Further note on the probabilistic constraint handling

Abstract

Abstract-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.

Precision constrained optimization by exponential ranking

“…The approach is based on a probabilistic model of the random solutions that serves to derive a nonlinear distance measure for grading the constraint satisfaction performance of every population member. While the details of the probabilistic distance measure are revealed in another paper [1], this paper presents the implementation results in order to verify the theoretical considerations. In the present work the nonlinear distance measure is used to rank the genetic population members for effective tournament selection.…”

“…Although some basic information about the probabilistic treatment used in the NS-NR approach is given in [1], some basic information is also included here for the stand-alone representation and completeness of this paper.…”