Using knowledge-based evolutionary computation to solve nonlinear constraint optimization problems: a cultural algorithm approach

The key idea behind cultural algorithms is to acquire problem solving knowledge (beliefs) from the evolving population and in return apply that knowledge to guide the search (R.G. Reynolds et al., 1993; 1996), In solving nonlinear constraint optimization problems, the key problem is how to represent and store the knowledge about the constraints. Previously, Chung (Chan-Jin Chung and R.G. Reynolds, 1996; 1998) used cultural algorithms to solve unconstraint optimization problems. Use was made of interval schemata proposed by L.J. Eshelman and J.D. Schaffer (1992) to represent global knowledge about the independent problem parameters. However, in constraint optimization, the problem intervals generally 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. We define an n-dimensional regional based schema, called belief cell, which can provide an explicit mechanism to support the acquisition, storage and integration of 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, i.e. these 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