer, pp. 482-491, 2004.

We address a new problem of automatic metro map layout. In general, a metro map consists of a set of lines which have intersections or overlaps. We present a method to produce a good layout of a metro map automatically. Our method uses a variation of the spring algorithm with a suitable preprocessing step. The experimental results with real world data sets show that our approach is promising.

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