52 lines
1.9 KiB
Python
52 lines
1.9 KiB
Python
import numpy as np
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from typing import List, Dict, Tuple
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import numpy as np
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# 动态生成收益函数
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def revenue_functions(num_projects):
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functions = []
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for i in range(num_projects):
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# 这里可以根据实际需求调整系数
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a = -0.1 - 0.05 * i # 二次项系数，每次递减 0.05
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b = 2 + 0.5 * i # 一次项系数，每次递增 0.5
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def r(x, a=a, b=b):
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return a * x**2 + b * x
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functions.append(r)
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return functions
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def dpsa(num_projects, total_resource, num_iterations, step_size):
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# 初始化每个项目的资源分配为 0
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resource_allocation = [0] * num_projects
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revenue_funs = revenue_functions(num_projects)
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for _ in range(num_iterations):
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# 保存上一次的资源分配结果
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prev_allocation = resource_allocation.copy()
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for i in range(num_projects):
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# 计算当前项目的梯度（导数）
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gradient = (revenue_funs[i](resource_allocation[i] + step_size) - revenue_funs[i](resource_allocation[i])) / step_size
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# 更新资源分配
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resource_allocation[i] += gradient * step_size
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# 确保资源分配不超过总资源
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if sum(resource_allocation) > total_resource:
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# 调整资源分配以满足约束条件
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excess = sum(resource_allocation) - total_resource
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# 按比例减少每个项目的资源分配
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factor = (total_resource - sum(resource_allocation[:i])) / (sum(resource_allocation[i:]))
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for j in range(i, num_projects):
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resource_allocation[j] *= factor
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# 判断是否收敛
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if np.linalg.norm(np.array(resource_allocation) - np.array(prev_allocation)) < 1e-6:
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break
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# 计算总收益
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total_revenue = sum(revenue_funs[i](resource_allocation[i]) for i in range(num_projects))
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return resource_allocation, total_revenue
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