Online knowledge-based evolutionary multi-objective optimization

Knowledge extraction from a multi-objective optimization process has important implications including a better understanding of the optimization process and the relationship between decision variables. The extant approaches, in this respect, rely on processing the post-optimization Pareto sets for automatic rule discovery using statistical or machine learning methods. However such approaches fall short of providing any information during the progress of the optimization process, which can be critical for decision analysis especially if the problem is dynamic. In this paper, we present a multi-objective optimization framework that uses a knowledge-based representation to search for patterns of Pareto optimal design variables instead of conventional point form solution search. The framework facilitates the online discovery of knowledge during the optimization process in the form of interpretable rules. The core contributing idea of our research is that we apply multi-objective evolutionary process on a population of bounding hypervolumes, or rules, instead of evolving individual point-based solutions. The framework is generic in a sense that any existing multi-objective optimization algorithm can be adapted to evaluate the rule quality based on the sampled solutions from the bounded space. An instantiation of the framework using hyperrectangular representation and non-dominated sorting based rule evaluation is presented in this paper. Experimental results on a specifically designed test function as well as some standard test functions are presented to demonstrate the working and convergence properties of our algorithm.