Upper and lower bounds of the solution for an elliptic plate problem using a genetic algorithm

Summary This paper presents a new method of treating engineering problems, in which Mathematical Programming is combined with the Method of Weighted Residual (MWR), and is, therefore, referred to as Mathematical Programming MWR (MP-MWR). If a solutionZ(x) exists in the defining domainV of a problem, it is limited bound by any two functionsZ_u(x) andZ_l(x). These functions satisfy the definite condition that ifRZ_u(x)>0>RZ₁(x), thenZ_uZZ_l inV, whereR is the residual operator. By using the optimization method of genetic algorithms (GAs), it is also possible to obtain the values of minimumZ_u(x) and maximumZ_l(x) which satisfy the above inequality. One advantage of MP-MWR is that the demands on computer memory are less than those required when applying the finite element method. In this paper a boundary value problem is studied as an example. The efficiency, accuracy, and simplicity of the MP-MWR approach are fully illustrated, indicating that the proposed method may be readily extended to solve a wide range of physical engineering problems.