Further Note on the Probabilistic Constraint Handling

A robust probabilistic constraint handling approach in the framework of joint evolutionary-classical optimization has been presented earlier. In this work, the
theoretical foundations of the method are presented in detail. The method is known as bi-objective method, where the conventional penalty function approach is implemented. The present work highlights the dynamic variation of the commensurate penalty parameter for each objective treated as constraint. It is shown that the constraint parameters collectively define the right slope of the tangent as to the optimal front during the search. The robust and sustained convergence throughout the search up to micro level in the range of 10-10 or beyond is explained. The work here is presented as a further note in connection with the previous publication, where the subtle theoretical considerations and
their details had been omitted for the sake of detailed results of the experiments demonstrating the effective working of the approach. In contrast to the implementation-centered reporting of the previous work, this work can be considered as a description of the detailed probabilistic basis underlying the previous work. Therefore, this study is of great importance to let the researchers conveniently gain the insight into the work and its implications reported earlier.