A Modular Knowledge-Driven Mutation Operator for Reference-Point Based Evolutionary Algorithms

Although an entire frontier of Pareto-optimal solutions exists for multi-objective optimization problems, in practice, decision makers are often only interested in a small subset of these solutions, called the region of interest. Specialized optimizers, such as reference-point based evolutionary algorithms, exist that can focus the search to only find solutions inside this region of interest. These algorithms typically only modify the selection mechanism of regular multi-objective optimizers to preferentially select solutions that conform to the reference point. However, a more effective search may be performed by additionally modifying the variation mechanism of the optimizers, namely the crossover and the mutation operators, to preferentially generate solutions conforming to the reference point. In this paper, we propose a modular mutation operator that uses a recent knowledge discovery technique to first find decision rules unique to the preferred solutions in each generation. These rules are then used to build an empirical distribution in the decision space that can be sampled to generate new mutated solutions which are more likely to be closer to the preferred solutions. The operator is modular in the sense that it can be used with any existing reference-point based evolutionary algorithm by simply replacing the mutation operator. We incorporate the proposed knowledge-driven mutation operator into three such algorithms, and through benchmark test problems up to 10 objectives, demonstrate that their performance improves significantly in the majority of cases according to two different performance indicators.