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[×ÊÔ´] ¡¾·ÖÏí¡¿¹ØÓÚBoltzmann µÄ¼ÆËã´úÂ루MATLAB£©

¿¼Âǵ½Boltzmann·Ö²¼È·ÊµÔÚÄ£Äâ¹ý³ÌµÄÖØÒªÐÔ£¬ Ôø¾­ÊÕ¼¯¹ý¸ÃÀà´úÂ루ֻÊDz£¶û×ÈÂü»ú£©£¬Ïȹ²Ïí¸ø´ó¼Ò£¨¾­µäËã·¨£¬ÐèÒªÐÞÕý£©¡£
²£¶û×ÈÂü»ú¡¾BM£¬BoltzmannMachine¡¿ÔÚ¹¤×÷½×¶ÎµÄËÑË÷·¨²»Äܱ£Ö¤»ñµÃÈ«²¿×îÓŽâµÄÎÊÌâ
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Usage:
[MINIMUM,FVAL] = ANNEAL(LOSS,NEWSOL,[OPTIONS]);
MINIMUM is the solution which generated the smallest encountered value when input into LOSS.
FVAL is the value of the LOSS function evaluated at MINIMUM.
OPTIONS = ANNEAL();
OPTIONS is the default options structure.


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Example:
The so-called six-hump camelback function has several local minima in the range -3<=x<=3 and -2<=y<=2. It has two global minima, namely f(-0.0898,0.7126) = f(0.0898,-0.7126) = -1.0316. We can define and minimise it as follows:
camel = @(x,y)(4-2.1*x.^2+x.^4/3).*x.^2+x.*y+4*(y.^2-1).*y.^2;
loss = @(p)camel(p(1),p(2));
[x f] = anneal(loss,[0 0])
We get output:
Initial temperature: 1
Final temperature: 3.21388e-007
Consecutive rejections: 1027
Number of function calls: 6220
Total final loss: -1.03163
x =
-0.0899 0.7127
f =
-1.0316
Which reasonably approximates the analytical global minimum (note that due to randomness, your results will likely not be exactly the same).

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General simulated annealing algorithm anneal Minimizes a function with the method of simulated annealing (Kirkpatrick et al., 1983)


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