Skyrim Alchemy Optimizer

Blake Rayvid - https://github.com/brayvid

Make the most of the ingredients you have. Maximize total magnitude (essentially in-game value) with integer linear programming in scipy.

import numpy as np
import pandas as pd
from scipy.optimize import milp, Bounds, LinearConstraint

Read in ingredients and recipes

Uses local files "ingredients_have.csv" and "recipes_can_make.csv"

I made my CSVs using this helpful spreadsheet: https://docs.google.com/spreadsheets/d/1010C6ltqv7apuBoNYuFIFSBZER4YI03Y54kIsoKs5RI/edit?usp=sharing

# Ingredients we have with quantity on hand
ingredients = pd.read_csv('ingredients_have.csv');ingredients

	Ingredient	Quantity
0	Blisterwort	4
1	Blue Butterfly Wing	4
2	Blue Dartwing	1
3	Blue Mountain Flower	24
4	Bone Meal	5
5	Butterfly Wing	6
6	Canis Root	2
7	Creep Cluster	1
8	Deathbell	6
9	Dragons Tongue	5
10	Ectoplasm	5
11	Elves Ear	10
12	Fire Salts	1
13	Fly Amanita	1
14	Frost Mirriam	3
15	Garlic	7
16	Giant Lichen	2
17	Glow Dust	2
18	Hagraven Feathers	2
19	Histcarp	2
20	Honeycomb	4
21	Ice Wraith Teeth	2
22	Imp Stool	2
23	Lavender	17
24	Luna Moth Wing	4
25	Mora Tapinella	2
26	Mudcrab Chitin	2
27	Nightshade	7
28	Nirnroot	3
29	Nordic Barnacle	2
30	Orange Dartwing	2
31	Purple Mountain Flower	15
32	Red Mountain Flower	1
33	River Betty	2
34	Rock Warbler Egg	3
35	Salt Pile	14
36	Scaly Pholiota	1
37	Skeever Tail	2
38	Slaughterfish Scales	3
39	Snowberries	6
40	Spider Egg	8
41	Spriggan Sap	3
42	Swamp Fungal Pod	2
43	Taproot	2
44	Thistle Branch	2
45	Torchbug Thorax	3
46	Troll Fat	3
47	Tundra Cotton	7
48	Vampire Dust	1
49	Void Salts	1
50	White Cap	6

# Potions list with magnitude and ingredient names (1,2 + optional 3rd)
recipes = pd.read_csv('recipes_can_make.csv')
recipes = recipes[recipes['Magnitude'] > 0];
recipes.head(20)

	Magnitude	Type	Ingredient 1	Ingredient 2	Ingredient 3	Effects	Effect 1	Effect 2	Effect 3	Effect 4	Effect 5	MyPotionID	Can Make
0	159	Mixed	Blue Dartwing	Blue Mountain Flower	Glow Dust	3	Restore Health	Damage Magicka Regen	Resist Shock	NaN	NaN	3028	True
1	156	Mixed	Blue Dartwing	Blue Mountain Flower	Nightshade	2	Restore Health	Damage Magicka Regen	NaN	NaN	NaN	3037	True
2	156	Mixed	Blue Dartwing	Blue Mountain Flower	Spider Egg	2	Restore Health	Damage Magicka Regen	NaN	NaN	NaN	3045	True
3	156	Mixed	Blue Dartwing	Blue Mountain Flower	Spriggan Sap	2	Restore Health	Damage Magicka Regen	NaN	NaN	NaN	3046	True
4	113	Mixed	Blisterwort	Blue Butterfly Wing	Blue Mountain Flower	4	Damage Stamina	Restore Health	Fortify Conjuration	Damage Magicka Regen	NaN	2130	True
5	113	Mixed	Blue Butterfly Wing	Blue Mountain Flower	Rock Warbler Egg	4	Fortify Conjuration	Damage Magicka Regen	Restore Health	Damage Stamina	NaN	2680	True
6	112	Mixed	Frost Mirriam	Histcarp	Purple Mountain Flower	4	Damage Stamina Regen	Restore Stamina	Fortify Sneak	Resist Frost	NaN	10371	True
7	110	Mixed	Blue Butterfly Wing	Blue Mountain Flower	Butterfly Wing	3	Fortify Conjuration	Damage Magicka Regen	Restore Health	NaN	NaN	2666	True
8	110	Mixed	Blue Butterfly Wing	Blue Mountain Flower	Imp Stool	3	Fortify Conjuration	Damage Magicka Regen	Restore Health	NaN	NaN	2677	True
9	110	Mixed	Blue Butterfly Wing	Blue Mountain Flower	Swamp Fungal Pod	3	Fortify Conjuration	Damage Magicka Regen	Restore Health	NaN	NaN	2684	True
10	110	Mixed	Glow Dust	Nightshade	River Betty	3	Damage Magicka Regen	Fortify Destruction	Damage Health	NaN	NaN	11628	True
11	109	Mixed	Blisterwort	Blue Mountain Flower	Spriggan Sap	3	Restore Health	Damage Magicka Regen	Fortify Smithing	NaN	NaN	2210	True
12	109	Mixed	Blue Butterfly Wing	Bone Meal	Spriggan Sap	4	Damage Stamina	Fortify Conjuration	Damage Magicka Regen	Fortify Enchanting	NaN	2703	True
13	109	Mixed	Butterfly Wing	Glow Dust	Nightshade	4	Damage Magicka	Damage Magicka Regen	Lingering Damage Stamina	Fortify Destruction	NaN	4738	True
14	109	Mixed	Creep Cluster	Ectoplasm	Histcarp	3	Restore Magicka	Fortify Magicka	Damage Stamina Regen	NaN	NaN	6302	True
15	109	Mixed	Creep Cluster	Histcarp	Red Mountain Flower	3	Damage Stamina Regen	Restore Magicka	Fortify Magicka	NaN	NaN	6550	True
16	109	Mixed	Creep Cluster	River Betty	Skeever Tail	3	Fortify Carry Weight	Damage Stamina Regen	Damage Health	NaN	NaN	6725	True
17	109	Mixed	Nightshade	River Betty	Spriggan Sap	3	Damage Health	Damage Magicka Regen	Fortify Alteration	NaN	NaN	14461	True
18	108	Mixed	Blisterwort	Blue Butterfly Wing	Spriggan Sap	4	Damage Stamina	Damage Magicka Regen	Fortify Enchanting	Fortify Smithing	NaN	2154	True
19	108	Mixed	Blisterwort	Blue Mountain Flower	Spider Egg	3	Restore Health	Damage Stamina	Damage Magicka Regen	NaN	NaN	2209	True

