适用于噪声环境的简单一维粒子群优化算法
我正在尝试粒子群优化，并试图确定以下简单场景的最佳方法：
- 优化一维函数（即粒子沿单线移动）
- 要优化的函数可以在任意点采样该行为
- 每个位置采样的“值”非常嘈杂
- 要优化的基础函数（排除噪声）非常简单（例如具有单个全局最大值的金字塔，或具有不同高度的两个驼峰）
什么是最好的粒子群设计来解决这个问题，即用最少的样本有效地发现最优值？
I'm experimenting with particle swarm optimisation and am trying to determine the best approach for the following simple scenario:
- Optimizing a 1-dimensional function (i.e. particles are moving along a single line)
- The function to be optimised can be sampled at any point on the line
- The "value" sampled for each position is very noisy
- The underlying function to optimise (excluding the noise) is quite simple (e.g. a pyramid with a single global maximum, or two humps with different heights)
What would be the best particle swarm design to solve this problem, i.e to efficiently discover the optimum with the minimum number of samples?
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我认为粒子群优化不适合您的情况...
PSO 存储迄今为止找到的最大值及其位置。因此，如果该最大值仅由噪声引起，那么它将一直卡在那里..
您必须修改普通 PSO 才能考虑最近找到的最大值（而不是最终的全局最大值）的加权平均值，
我建议您查看：模糊粒子群优化
但那个课题还处于研究阶段，所以你可能会发现很难理解......
你也可以去模拟退火，这更适合你的情况......
I do not think that Particle Swarm Optimization is suitable for your case...
PSO stores the maximum value found so far and its location.. So if that largest value was caused only by the noise, it will stuck there all along the way..
You must modify the ordinary PSO in order to consider the weighted average of recently found maximums (not the ultimate global maximum)
I recommend to you looking at: Fuzzy Particle Swarm Optimization
But that subject is still in research phase, so you may find it hard to get to it...
You may also go to Simulated annealing, that suits your case better...
尝试向适应度函数添加一个范围，并评估统计值，例如平均值、方差以及粒子的 y 值与周围标准差之间的差异。
Try adding a range to the fitness function and evaluating statistical values like mean, variation, and the difference between your particle's y value and the surrounding standard deviation.