c2_2.htm

找的一些基於MATLAB的遺傳算法的東東。。及其將其應用於圖像分割的一些程序和文件 （畢業論文）

mso-hansi-font-family:"Times New Roman"'>一</span></p>

<p class=MsoNormal align=center style='mso-margin-top-alt:auto;mso-margin-bottom-alt:
auto;text-align:center'><span lang=EN-US>&nbsp;<u1:p> </u1:p><o:p></o:p></span></p>

<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
text-indent:24.0pt;mso-char-indent-count:2.0;tab-stops:list 0cm;mso-char-indent-size:
10.5pt'><span style='mso-bidi-font-size:13.5pt;mso-hansi-font-family:"Times New Roman"'>人生就是不断选择的过程！<u1:p>
</span><span lang=EN-US></u1:p><o:p></o:p></span></p>

<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
text-indent:24.0pt;mso-char-indent-count:2.0;tab-stops:list 0cm;mso-char-indent-size:
10.5pt'><span style='mso-bidi-font-size:13.5pt;mso-hansi-font-family:"Times New Roman"'>我们总是希望我们能选择最好的选择</span><span
style='mso-bidi-font-size:13.5pt'>—</span><span style='mso-bidi-font-size:13.5pt;
mso-hansi-font-family:"Times New Roman"'>这就叫优化<span lang=EN-US>.<u1:p> </u1:p></span></span><span
lang=EN-US><o:p></o:p></span></p>

<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
text-indent:24.0pt;mso-char-indent-count:2.0;tab-stops:list 0cm;mso-char-indent-size:
10.5pt'><span style='mso-bidi-font-size:13.5pt;mso-hansi-font-family:"Times New Roman"'>所谓最好<span
lang=EN-US>,首先是主观的,你认为最好的选择对我来说未必是最好的.而且是有条件的.</span></span><span lang=EN-US
style='font-size:13.5pt;mso-hansi-font-family:"Times New Roman"'><u1:p> </span><span
lang=EN-US></u1:p><o:p></o:p></span></p>

<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
text-indent:24.0pt;mso-char-indent-count:2.0;tab-stops:list 0cm;mso-char-indent-size:
10.5pt'><span lang=EN-US style='font-family:"Times New Roman";mso-ascii-font-family:
宋体;mso-bidi-font-family:宋体'>&nbsp;<u1:p></span><span lang=EN-US
style='mso-hansi-font-family:"Times New Roman"'> </u1:p></span><span
lang=EN-US><o:p></o:p></span></p>

<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
text-indent:24.0pt;mso-char-indent-count:2.0;tab-stops:list 0cm;mso-char-indent-size:
10.5pt'><span style='mso-hansi-font-family:"Times New Roman"'>值得一提的是<span
lang=EN-US>:优化是有成本的.为了买一件西安市场上最便宜的皮鞋,花一个月时间跑遍西安显然是不值得的.一个老太太干这种事情或许还可以理解,因为她的成本低,但是一个交大的将要参加考研的大学生干这种事情就有一点傻.这都是生活中的常识,但是我们在优化算法的学习过程中也是可以体会的.如果把精度提高1%付出的成本要大于我们由此而带来的收益,那么我们就不去做这种努力.<u1:p>
</u1:p></span></span><span lang=EN-US><o:p></o:p></span></p>

<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
text-indent:24.0pt;mso-char-indent-count:2.0;tab-stops:list 0cm;mso-char-indent-size:
10.5pt'><span lang=EN-US style='font-family:"Times New Roman";mso-ascii-font-family:
宋体;mso-bidi-font-family:宋体'>&nbsp;<u1:p></span><span lang=EN-US
style='mso-hansi-font-family:"Times New Roman"'> </u1:p></span><span
lang=EN-US><o:p></o:p></span></p>

<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
text-indent:24.0pt;mso-char-indent-count:2.0;tab-stops:list 0cm;mso-char-indent-size:
10.5pt'><span style='mso-hansi-font-family:"Times New Roman"'>人们的目的永远是最优<span
lang=EN-US>.一般我们说的较优解等等其实对于我们来说是最优,因为你要求得真正的数学上的“最优”所付出的成本将会大于为此的收益.理解这一点,在我们以后将会很重要.<u1:p>
</u1:p></span></span><span lang=EN-US><o:p></o:p></span></p>

<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
text-indent:24.0pt;mso-char-indent-count:2.0;tab-stops:list 0cm;mso-char-indent-size:
10.5pt'><span lang=EN-US style='font-family:"Times New Roman";mso-ascii-font-family:
宋体;mso-bidi-font-family:宋体'>&nbsp;<u1:p></span><span lang=EN-US
style='mso-hansi-font-family:"Times New Roman"'> </u1:p></span><span
lang=EN-US><o:p></o:p></span></p>