Create recipe matrix A in Ax <= b

One row for each ingredient, one column for each potion. "1" indicates the ingredient is used in the potion.

# Boolean matrix A says what ingredients are in what recipes
A = pd.DataFrame(0, index=range(len(ingredients)),columns=range(len(recipes)))
for i in range(len(recipes)):
  if ingredients.iloc[ingredients["Ingredient"].str.find(recipes.loc[i, "Ingredient 1"]).idxmax()]["Quantity"] > 0:
    A.iloc[ingredients["Ingredient"].str.find(recipes.loc[i, "Ingredient 1"]).idxmax(), i] = 1
  if ingredients.iloc[ingredients["Ingredient"].str.find(recipes.loc[i, "Ingredient 2"]).idxmax()]["Quantity"] > 0:
    A.iloc[ingredients["Ingredient"].str.find(recipes.loc[i, "Ingredient 2"]).idxmax(), i] = 1
  if not pd.isnull(recipes.loc[i, "Ingredient 3"]):
    if ingredients.iloc[ingredients["Ingredient"].str.find(recipes.loc[i, "Ingredient 3"]).idxmax()]["Quantity"] > 0:
      A.iloc[ingredients["Ingredient"].str.find(recipes.loc[i, "Ingredient 3"]).idxmax(), i] = 1
A.head(20)

	0	1	2	3	4	5	6	7	8	9	...	2375	2376	2377	2378	2379	2380	2381	2382	2383	2384
0	0	0	0	0	1	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	0
1	0	0	0	0	1	1	0	1	1	1	...	0	0	0	0	0	0	0	0	0	0
2	1	1	1	1	0	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	0
3	1	1	1	1	1	1	0	1	1	1	...	0	0	0	0	0	0	0	0	0	0
4	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	0
5	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	0
6	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	0
7	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	0
8	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	0
9	0	0	0	0	0	0	0	0	0	0	...	1	0	0	0	0	0	0	0	0	0
10	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	0
11	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	0
12	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	0
13	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	0
14	0	0	0	0	0	0	1	0	0	0	...	0	0	0	0	0	0	0	0	0	0
15	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	0
16	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	0
17	1	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	0
18	0	0	0	0	0	0	0	0	0	0	...	0	0	0	0	0	0	0	0	0	0
19	0	0	0	0	0	0	1	0	0	0	...	0	0	0	0	0	0	0	0	0	0

20 rows × 2385 columns

Set up optimization variables

find x to minimize f.x with Ax <= b, x >= lb

f = -1 * magnitude, b = qty of each ingredient on hand

# Objective function f.x to minimize
f = np.array(-1 * recipes['Magnitude'],dtype=int); # f = -1*value so that minimizing f.x maximizes total value

