异星工厂中的高品质产率分析

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异星工厂中的高品质产率分析

ControlNet · 2024-12-31 · via ControlNet Blog

异星工厂的品质扩展包给游戏带来了新的生产规划挑战，比起像以前只能横向扩张工厂的规模，现在可以通过使用高品质的工厂和插件，大幅增加产量。为了最大化如传奇品质的高品质物品的生产，我们需要对高品质产率的计算和规划进行一些分析。

这里先初步的设计了两个蓝图，一个是用于电星蓝图的高品质原料生产，通过读取当前物流网络的信号，自动的将多余物品拿去回收，不断的生产高品质的原料。对于原料级别的物品（如铁板、铜板），比起直接放入回收机拿到同样的物品，将其放入到组装机里生产更高级别的物品，然后再回收回来，可以获得更高的品质。

例如下图里的：
blueprint1
Fig. 1. 回收原料生产高品质物品的例子.

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blueprint2
Fig. 1. 回收产物生产高品质物品的例子.

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如果是生产高品质的原料，比如说铜板，那么将铜板生产成铜线，就会考虑到底是使用产能插件好还是质量插件好。虽然质量插件提升了出现高品质物品的概率，但是产能插件大幅增加了产率，特别是高品质的高级产能插件，能提升相当大比例的产率，可能能生产出更多的高品质物品。

$$
\begin{align*}
T &= \begin{pmatrix}
T_{普通到普通} & T_{普通到罕见} & T_{普通到稀有} & T_{普通到史诗} & T_{普通到传奇} \\
0 & T_{罕见到罕见} & T_{罕见到稀有} & T_{罕见到史诗} & T_{罕见到传奇} \\
0 & 0 & T_{稀有到稀有} & T_{稀有到史诗} & T_{稀有到传奇} \\
0 & 0 & 0 & T_{史诗到史诗} & T_{史诗到传奇} \\
0 & 0 & 0 & 0 & T_{传奇到传奇} \\
\end{pmatrix} \\
&= (1 + P)\begin{pmatrix}
Q_{普通到普通} & Q_{普通到罕见} & Q_{普通到稀有} & Q_{普通到史诗} & Q_{普通到传奇} \\
0 & Q_{罕见到罕见} & Q_{罕见到稀有} & Q_{罕见到史诗} & Q_{罕见到传奇} \\
0 & 0 & Q_{稀有到稀有} & Q_{稀有到史诗} & Q_{稀有到传奇} \\
0 & 0 & 0 & Q_{史诗到史诗} & Q_{史诗到传奇} \\
0 & 0 & 0 & 0 & Q_{传奇到传奇} \\
\end{pmatrix}
\end{align*}
$$
其中$P$是额外产率，比如说用了产能插件之后会增加，而对于回收机来说，应该取值$P=-0.75$。而矩阵中的$Q_{*}$是指在给定总共的质量加成$Q$的情况下，计算出的
每一个品级到另一个品级的转换率。这部分的计算可以参考官方wiki^[1]。

type production_after_assembler(bound iter: i32, common: f32, uncommon: f32, rare: f32, epic: f32, legendary: f32)
type production_after_recycler(bound iter: i32, common: f32, uncommon: f32, rare: f32, epic: f32, legendary: f32)

type prod_rate(f32)
type qual_rate(f32)
type assembler_base_prod(f32)

type MachineType = ASSEMBLER | RECYCLER  
type n_slots(f32, MachineType)
type n_qual(f32, MachineType)
type n_prod(f32, MachineType)
type base_prod(f32, MachineType)
type P(f32, MachineType)
type Q(f32, MachineType)
type T_self(f32, MachineType)
type T_c2l(f32, MachineType)
type T_c2e(f32, MachineType)
type T_c2r(f32, MachineType)
type T_c2u(f32, MachineType)
type T_u2l(f32, MachineType)
type T_u2e(f32, MachineType)
type T_u2r(f32, MachineType)
type T_r2l(f32, MachineType)
type T_r2e(f32, MachineType)
type T_e2l(f32, MachineType)

rel n_slots(4, RECYCLER)
rel base_prod(-0.75, RECYCLER)  
rel base_prod(b_p, ASSEMBLER) = assembler_base_prod(b_p)
rel n_qual(4, RECYCLER)
rel n_prod(x, m) = n_qual(y, m) and x + y == n_s and n_slots(n_s, m)

rel P(p_r * n_p + b_p, m) = n_prod(n_p, m) and base_prod(b_p, m) and prod_rate(p_r)
rel Q(q_r * n_q, m) = n_qual(n_q, m) and qual_rate(q_r)


rel T_self(1 - q, m) = Q(q, m)

rel T_c2l(q * 0.001, m) = Q(q, m)
rel T_c2e(x, m) = Q(q, m) and T_c2l(t, m) and q * 0.01 == x + t
rel T_c2r(x, m) = Q(q, m) and T_c2e(t1, m) and T_c2l(t2, m) and q * 0.1 == x + t1 + t2
rel T_c2u(x, m) = Q(q, m) and T_c2r(t1, m) and T_c2e(t2, m) and T_c2l(t3, m) and q == x + t1 + t2 + t3

rel T_u2l(q * 0.01, m) = Q(q, m)
rel T_u2e(x, m) = Q(q, m) and T_u2l(t, m) and q * 0.1 == x + t
rel T_u2r(x, m) = Q(q, m) and T_u2e(t1, m) and T_u2l(t2, m) and q == x + t1 + t2

rel T_r2l(q * 0.1, m) = Q(q, m)
rel T_r2e(x, m) = Q(q, m) and T_r2l(t, m) and q == x + t

