So one issue I believe would be had with implementing this is that I think the search pages are actually not indexed, so even by providing a user readable link as described above will still not make such items appear in search engine statistics... Not without other modifications to address such a possibility. But, to specifically provide the above result, would need to create .htaccess in your store's root directory or above it. (Anything placed in a .htaccess before the current folder tends to apply to everything below that folder so again, be careful here.)
In it need at least one instance of RewriteEngine on and add (iin an appropriate order) the content shown below the RewriteEngine on statement:
Code:
RewriteEngine on
RewriteCond %{REQUEST_URI} ^/cheap/fashion-clothing [NC]
RewriteRule ^(.*) http://www.mydomain.com/index.php?main_page=advanced_search_result&search_in_description=1&keyword=fashion+clothing&x=0&y=0
Additional tags may be necessary, additional RewriteCond may be necessary depending on the websites offered from this point and other rules needed to be processed in the .htaccess... Further, search engines won't even know this link exists if it is not used somewhere...