# Bounds
b_max = np.array(ingredients['Quantity'],dtype=int) # Cannot use more than we have on hand
x_lb = np.zeros(shape=len(recipes)) # Cannot use less than 0

# milp parameters
bounds = Bounds(lb=x_lb)
constraint = LinearConstraint(A, ub=b_max)
integrality = np.ones(shape=len(recipes),dtype=int) # All x should be integers

Perform optimization with scipy.optimize.milp

# Perform optimization
res = milp(c=f, integrality=integrality, bounds=bounds, constraints=constraint)

Display recommended potions to make

# Display the potions we should make to maximize magnitude where the last column is quantity to make
total_magnitude = int(-res.fun)
num_potions = int(sum(res.x))
indices_to_make = np.nonzero(res.x > 0)
to_make_df = recipes.iloc[indices_to_make].copy()
to_make_df.loc[:,'QtyToMake'] = res.x[indices_to_make].astype(int)
to_make_df.head(len(to_make_df))

	Magnitude	Type	Ingredient 1	Ingredient 2	Ingredient 3	Effects	Effect 1	Effect 2	Effect 3	Effect 4	Effect 5	MyPotionID	Can Make	QtyToMake
6	112	Mixed	Frost Mirriam	Histcarp	Purple Mountain Flower	4	Damage Stamina Regen	Restore Stamina	Fortify Sneak	Resist Frost	NaN	10371	True	2
7	110	Mixed	Blue Butterfly Wing	Blue Mountain Flower	Butterfly Wing	3	Fortify Conjuration	Damage Magicka Regen	Restore Health	NaN	NaN	2666	True	4
11	109	Mixed	Blisterwort	Blue Mountain Flower	Spriggan Sap	3	Restore Health	Damage Magicka Regen	Fortify Smithing	NaN	NaN	2210	True	3
19	108	Mixed	Blisterwort	Blue Mountain Flower	Spider Egg	3	Restore Health	Damage Stamina	Damage Magicka Regen	NaN	NaN	2209	True	1
31	108	Mixed	Blue Mountain Flower	Bone Meal	Spider Egg	3	Fortify Conjuration	Damage Stamina	Damage Magicka Regen	NaN	NaN	3416	True	4
33	108	Mixed	Blue Mountain Flower	Glow Dust	Hagraven Feathers	3	Damage Magicka Regen	Damage Magicka	Fortify Conjuration	NaN	NaN	3628	True	1
34	108	Mixed	Blue Mountain Flower	Glow Dust	Swamp Fungal Pod	3	Damage Magicka Regen	Resist Shock	Restore Health	NaN	NaN	3643	True	1
35	108	Mixed	Blue Mountain Flower	Rock Warbler Egg	Spider Egg	3	Restore Health	Damage Stamina	Damage Magicka Regen	NaN	NaN	3780	True	1
45	107	Mixed	Creep Cluster	Ectoplasm	Skeever Tail	3	Restore Magicka	Damage Stamina Regen	Damage Health	NaN	NaN	6318	True	1
57	107	Mixed	Frost Mirriam	Purple Mountain Flower	Skeever Tail	3	Resist Frost	Fortify Sneak	Damage Stamina Regen	NaN	NaN	10519	True	1
103	105	Mixed	Blue Mountain Flower	Lavender	Nightshade	2	Fortify Conjuration	Damage Magicka Regen	NaN	NaN	NaN	3749	True	7
104	105	Mixed	Blue Mountain Flower	Lavender	Spider Egg	2	Fortify Conjuration	Damage Magicka Regen	NaN	NaN	NaN	3755	True	2
303	59	Potion	Blue Dartwing	Swamp Fungal Pod	NaN	2	Resist Shock	Restore Health	NaN	NaN	NaN	3388	True	1
334	57	Mixed	Deathbell	Salt Pile	Taproot	3	Slow	Weakness to Magic	Regenerate Magicka	NaN	NaN	8001	True	1
361	55	Poison	River Betty	Salt Pile	Troll Fat	2	Slow	Damage Health	NaN	NaN	NaN	15006	True	2
367	53	Poison	Deathbell	Nirnroot	Salt Pile	2	Damage Health	Slow	NaN	NaN	NaN	7937	True	2
370	53	Poison	Deathbell	Salt Pile	Troll Fat	2	Slow	Damage Health	NaN	NaN	NaN	8004	True	1
379	50	Poison	Deathbell	Salt Pile	NaN	1	Slow	NaN	NaN	NaN	NaN	8006	True	2
