AN ADAPTIVE SEARCH METHOD FOR MATHEMATICAL PROGRAMMING PROBLEMS (COMPUTER, MANAGEMENT SCIENCE, OPTIMIZATION, OPERATIONS RESEARCH, PERSONAL)

A method to solve mathematical programming problems of any functional form with continuous and/or integer variables is developed and tested. The approach is philosophically different from classical methods such as the Simplex Method, Lagrange Multipliers, Cutting Plane Method, Branch and Bound, etc. in that random sampling and or deterministic algorithms are used in a series of heuristic methods to estimate the optimum. The method is called the Adaptive Search Method (ASM) and uses a learning technique of Artificial Intelligence (heretofore not used for solving mathematical programming problems) during the solution process. The method selects from a library of heuristics "adaptively" so as to arrive at an estimate of the optimum with minimum computation. Some of these heuristic methods have been developed for this research while others have been improved from the literature. Still other heuristics, though not evaluated in this research, could be added to the library and thus the ASM is "expandable" as further research reveals these new heuristics.; A survey of the literature shows that random sampling has been used by other authors in a more limited sense. Some have solved only linear problems, others have used a single simple search technique not suitable for as broad a class of problems as the ASM. The ASM could be used on any.; Twenty two test problems are used to evaluate the ASM. Results show that the method has much promise in opening up a broad class of problems to solution which heretofore have been computationally intractable. These include problems with highly complex functional forms such as exponentials, high exponent values, transcendental functions and even problems where no closed form representation of constraints are possible.