<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
text-indent:24.0pt;mso-char-indent-count:2.0;tab-stops:list 0cm;mso-char-indent-size:
10.5pt'><span style='mso-hansi-font-family:"Times New Roman"'>学习过《</span><b><span
style='mso-bidi-font-size:18.0pt;mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>最优化计算方法</span></b><span
style='mso-hansi-font-family:"Times New Roman"'>》这门课的都知道：</span><span
style='mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>最优化在数学中就是极值问题。如何利用数学知识来求解这些极值问题就是这门课的主题。</span><span
lang=EN-US><o:p></o:p></span></p>

<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
text-indent:24.0pt;mso-char-indent-count:2.0;tab-stops:list 0cm;mso-char-indent-size:
10.5pt'><span style='mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"'>用进退法搜索区间，用</span><span lang=EN-US>0.618</span><span
style='mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>法求一维无约束问题，用共轭梯度法求多维无约束优化问题，用单纯形法求解约束无优化问题。我用心学的和编过程序的就是这些。对于我来说，这基本上就足够了！如果学的多了，在实际中还得考虑用那个方法，可是这本身就是一个优化问题！！</span><span
lang=EN-US><o:p></o:p></span></p>

<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
text-indent:24.0pt;mso-char-indent-count:2.0;tab-stops:list 0cm;mso-char-indent-size:
10.5pt'><span lang=EN-US>&nbsp;<u1:p> </u1:p><o:p></o:p></span></p>

<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
text-indent:24.0pt;mso-char-indent-count:2.0;tab-stops:list 0cm;mso-char-indent-size:
10.5pt'><span lang=EN-US>&nbsp;<u1:p> </u1:p><o:p></o:p></span></p>

<p class=MsoNormal align=center style='mso-margin-top-alt:auto;mso-margin-bottom-alt:
auto;text-align:center;text-indent:24.0pt;mso-char-indent-count:2.0;tab-stops:
list 0cm;mso-char-indent-size:10.5pt'><span style='mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>二</span><span lang=EN-US><o:p></o:p></span></p>

<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
text-indent:24.0pt;mso-char-indent-count:2.0;tab-stops:list 0cm;mso-char-indent-size:
10.5pt'><span lang=EN-US>&nbsp;<u1:p> </u1:p><o:p></o:p></span></p>

<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
text-indent:24.0pt;mso-char-indent-count:2.0;tab-stops:list 0cm;mso-char-indent-size:
10.5pt'><span style='mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"'>我们需要注意的是</span><span lang=EN-US>:<o:p></o:p></span></p>

<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
text-indent:24.0pt;mso-char-indent-count:2.0;tab-stops:list 0cm;mso-char-indent-size:
10.5pt'><span lang=EN-US>&nbsp;<u1:p> </u1:p><o:p></o:p></span></p>

<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
text-indent:24.0pt;mso-char-indent-count:2.0;tab-stops:list 0cm;mso-char-indent-size:
10.5pt'><span style='mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman"'>首先，</span><b><span style='mso-bidi-font-size:18.0pt;
mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>最优化计算方法</span></b><span
style='mso-bidi-font-size:18.0pt;mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>中的前面讲述的各种方法都是基于函数的分析学性质的，最起码是连续性（对这一点在混沌理论中会有更深入的说明）。这一点很重要</span><span
lang=EN-US style='mso-bidi-font-size:18.0pt'>.</span><span style='mso-bidi-font-size:
18.0pt;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>所以适用范围很有限</span><span
lang=EN-US style='mso-bidi-font-size:18.0pt'>!</span><span style='mso-bidi-font-size:
18.0pt;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>　我们在现实生活中遇到的很多问题甚至就连连续都谈不上</span><span
lang=EN-US style='mso-bidi-font-size:18.0pt'>,</span><span style='mso-bidi-font-size:
18.0pt;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>譬如说</span><span
lang=EN-US style='mso-bidi-font-size:18.0pt'>TSP</span><span style='mso-bidi-font-size:
18.0pt;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>问题（</span><span
style='mso-hansi-font-family:"Times New Roman"'>又叫旅行商问题，</span><span
lang=EN-US>Traveling Salesman Problem</span><span style='mso-ascii-font-family:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>，简称</span><span
lang=EN-US>TSP</span><span style='mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>：</span><span style='mso-hansi-font-family:
"Times New Roman"'> 给定一些城市和这些城市间的距离。</span><span style='mso-ascii-font-family:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>旅行商要到所有这些城市中去做产品宣传，但是它不能花太多时间和费用。请寻找一个到所有这些城市的顺序以使得旅行路程最短。）</span><span
style='mso-bidi-font-size:18.0pt;mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>何谈分析学性质</span><span lang=EN-US
style='mso-bidi-font-size:18.0pt'>?</span><span style='mso-bidi-font-size:18.0pt;
mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>单峰性</span><span
lang=EN-US style='mso-bidi-font-size:18.0pt'>,</span><span style='mso-bidi-font-size:
18.0pt;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>可导</span><span
lang=EN-US style='mso-bidi-font-size:18.0pt'>,</span><span style='mso-bidi-font-size:
18.0pt;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>二阶导等等更谈不上了</span><span
lang=EN-US style='mso-bidi-font-size:18.0pt'>.</span><b><span style='mso-bidi-font-size:
18.0pt;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>其次，最优化计算方法</span></b><span
style='mso-bidi-font-size:18.0pt;mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>中所有的方法得到的解理论上都只是局部极值</span><span
lang=EN-US style='mso-bidi-font-size:18.0pt'>;</span><span style='mso-bidi-font-size:
18.0pt;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>但我们需要的都是全局极值</span><span
lang=EN-US style='mso-bidi-font-size:18.0pt'>.</span><span lang=EN-US
style='mso-hansi-font-family:"Times New Roman"'><u1:p> </span><span lang=EN-US></u1:p></span></p>

