The use of mathematical programming with artificial intelligence and expert systems

Researchers have developed artificially intelligent (AI) and expert systems (ES) to assist in the formulation, solution and interpretation of generic mathematical programs (MP). In addition, re­ searchers also have built domain-specific systems either modeled around a mathematical program or which include a mathematical program module. In these systems, the specificity of the domain allows researchers to extend the interpretation or formulation beyond that available from the generic set of assumptions about mathematical programming. Further, researchers have begun to investigate the use of mathematical program formulations of expert systems. The purpose of their research has been to, e.g., understand the complexity of the expert systems and also to examine the feasibility of mathematical programming as an alternative solution methodology for those expert systems. This paper surveys and extends some of that literature that integrates AIlES and MP, and elicits some of the current research issues of concern.