Coarse optimization for complex systems: an application of orthogonal experiments

Abstract In optimization problems, if the objective function together with (or without) the constraint conditions is so complicated that it is very time consuming to calculate the function values, the system is termed a complex system. In the present paper, partial derivative values are not required, and the optimization procedure is unconstrained. The aim is to find a method of dealing with the coarse optimization of a complex system. This requires fewer function values which will result in favourable points in the context of coarse optimization. The proposed method is an orthogonal experiment, which is based on an orthogonal table (in combinatorial mathematics) which satisfies the principle of orthogonality, i.e. uniform scatterance and orderly comparability. The method is described in detail, an orthogonal table generator ORTHTAB which generates ordinary orthogonal tables is provided, and a comparison with a standard simplex optimization method is given in the numerical results. The numerical examples demonstrate that the proposed method is effective, and can reduce the frequency of evaluating function values (compared with a simplex method). In addition, the solution is characterized as being optimal within the overall context.