rel T_e2l(q, m) = Q(q, m)

rel production_after_recycler(0, 1.0, 0.0, 0.0, 0.0, 0.0) 
rel production_after_assembler(
    iter, 
    (1 + p) * (c * t_self),
    (1 + p) * (c * t_c2u + u * t_self),
    (1 + p) * (c * t_c2r + u * t_u2r + r * t_self),
    (1 + p) * (c * t_c2e + u * t_u2e + r * t_r2e + e * t_self),
    (1 + p) * (c * t_c2l + u * t_u2l + r * t_r2l + e * t_e2l) + l
) = production_after_recycler(iter, c, u, r, e, l) and T_self(t_self, m) and T_c2u(t_c2u, m) 
    and T_c2r(t_c2r, m) and T_c2e(t_c2e, m) and T_c2l(t_c2l, m)
    and T_u2l(t_u2l, m) and T_u2e(t_u2e, m) and T_u2r(t_u2r, m)
    and T_r2l(t_r2l, m) and T_r2e(t_r2e, m) and T_e2l(t_e2l, m)
    and P(p, m) and m == ASSEMBLER and iter >= 0

rel production_after_recycler(
    iter + 1, 
    (1 + p) * (c * t_self),
    (1 + p) * (c * t_c2u + u * t_self),
    (1 + p) * (c * t_c2r + u * t_u2r + r * t_self),
    (1 + p) * (c * t_c2e + u * t_u2e + r * t_r2e + e * t_self),
    (1 + p) * (c * t_c2l + u * t_u2l + r * t_r2l + e * t_e2l) + l
) = production_after_assembler(iter, c, u, r, e, l) and T_self(t_self, m) and T_c2u(t_c2u, m)
    and T_c2r(t_c2r, m) and T_c2e(t_c2e, m) and T_c2l(t_c2l, m)
    and T_u2l(t_u2l, m) and T_u2e(t_u2e, m) and T_u2r(t_u2r, m)
    and T_r2l(t_r2l, m) and T_r2e(t_r2e, m) and T_e2l(t_e2l, m)
    and P(p, m) and m == RECYCLER and iter >= 0
    
rel legendary(l, n_s, n_q, p_r, q_r, b_p) = production_after_recycler(20, c, u, r, e, l) 
    and n_slots(n_s, ASSEMBLER) and n_qual(n_q, ASSEMBLER) and prod_rate(p_r) and qual_rate(q_r) and assembler_base_prod(b_p)

from scallopy import ScallopContext
from scallopy.collection import ScallopCollection
import time
import pandas as pd


possible_n_slots = [4, 5, 6, 8]

possible_prod_rate = sorted(list({
    0.04, 0.05, 0.06, 0.07, 0.10, 
    0.06, 0.07, 0.09, 0.11, 0.15, 
    0.10, 0.13, 0.16, 0.19, 0.25, 
}))

possible_qual_rate = sorted(list({
    0.01, 0.013, 0.016, 0.019, 0.025, 
    0.02, 0.026, 0.032, 0.038, 0.05, 
    0.025, 0.032, 0.04, 0.047, 0.062, 
}))

possible_assembler_base_prod = [0.0, 0.5]



inputs = {
    "n_slots": [], "prod_rate": [], "qual_rate": [], "n_qual": [], "assembler_base_prod": []
}
for n_slots in possible_n_slots:
    for prod_rate in possible_prod_rate:
        for qual_rate in possible_qual_rate:
            for n_qual in range(n_slots + 1):
                for assembler_base_prod in possible_assembler_base_prod:
                    inputs["n_slots"].append([(n_slots, 0)])
                    inputs["prod_rate"].append([(prod_rate,)])
                    inputs["qual_rate"].append([(qual_rate,)])
                    inputs["n_qual"].append([(n_qual, 0)])
                    inputs["assembler_base_prod"].append([(assembler_base_prod,)])

print("Total number of inputs: ", len(inputs["n_slots"]))

ctx = ScallopContext()
ctx.import_file("model.scl")
t0 = time.time()
ctx.compile()
print("Time: ", (t1 := time.time()) - t0)

result = [
    ScallopCollection(ctx.provenance, coll) 
    for coll in ctx._internal.run_batch([["legendary"]] * len(inputs["n_slots"]), inputs, parallel=True)
]

output = [list(*each) for each in result]
print("Time: ", (t2 := time.time()) - t1)


output = [list(each[0]) for each in output]
df = pd.DataFrame(output)
df.to_csv("output.csv", index=False, header=["output", "n_slots", "n_qual", "prod_rate", "qual_rate", "assembler_base_prod"])

在代码中，预先定义了每一种组合（不同的产能插件和品质插件的组合，还有是否有50%自带产能），然后编译Scallop模型，把每一种可能性都放进去模拟，计算出传奇物品的总产量。

heatmap_slots_4_base_prod_0.0
Fig. 3. 最优的品质插件数量，4插槽组装机，无基础产能加成 (组装机3型)

heatmap_slots_5_base_prod_0.5
Fig. 4. 最优的品质插件数量，5插槽组装机，50%基础产能加成 (电磁工厂)

heatmap_slots_8_base_prod_0.0
Fig. 5. 最优的品质插件数量，8插槽组装机，无基础产能加成 (低温工厂)

从上图可见，最大化传奇物品的产量，并不是直接堆质量插件即可，而是需要根据产能插件和品质插件提供的加成来灵活选择，主要是考虑产能插件的数值。具体的最优化选择可以以上面几张图作为参考。

此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。原文来自 — 版权归原作者所有。

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