Mathematical model to optimize visualization

Mathematic Guru with design competence needed

The project involves the development of a mathematical algorithm to visualize project relationships. Please take now a look at the attached sample graphic. The goal of your work is to find the best Project positioning (x and y) to make the overall graphic for the user easy to follow and understand.

The graphic can be explained the following way:
Green = one way relationship
Red = two way relationship
Solid line = strong relationship
Dotted line = weak relationship
Red Line with dots = two way relationship. (strong and weak)

The algorithm (placement of the projects) should minimize the overall combined length of all lines as well the number of points where lines cross each other. The algorithm should also avoid lines on-top of each other.

Your mathematical model will be used to optimize the visualization. The mathematical algorithm should work Model should work with any number of projects.

Please message me if further explanation is needed to make a bid.

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