理解scipy盆地跳跃优化函数的例子

哇，好吧.抛开这些不谈，让我们考虑一下如何使用 basinhopping 函数.从文档中我们可以看到典型的接受条件是通过 take_step 参数访问的，并且文档说:默认的步进例程是坐标的随机位移，但其他步进算法可能对某些系统更好."因此，即使除了您的 mybounds 边界检查器之外，该函数也会对坐标进行随机位移以生成要尝试的新点.由于这个函数的梯度只是常数1，所以它总是在负梯度的方向上做同样的大步(为了最小化).在实际层面，这意味着 x1 的建议点总是在区间 [0,1] 之外，你的边界检查器将总是否决他们.当我运行你的代码时，我看到这种情况一直在发生:在 [5]: spo.basinhopping(f1,x0,accept_test=mybounds,callback=print_fun,niter=200,minimizer_kwargs=minimizer_kwargs)在最小值 -180750994.1924 接受 0[ -1.80746874e+08]错误的在最小值 -180746877.5530 接受 0[ -1.80746873e+08]错误的在最小值 -180746877.3896 接受 0[ -1.80750991e+08]错误的在最小值 -180750994.7281 接受 0[ -1.80746874e+08]错误的在最小值 -180746878.2433 接受 0[ -1.80746874e+08]错误的在最小值 -180746877.5774 接受 0[ -1.80746874e+08]错误的在最小值 -180746878.3173 接受 0[ -1.80750990e+08]错误的在最小值 -180750994.3509 接受 0[ -1.80750991e+08]错误的在最小值 -180750994.6605 接受 0[ -1.80746874e+08]错误的在最小值 -180746877.6966 接受 0[ -1.80746874e+08]错误的在最小值 -180746877.6900 接受 0[ -1.80750990e+08]错误的在最小值 -180750993.9707 接受 0[ -1.80750990e+08]错误的在最小值 -180750994.0494 接受 0[ -1.80750991e+08]错误的在最小值 -180750994.5824 接受 0[ -1.80746874e+08]错误的在最小值 -180746877.5459 接受 0[ -1.80750991e+08]错误的在最小值 -180750994.6679 接受 0[ -1.80750991e+08]错误的在最小值 -180750994.5823 接受 0[ -1.80750990e+08]错误的在最小值 -180750993.9308 接受 0[ -1.80746874e+08]错误的在最小值 -180746878.0395 接受 0[ -1.80750991e+08]错误的# ... 等等.所以它从不接受posposal点.输出并没有告诉您它已找到解决方案.它告诉您，探索可能的解决方案的随机扰动不断导致优化器看起来越来越好，但始终无法满足您的标准.它无法一路回到 [0,1] 来获得 do 满足 mybounds 的点数.I came across the basin hopping algorithm in scipy and created a simple problem to understand how to use it but it doesnt seem to be working correctly for that problem. May be I'm doing something completely wrong.Here is the code:import scipy.optimize as spoimport numpy as npminimizer_kwargs = {"method":"BFGS"}f1=lambda x: (x-4)def mybounds(**kwargs): x = kwargs["x_new"] tmax = bool(np.all(x <= 1.0)) tmin = bool(np.all(x >= 0.0)) print x print tmin and tmax return tmax and tmindef print_fun(x, f, accepted): print("at minima %.4f accepted %d" % (f, int(accepted)))x0=[1.]spo.basinhopping(f1,x0,accept_test=mybounds,callback=print_fun,niter=200,minimizer_kwargs=minimizer_kwargs)The solution it gives is x: array([ -1.80746874e+08]) 解决方案 The function you are testing makes use of an approach called Metropolis-Hastings, which can be modified into a procedure called simulated annealing that can optimze functions in a stochastic way.The way this works is as follows. First you pick a point, like your point x0. From that point, you generate a random perturbation (this is called a "proposal"). Once there is a proposed perturbation, you get your candidate for a new point by applying the perturbation to your current out. So, you could think of it like x1 = x0 + perturbation.In regular old gradient descent, the perturbation term is just a deterministically calculated quantity, like a step in the direction of the gradient. But in Metropolis-Hastings, perturbation is generated randomly (sometimes by using the gradient as a clue about where to randomly go... but sometimes just randomly with no clues).At this point when you've got x1, you have to ask yourself: "Did I do a good thing by randomly perturbing x0 or did I just mess everything up?" One part of that has to do with sticking inside of some bounds, such as your mybounds function. Another part of it has to do with how much better/worse the objective function's value has become at the new point.So there are two ways to reject the proposal of x1: first, it could violate the bounds you have set and be an infeasible point by the problem's definition; second, from the accept/reject assessment step of Metropolis-Hastings, it could just be a very bad point that should be rejected. In either case, you will reject x1 and instead set x1 = x0 and pretend as if you just stayed in the same spot to try again.Contrast that with a gradient-type method, where you'll definitely, no matter what, always make at least some kind of movement (a step in the direction of the gradient).Whew, all right. With that all aside, let's think about how this plays out with the basinhopping function. From the documentation we can see that the typical acceptance condition is accessed by the take_step argument, and the documentation saying this: "The default step taking routine is a random displacement of the coordinates, but other step taking algorithms may be better for some systems." So, even apart from your mybounds bounds checker, the function will be making a random displacement of the coordinates to generate its new point to try. And since the gradient of this function is just the constant 1, it will always be making the same big steps in the direction of negative gradient (for minimizing).At a practical level, this means that the proposed points for x1 are always going to be quite outside of the interval [0,1] and your bounds checker will always veto them.When I run your code, I see this happening all the time:In [5]: spo.basinhopping(f1,x0,accept_test=mybounds,callback=print_fun,niter=200,minimizer_kwargs=minimizer_kwargs)at minima -180750994.1924 accepted 0[ -1.80746874e+08]Falseat minima -180746877.5530 accepted 0[ -1.80746873e+08]Falseat minima -180746877.3896 accepted 0[ -1.80750991e+08]Falseat minima -180750994.7281 accepted 0[ -1.80746874e+08]Falseat minima -180746878.2433 accepted 0[ -1.80746874e+08]Falseat minima -180746877.5774 accepted 0[ -1.80746874e+08]Falseat minima -180746878.3173 accepted 0[ -1.80750990e+08]Falseat minima -180750994.3509 accepted 0[ -1.80750991e+08]Falseat minima -180750994.6605 accepted 0[ -1.80746874e+08]Falseat minima -180746877.6966 accepted 0[ -1.80746874e+08]Falseat minima -180746877.6900 accepted 0[ -1.80750990e+08]Falseat minima -180750993.9707 accepted 0[ -1.80750990e+08]Falseat minima -180750994.0494 accepted 0[ -1.80750991e+08]Falseat minima -180750994.5824 accepted 0[ -1.80746874e+08]Falseat minima -180746877.5459 accepted 0[ -1.80750991e+08]Falseat minima -180750994.6679 accepted 0[ -1.80750991e+08]Falseat minima -180750994.5823 accepted 0[ -1.80750990e+08]Falseat minima -180750993.9308 accepted 0[ -1.80746874e+08]Falseat minima -180746878.0395 accepted 0[ -1.80750991e+08]False# ... etc.So it's never accepting the posposal points. The output is not telling you that it has found a solution. It's telling you than the random perturbing to explore possible solutions keeps resulting in points that look better and better to the optimizer, but which keep failing to satisfy your criteria. It can't find its way all the way back to [0,1] to get points that do satisfy mybounds. 这篇关于理解scipy盆地跳跃优化函数的例子的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持！