使用 DEAP 最小化 multi-objective 函数

Question

我正在尝试通过使用 DEAP 库最小化自定义函数来执行多重 objective 优化。虽然我在对几个 objectives（目标）进行最小化时得到了不错的结果，但对于超过 3 或 4 个，它无法收敛。通常它会将第一个 objective 最小化为 0，同时让其他 objective 跳来跳去（不最小化）。

我使用 sci-kit 库构建了一个元模型（岭回归）来描述一些模拟数据，因此我的模型基于系数和截距（包含在我的代码中）。新预测基于约 150 个均匀变化的输入。

有一个最小化 3 个目标的年份选项，以及一个最小化 8 个目标的月份选项。

我已经将我的代码作为要点包括在内，因为它非常大。 请找HERE.

问题： 任何人都知道剩余的 objective 未被最小化的原因可能是什么？我尝试过选择、变异和交叉过程，但还没有成功。或者它可能与模型本身有关？我也尝试过不同的重量来健身，但不知为何似乎并没有什么不同。

年度目标的结果：

每月目标的结果：

Answer 1

只是回答我自己的问题。

看来我在评估期间没有返回正确类型的值。

更改为差异的 RMSE 而不是目标和预测之间的绝对差异达到了目的：

def EvaluateObjective(individual):
    prediction = calculate(individual, for_sensitivity)
    prediction = [int(i) for i in prediction]

    # diff = []
    # for y in range(len(targets)):
    #     output = math.sqrt((targets[y] - prediction[y]) ** 2)
    #     #output = abs(targets[y] - prediction[y])
    #     diff.append(output)

    rmse = np.sqrt((sum((i - j)**2 for i, j in zip(prediction, targets)) / len(targets)))

    return (rmse,)

Answer 2

您为我一直苦苦挣扎的问题提供了解决方案。好方法，一个小技巧让我的程序也能运行！

我很确定一定有很多 deap 用户像我一样尝试使用两个以上的权重，比如 weights=(-1.0, -1.0, 1.0)。

我将post 3 个参数的简单示例（2 个参数最小化，1 个参数最大化。）

例子是关于"How to load as many items as possible with conditions of maximum weight, maximum size"
条件：
1. 最小化权重总和。
2. 最小化大小和。
3. 最大化值的总和。

from numpy import array
import numpy
import random
from deap import base, creator, tools, algorithms

###  Multi-objective Optimization Problem  ###

IND_INIT_SIZE = 5

MAX_WEIGHT = 2000 # kg
MAX_SIZE = 1500 # m**3


# Create the item dictionary:

r = array([[213, 508,  22],  # 1st arg : weight / 2nd arg : size / 3rd arg : value
       [594, 354,  50],
       [275, 787,  43],
       [652, 218,  46],
       [728, 183,  43],
       [856, 308,  33],
       [727, 482,  45],
       [762, 683,  26],
       [707, 450,  19],
       [909, 309,  45],
       [979, 247,  42],
       [259, 705,  42],
       [260, 543,  14],
       [899, 825,  17],
       [446, 360,  35],
       [491, 818,  47],
       [647, 404,  17],
       [604, 623,  32],
       [900, 840,  45],
       [374, 127,  33]] )


NBR_ITEMS = r.shape[0]

items = {}
# Create random items and store them in the items' dictionary.
for i in range(NBR_ITEMS):
    items[i] = ( r[i][0] , r[i][1] , r[i][2] )


creator.create("Fitness", base.Fitness, weights=(-1.0, 1.0 ))  # Note here <- I used only two weights!  (at first, I tried weights=(-1.0 , -1.0, 1.0)) but it crashes. With deap, you cannot do such a thing.

creator.create("Individual", set, fitness=creator.Fitness)

toolbox = base.Toolbox()

# Attribute generator
toolbox.register("attr_item", random.randrange, NBR_ITEMS)

# Structure initializers
toolbox.register("individual", tools.initRepeat, creator.Individual, toolbox.attr_item, n=IND_INIT_SIZE) #
toolbox.register("population", tools.initRepeat, list, toolbox.individual)


def evaluation(individual):
    weight = 0.0
    size =0.0
    value = 0.0

    # Maximize or Minimize Conditions
    for item in individual:
        weight += items[item][0]  # It must be minimized.
        size += items[item][1]  # It must be minimized.
        value += items[item][2]  # It must be maximized.

    # Limit Conditions
    if weight > MAX_WEIGHT or size > MAX_SIZE:
        return 10000, 0

    if value == 0:
        value = 0.0000001

    MinFitess_score = weight + size   # NOTE : Minimize weight, size
    MaxFitenss_score = value  # NOTE : Maximize weight, size

    return MinFitess_score , MaxFitenss_score,



def cxSet(ind1, ind2):
    """Apply a crossover operation on input sets. The first child is the
    intersection of the two sets, the second child is the difference of the
    two sets.
    """
    temp = set(ind1)  # Used in order to keep type
    ind1 &= ind2  # Intersection (inplace)
    ind2 ^= temp  # Symmetric Difference (inplace)
    return ind1, ind2


def mutSet(individual):
    """Mutation that pops or add an element."""
    if random.random() < 0.5:
        if len(individual) > 0:  # We cannot pop from an empty set
            individual.remove(random.choice(sorted(tuple(individual))))
    else:
        individual.add(random.randrange(NBR_ITEMS))
    return individual,  # NOTE comma(,) , if there's no comma, an error occurs.



toolbox.register("mate", cxSet)
toolbox.register("mutate", mutSet)
toolbox.register("select", tools.selNSGA2) # NSGA-2 applies to multi-objective problems such as knapsack problem
toolbox.register("evaluate", evaluation)


def main():
    ngen = 300  # a number of generation  < adjustable value >

    pop = toolbox.population(n= 300)
    hof = tools.ParetoFront() # a ParetoFront may be used to retrieve the best non dominated individuals of the evolution
    stats = tools.Statistics(lambda ind: ind.fitness.values)
    stats.register("avg", numpy.mean, axis=0)
    stats.register("std", numpy.std, axis=0)
    stats.register("min", numpy.min, axis=0)
    stats.register("max", numpy.max, axis=0)

    algorithms.eaSimple(pop, toolbox, 0.7, 0.2, ngen=ngen, stats=stats, halloffame=hof, verbose=True)

    return hof, pop


if __name__ == "__main__":
    hof, pop = main()

    print(hof) # non-dominated individuals' list  # the fittest value is placed on the most right side.

理想结果：

个人({1, 2, 19, 4}) 或
个人({1, 2, 19, 3})

因为他们的总分很相近。您将获得其中一个结果。

使用 DEAP 最小化 multi-objective 函数

Minimizing multi-objective function using DEAP

python

scikit-learn

deap