This report will look at optimization under parameters of uncertainties. It will describe the subject in its wider form, then two model examples will be studied, followed by an application to an ABB product. The Monte Carlo method will be described and scrutinised, with the quasi-Monte Carlo method being favoured for large problems. An example will illustrate how the choice of Monte Carlo method will affect the efficiency of the simulation when evaluating  functions of different dimensions. Then an overview of mathematical optimization is given, from its simplest form to nonlinear, nonconvex  optimization problems containing uncertainties.A Monte Carlo simulation is applied to the design process and cost function for a custom made ABB transformer, where the production process is assumed to contain some uncertainties.The result from optimizing an ABB cost formula, where the in-parameters contains some uncertainties, shows how the price can vary and is not fixed as often assumed, and how this could influence an accept/reject decision.

This work presents a new test case generation methodology, which has a high degree of automation (cost reduction); while providing increased power in terms of defect detection (benefits increase). Our solution is a variation of model-based testing, which takes advantage of symbolic grammars (a context-free grammar where terminals are replaced by regular expressions that represent their solution space) and quasi-random sequences to generate test cases. Previous test case generation techniques are enhanced with adaptive random testing to maximize input space coverage; and selective and directed sentence generation techniques to optimize sentence generation. Our solution was tested by generating 200 firewall policies containing up to 20 000 rules from a generic firewall grammar. Our results show how our system generates test cases with superior coverage of the input space, increasing the probability of defect detection while reducing considerably the needed number the test cases compared with other previously used approaches. / Software Engineering and Intelligent Systems

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