Using Python Pulp for binary optimization for multi-day player selection

Question

I am struggling with an integer optimization question using pulp. I am creating a fantasy sports team - where I need to select 11 players on each game day. [assume only 2 game days for simplicity]. The other constraint is that I cannot make more than 3 changes over the 2 days. In other words, 8 players need to be the same between the 2 days. The players I buy need to be within a budget of 100 credits.

I have 2 decision variables: i.e. the selected team for each of the 2 days.

    prob = LpProblem("Fantasy_Cricket", LpMaximize)
    player_names = list(squad.Player)
    player_gd1 = LpVariable.dicts("playerChosen1", player_names, 0, 1, cat='Integer')
    player_gd2 = LpVariable.dicts("playerChosen2", player_names, 0, 1, cat='Integer')

FYI: player_names refers to a list of all available players. The objective function is to maximize the predicted score over the 2 days (gd1 and gd2 refer to gameday 1 and game day 2). This is a function of the player selected * his 'Value' and whether his team is playing on a given day.

    prob += lpSum([player_gd1[p]*squad[squad.Player==p]['Value'].sum()*squad[squad.Player==p]['gd1'].sum() + player_gd2[p]*squad[squad.Player==p]['Value'].sum()*squad[squad.Player==p]['gd2'].sum() for p in player_names])

Constraints set are as follows:

    prob += lpSum([player_gd1[p]*squad[squad.Player==p]['Points'].sum() for p in player_names]) <=100
    prob += lpSum([player_gd2[p]*squad[squad.Player==p]['Points'].sum() for p in player_names]) <=100
    
    prob += lpSum([player_gd1[p] for p in player_names]) == 11
    prob += lpSum([player_gd2[p] for p in player_names]) == 11
    
    prob += lpSum([((player_gd1[p] + player_gd2[p]) ==2) for p in player_names]) >=8

The first 4 constraints are working fine. It is the 5th one that results in an 'infeasible' solution. Basically, I am enforcing a rule that at least 8 players are common across the 2 days.

prob.solve()
print("Status:", LpStatus[prob.status])

Status: Infeasible

I am new to Python and PuLP. Can anyone help? What am I missing?

Reiterating here that the first 4 constraints are working fine. It is the introduction of the 5th (which is a constraint on multi-day selection) that causes issues.

Thanks in advance.

I think this is going to involve adding a second index for the game and a few other things. But let's back up a second... I don't see anything in your model that would motivate swapping players? You are selecting players for just 1 team, right? and that team has a series of games. Each player has a cost and a value. What in your model would make the team selection different from game 1, game 2, ..., game N? Also, it would be highly beneficial if you edited your post and included a chunk of the squad dataframe. — AirSquid
– AirSquid, Commented Oct 3, 2020 at 16:53
@AirSquid, to clarify: I am allowed to change upto 3 players per day. My team is a composite team of multiple teams and hence the ability to accrue points on a day is a function of whether a particular team is really playing or not. — Venu
– Venu, Commented Oct 4, 2020 at 9:06

kabdulla · Accepted Answer · 2020-10-03 13:37:43Z

1

Your last constraint:

prob += lpSum([((player_gd1[p] + player_gd2[p]) ==2) for p in player_names]) >=8

Is not a valid constraint in PuLP. I can see what you are trying to achieve, creating an intermediary binary variable ((player_gd1[p] + player_gd2[p]) ==2) which is then summed across the players. If you want to do it this way you would have to explicitly declare this binary variable and find a way of forcing it to take a true value if (and only if) that condition is satisfied.

For example you could create a new set of variables:

player_swapped = LpVariable.dicts("player_swapped", player_names, 0, 1, cat='Integer')

And then have a set of constaints as:

for p in player_names:
    player_swapped[p] >= player_gd1[p] - player_gd2[p]
    player_swapped[p] >= player_gd2[p] - player_gd1[p]

You can then set a constraint on how many players can be swapped between the games.

answered Oct 3, 2020 at 13:37

kabdulla

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2 Comments

Venu Over a year ago

brilliant! Thanks for your prompt response. It absolutely resolved the issue.

kabdulla Over a year ago

I'm glad it helped. If you're question is answered consider marking my answer as such (small tick)

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