Hypervolume Indicator as an Estimator for Adaptive Operator Selection in an On-Line Multi-objective Hyper-heuristic

Online hyper-heuristics are algorithms capable of solving complex real-world problems. This approach dynamically selects, based on the quality of a given solution state, the most promising operator from a pool to continue a search process. In multi-objective optimization problems, more than one objective function has to be optimized simultaneously. Many multi-objective optimization problems commonly represent complex real-world problems. Despite the success of online hyper-heuristics applied to single-objective problems, there is a lack of work on Hyper-heuristics applied to multi-objective optimization. In this paper, we propose an approach to deal with multi-objective optimization with an online hyper-heuristic using as a quality metric, the Hypervolume (Hv) indicator, in a MOEA/D as a high-Level algorithm. The Hypervolume metric is a set measure used in multi-objective optimization to evaluate the performance of a search process transforming multiple objective problems into single-objective ones. This allows us to apply a single objective online hyper-heuristic to multi-objective problems. For experimentation, we use the well-known ZDT and DTLZ benchmarks.