Information Entropy based Performance Index and Meta Optimization

Krus Petter - Linköping University (Sweden)


Design optimization is becoming an increasingly important tool for design. Complex design problems, in general, often need to be evaluated using non-linear simulation. Consequently, gradients of the objective function are not readily available. For such problems, direct optimization using non-gradient methods is an attractive alternative.
A measure of the efficiency of an optimization algorithm is of great importance when comparing methods. Here a singular performance criterion, the Entropy Rate Index, ERI, is introduced. This is based on Shannon's information theory, taking both reliability (chance of finding the true optimum) and the rate of convergence into account. It can also be used to characterize the difficulty of different optimization problems through the introduction of the objective function temperament factor, OTF, This is an indication of the degree of difficulty of the objective function. Using ERI and OTF it is possible to predict the resources needed for optimization
The ERI performance criterion can also be used as an objective function for optimization of the optimization algorithms itself.
The Complex-RF direct search optimization method is used as an example, and its performance is evaluated and optimized using the established performance criterion. This is a method that has been used extensively for simulation based optimization.