Knowledge-Driven Reference-Point Based Multi-Objective Optimization: First Results

Multi-objective optimization problems in the real world often involve a decision maker who has certain preferences for the objective functions. When such preferences can be expressed as a reference point, the goal of optimization changes from generating a complete set of Pareto-optimal solutions to generating a small set of non-dominated solutions close to the reference point. Reference-point based optimization algorithms are used for this purpose. The preferences of the decision maker in the objective space can be interpreted as knowledge in the decision space. Extracting this knowledge iteratively from the solutions generated during optimization, and feeding it back into the optimization algorithm can in principle improve convergence towards the reference point. Since the knowledge is extracted during runtime, this approach is termed as online knowledge-driven optimization. In this paper a recent knowledge discovery technique called flexible pattern mining is used to extract explicit rules that are used to generate new solutions in R-NSGA-II. The performance of the proposed FPM-R-NSGA-II is demonstrated on 3, 5 and 10 objective DTLZ problems. In addition to converging to a set of preferred solutions, FPM-R-NSGA-II also converges to a set of explicit rules which describe the decision maker's preferences in the decision space.