Using Region-Schema to Solve Nonlinear Constraint Optimization Problems: a Cultural Algorithm Approach

The key idea behind Cultural Algorithms is to explcitly acquire problem-solving knowledge (beliefs) from the evolving population in the form of schemata and in return apply that knowledge to guide the search [Reynolds 1993, 1996]. In solving nonlinear constraint optimization problems, the key problem is how to represent and store the knowledge about the constraints. Previously, Chung [1996, 1998] used Cultural Algorithms to solve unconstraint optimization problems. There, he used interval schemata proposed by Eshelman and Schaffer [Eshelman 1992] to represent global knowledge about the independent problem parameters. However, in constraint optimization the problem intervals must be modified dependently. In order to solve constraint optimization problems, we need to extend the interval representation to allow for the representation of constraints. In this paper, we define an n-dimensional regional-based schema in terms of beliefcells, which can provide an explicit mechanism to support the acquisition, storage and integration of schematic knowledge about the constraints. In a Cultural Algorithm framework, the belief space can "contain" a set of these schemata, each of them can be used to guide the search of the evolving population. This kind of region-based schemata can be used to guide the optimization search in a direct way by pruning the unfeasible regions and promoting the promising regions. We compared the results of 4 CA configurations that manipulate these schemata for an example problem. An application to a problem in Cultural Evolution is also demonstrated.