| Solving the general real-valued constrained optimization problem remains a difficult and open question for Evolutionary Algorithms. Traditional methods may depend heavily on the acquisition of some problem-specific knowledge (about the functional landscape patterns) prior to the run of the algorithms. However, this knowledge is not generally available in advance. Therefore, (1) is it possible for an evolutionary system to learn this knowledge during the search instead of having to acquire it beforehand? And (2) how to benefit from this acquired knowledge? This dissertation makes an original contribution to the solution of these two problems. It proposes a new framework based on Cultural Algorithms and Regional Schemata to solve constrained optimization problems. Regional Schemata, an extension of the classic symbolic schemata, are proposed to represent the regional knowledge that concerns the complicated interdependent relationships among different parameters. The regional schemata and corresponding mechanisms will allow evolutionary algorithms to systemically and explicitly exploit symbolic representation of a problem's fitness landscape. The extracted regional patterns (constraint patterns) can be used to: (1) facilitate the evolutionary search; (2) provide information concerning emergent patterns in the functional landscape such as ridges. The former can help solve a constrained optimization problem in a direct way, by “pruning” the infeasible regions and “promoting” the promising regions. The latter is especially valuable when the search is used for extracting patterns from a large dataset, where constraint information is not known but very important.; Two implementations (configurations) of this proposed framework, the sliding window model and the hierarchical architecture model, are addressed here and used to solve an example nonlinear real-valued constrained optimization problem. The experiments show that the proposed mechanisms can be used to solve this complicated problem that contains a ridge more efficiently than an example population-only evolutionary algorithm. The hierarchical approach is also applied to the extraction of emergent knowledge about underlying patterns from a large-scale real world dataset. The dataset is taken from a large-scale survey of archaeological sites in the Valley of Oaxaca, Mexico. The results demonstrate that this approach: (1) can successfully extract interesting emergent patterns in the belief space; and (2) can improve search efficiency by “naturally selecting” records from the dataset so that often not all records need to be examined. These advantages suggest the great potential of the new approach. |
