Effect of size and order of variables in rules for multi-objective repair-based innovization procedure

Abstract

Innovization is a task of learning common principles that exist among some or all of the Pareto-optimal solutions of a multi-objective optimization problem. Except a few earlier studies, most innovization related studies were performed on the final non-dominated solutions found by an EMO algorithm. Recently, authors showed that these principles can be learned during an optimization run and simultaneously utilized in the same optimization run to repair variables to achieve a faster convergence to the Pareto-optimal set. Different principles learned during an optimization run can not only have different number of variables but, may also have variables that are common among a number of principles. Moreover, a preference order for repairing variables may play an important role for proper convergence. Thus, when multiple principles exist, it is important to use a strategy that is most beneficial for repairing evolving population of solutions. This paper makes a first attempt to assess and understand the effect of different strategies to make innovization-based repair of variables most useful. Based on results on test problems, the paper also makes useful suggestions, which require immediate further experimentation on more complex and real-world problems.