optimization - 如何在最小化目标参数的同时重新评估 Gekko 目标

Question

提前道歉，我刚开始学习Gekko，看看我是否可以将它用于项目。我正在尝试在玩游戏状态非常有限（50 ^ 2）和每回合选项（0-10 包括在内）的游戏时优化胜率。

据我了解，我可以使用m.solve()Gekko 功能来最小化我在这里设置的对手的赢率：

PLAYER_MAX_SCORE = 50 #Score player needs to win
OPPONENT_MAX_SCORE = 50 #Score opponent needs to win

#The opponent's current strategy: always roll 4 dice per turn
OPPONENT_MOVE = 4

m = GEKKO()
m.options.SOLVER = 1

"""
player_moves is a 2-d array where:
 - the row represents player's current score
 - the column represents opponent's current score
 - the element represents the optimal move for the above game state
Thus the player's move for a game is player_moves[pScore, oScore].value.value
"""
player_moves = m.Array(m.Var, (PLAYER_MAX_SCORE, OPPONENT_MAX_SCORE), value=3, lb=0, ub=10, integer=True)

m.Obj(objective(player_moves, OPPONENT_MOVE, PLAYER_MAX_SCORE, OPPONENT_MAX_SCORE, 100))

m.solve(disp=False)

作为参考，objective是一个函数，它根据当前玩家的行为（在 中表示）返回对手的胜率player_moves。

唯一的问题是 m.solve() 只调用一次目标函数，然后立即返回player_moves数组中的“已解决”值（结果只是定义时的初始值player_moves）。我希望 m.solve() 多次调用目标函数来确定新对手的胜率是下降还是上升。

Gekko 可以做到这一点吗？或者对于这类问题我应该使用不同的库吗？

标签： optimizationgekko

Answer 1

Gekko 创建了一个优化问题的符号表示，它被编译成字节码。因此，目标函数必须用 Gekko 变量和方程来表示。对于不使用 Gekko 变量的黑盒模型，另一种方法是使用scipy.optimize.minimize(). 有一个Gekko 和 Scipy 的比较。

西皮

import numpy as np
from scipy.optimize import minimize

def objective(x):
    return x[0]*x[3]*(x[0]+x[1]+x[2])+x[2]

def constraint1(x):
    return x[0]*x[1]*x[2]*x[3]-25.0

def constraint2(x):
    sum_eq = 40.0
    for i in range(4):
        sum_eq = sum_eq - x[i]**2
    return sum_eq

# initial guesses
n = 4
x0 = np.zeros(n)
x0[0] = 1.0
x0[1] = 5.0
x0[2] = 5.0
x0[3] = 1.0

# show initial objective
print('Initial Objective: ' + str(objective(x0)))

# optimize
b = (1.0,5.0)
bnds = (b, b, b, b)
con1 = {'type': 'ineq', 'fun': constraint1} 
con2 = {'type': 'eq', 'fun': constraint2}
cons = ([con1,con2])
solution = minimize(objective,x0,method='SLSQP',\
                    bounds=bnds,constraints=cons)
x = solution.x

# show final objective
print('Final Objective: ' + str(objective(x)))

# print solution
print('Solution')
print('x1 = ' + str(x[0]))
print('x2 = ' + str(x[1]))
print('x3 = ' + str(x[2]))
print('x4 = ' + str(x[3]))

壁虎

from gekko import GEKKO    
import numpy as np

#Initialize Model
m = GEKKO()

#initialize variables
x1,x2,x3,x4 = [m.Var(lb=1,ub=5) for i in range(4)]

#initial values
x1.value = 1
x2.value = 5
x3.value = 5
x4.value = 1

#Equations
m.Equation(x1*x2*x3*x4>=25)
m.Equation(x1**2+x2**2+x3**2+x4**2==40)

#Objective
m.Minimize(x1*x4*(x1+x2+x3)+x3)

#Solve simulation
m.solve()

#Results
print('')
print('Results')
print('x1: ' + str(x1.value))
print('x2: ' + str(x2.value))
print('x3: ' + str(x3.value))
print('x4: ' + str(x4.value))