<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
margin-left:21.1pt;tab-stops:162.75pt'><span lang=EN-US style='mso-bidi-font-size:
18.0pt'>&nbsp;<u1:p> </u1:p></span><span lang=EN-US><o:p></o:p></span></p>

<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
text-indent:24.0pt;mso-char-indent-count:2.0;tab-stops:162.75pt;mso-char-indent-size:
10.5pt'><span style='mso-bidi-font-size:18.0pt;mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>我就曾经遇到一个问题<b>。</b>这个问题我使用了<b><span
style='color:red'>最优化计算方法</span></b>中很多方法给作过</span><span lang=EN-US
style='mso-bidi-font-size:18.0pt'>,</span><span style='mso-bidi-font-size:18.0pt;
mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>但是没有成功</span><span
lang=EN-US style='mso-bidi-font-size:18.0pt'>.</span><span style='mso-bidi-font-size:
18.0pt;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>因为这个问题局部极值太多</span><span
lang=EN-US style='mso-bidi-font-size:18.0pt'>,</span><span style='mso-bidi-font-size:
18.0pt;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>所以收敛很慢</span><span
lang=EN-US style='mso-bidi-font-size:18.0pt'>.</span><span style='mso-bidi-font-size:
18.0pt;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>最后我查到的资料</span><span
lang=EN-US style='mso-bidi-font-size:18.0pt'>,</span><span style='mso-bidi-font-size:
18.0pt;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>发现这个问题国际上最好的结果是用一种极其特殊的方法做的</span><span
lang=EN-US style='mso-bidi-font-size:18.0pt'>,</span><span style='mso-bidi-font-size:
18.0pt;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>其中使用到了特殊函数。</span><span
style='mso-bidi-font-size:18.0pt'><u1:p> </span><span lang=EN-US></u1:p></span></p>

<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
margin-left:21.1pt;tab-stops:162.75pt'><span lang=EN-US style='mso-bidi-font-size:
18.0pt'>&nbsp;<u1:p> </u1:p></span><span lang=EN-US><o:p></o:p></span></p>

<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
text-indent:20.5pt;mso-char-indent-count:1.71;mso-char-indent-size:10.45pt'><span
style='mso-bidi-font-size:18.0pt;mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>于是</span><span lang=EN-US
style='mso-bidi-font-size:18.0pt'>,</span><span style='mso-bidi-font-size:18.0pt;
mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>就有了矛盾</span><span
lang=EN-US style='mso-bidi-font-size:18.0pt'>.</span><span lang=EN-US> </span><span
style='mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>一方面我们有很多问题需要解决</span><span
lang=EN-US>:</span><span style='mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>决策</span><span lang=EN-US>,</span><span
style='mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>优化</span><span
lang=EN-US>,</span><span style='mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>比如一个商人要去中国各省的省会城市去宣传自己的产品</span><span
lang=EN-US>,</span><span style='mso-ascii-font-family:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>他当然想花最少的钱干这件事了</span><span lang=EN-US>.</span><span
style='mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>这就是个</span><span
lang=EN-US>TSP</span><span style='mso-ascii-font-family:"Times New Roman";