Football player roaster formation algorithm

As for the algorithm, I tried using Google to find the solution but still can't (((

✅ v0.1 - Here are the basic requirements:

Input variables:

1. Total time to play (e.g. 120 mins)
2. Number of players with their names (e.g. 13)
3. Number of teams (e.g 2) - for now only consider 2 teams, and don't design application for other cases
4. Players per team (e.g. 5)

Output results:

1. Optimal amount of time between "switches", so that everybody plays ~ the same amount of total time.
2. Roaster of 2 teams for each of the "switches"
3. Each player shall play with as many people in his team as possible - "player rotation"

Use case:

1. User inputs the variables in a form of table, for example
2. User gets roaster of each "switch", including player names on each team
3. Some debug information may be presented:
   1. Optimal amount of time between "switches"
   2. Number of minutes every player plays (calculated based on formed roaster)
   3. Matrix of each player (x-axis) to each player (y-axis), where the intersection shows amount of minutes that each player plays with another player on the same team

Example :

Switch 1 - min 0-7:

Player A	Player F
Player B	Player G
Player C	Player H
Player D	Player I
Player E	Player J

Switch 2 - min 7-14:

Player K	Player F
Player L	Player G
Player C	Player H
Player D	Player A
Player E	Player B

…

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✅ v0.2 - Goalkeeper changes

Based on v.0.1 input variables form:

1. Roaster of goalkeepers with timestamps on each team

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✅ v0.3 - Players ranking affects roaster formation

Introduce new input variables:

1. For each player - ranking shall be introduced
2. scale: 1,2,3,4,5

Output:

1. Players ranking affects roaster formation so that each team is "balanced" - total amount of "ranking points" between teams deviates as little as possible (e.g. 23<->22)

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✅ v0.4 - Players role affects roaster

Introduce new input variables:

1. For each player - position
2. possible values: attack, middle, defense

Output:

1. Players role affects roaster formation so that each team is "balanced" - each team has ~ equal amount of attackers, midfielders & defenders