Web search engines typically respond to user keyword queries by retrieving relevant URL's from their own databases. Web search optimization is an attempt to discover useful information from web based repository. Based on Cultural Algorithms (CA), the web search process is supported by the constraints described in the belief space, and the optimization process is supported by Genetic Algorithms (GA) in the population space. This paper introduces the dual inheritance approach which include genetic and cultural algorithm to retrieve the web based information from the repository. Results suggest that the belief space is an important contributor to the problem solving process for both systems when the number of constraints on the problem becomes large enough.