384	17	Mixed	Elves Ear	Fire Salts	Salt Pile	4	Restore Magicka	Weakness to Frost	Resist Fire	Regenerate Magicka	NaN	8930	True	1
391	16	Potion	Dragons Tongue	Fly Amanita	Scaly Pholiota	4	Resist Fire	Fortify Two-handed	Fortify Illusion	Regenerate Stamina	NaN	8094	True	1
397	15	Potion	Garlic	Taproot	Vampire Dust	3	Regenerate Magicka	Restore Magicka	Regenerate Health	NaN	NaN	11060	True	1
400	14	Mixed	Ectoplasm	Giant Lichen	Void Salts	4	Restore Magicka	Weakness to Shock	Damage Health	Fortify Magicka	NaN	8576	True	1
443	12	Mixed	Canis Root	Imp Stool	Rock Warbler Egg	4	Paralysis	Restore Health	Fortify One-Handed	Damage Stamina	NaN	5088	True	2
461	12	Mixed	Luna Moth Wing	Nordic Barnacle	Orange Dartwing	3	Damage Magicka	Regenerate Health	Fortify Pickpocket	NaN	NaN	14094	True	1
465	12	Potion	Dragons Tongue	Elves Ear	Mora Tapinella	3	Resist Fire	Restore Magicka	Fortify Illusion	NaN	NaN	8058	True	2
468	12	Potion	Honeycomb	Purple Mountain Flower	Slaughterfish Scales	3	Restore Stamina	Resist Frost	Fortify Block	NaN	NaN	12905	True	1
469	12	Potion	Mudcrab Chitin	Purple Mountain Flower	Thistle Branch	3	Restore Stamina	Resist Frost	Resist Poison	NaN	NaN	14343	True	2
470	11	Mixed	Ectoplasm	Red Mountain Flower	NaN	3	Restore Magicka	Fortify Magicka	Damage Health	NaN	NaN	8873	True	1
493	11	Mixed	Dragons Tongue	Elves Ear	White Cap	3	Resist Fire	Weakness to Frost	Restore Magicka	NaN	NaN	8067	True	2
516	11	Mixed	Elves Ear	Snowberries	White Cap	3	Resist Fire	Weakness to Frost	Restore Magicka	NaN	NaN	9130	True	2
582	10	Mixed	Elves Ear	Ice Wraith Teeth	White Cap	3	Weakness to Frost	Fortify Heavy Armor	Restore Magicka	NaN	NaN	9037	True	2
658	9	Mixed	Bone Meal	Lavender	Nirnroot	3	Fortify Conjuration	Damage Stamina	Resist Magic	NaN	NaN	4095	True	1
704	9	Mixed	Purple Mountain Flower	Snowberries	Torchbug Thorax	3	Resist Frost	Restore Stamina	Lingering Damage Magicka	NaN	NaN	14933	True	3
760	9	Potion	Ectoplasm	Elves Ear	Tundra Cotton	2	Restore Magicka	Fortify Magicka	NaN	NaN	NaN	8459	True	1
765	9	Potion	Ectoplasm	Giant Lichen	Tundra Cotton	2	Restore Magicka	Fortify Magicka	NaN	NaN	NaN	8575	True	1
804	9	Potion	Garlic	Lavender	Luna Moth Wing	2	Fortify Stamina	Regenerate Health	NaN	NaN	NaN	10953	True	1
806	9	Potion	Garlic	Lavender	Salt Pile	2	Fortify Stamina	Regenerate Magicka	NaN	NaN	NaN	10961	True	5
855	9	Potion	Honeycomb	Purple Mountain Flower	Tundra Cotton	2	Restore Stamina	Fortify Block	NaN	NaN	NaN	12911	True	3
879	8	Mixed	Luna Moth Wing	Nordic Barnacle	NaN	2	Damage Magicka	Regenerate Health	NaN	NaN	NaN	14098	True	1
1017	8	Mixed	Hagraven Feathers	Lavender	Luna Moth Wing	2	Fortify Conjuration	Damage Magicka	NaN	NaN	NaN	12101	True	1
1144	8	Potion	Orange Dartwing	Purple Mountain Flower	Snowberries	2	Restore Stamina	Resist Frost	NaN	NaN	NaN	14612	True	1
1443	7	Potion	Purple Mountain Flower	Slaughterfish Scales	Tundra Cotton	2	Resist Frost	Fortify Block	NaN	NaN	NaN	14922	True	2

print(f"To maximize magnitude and therefore value, create {num_potions} potions of the {len(to_make_df)} unique types listed above for a total magnitude of {total_magnitude}.")

To maximize magnitude and therefore value, create 76 potions of the 42 unique types listed above for a total magnitude of 3905.