Does Commerce Kickstart distribution include "advanced search" capabilities?
Commerce kickstart includes the commerce search API module. http://drupal.org/project/commerce_search_api

Automatically created Search API db server, if none is found.
Auto-generated search index that includes all product display node types* and related product data.
Auto-generated facets for all node type categories and product attributes.
Optional integration with Search API Ranges (allowing for a price slider, for example).
Search API Filter class for product display node types* (allowing for an index composed only of product displays)
Facet API Filter class for removing facet items that do not change search results.
Facet API Filter class for hiding certain facets on the initial search (so that product attribute facets are only shown after the initial search, for example).