An R2 indicator and weight vector-based evolutionary algorithm for multi-objective optimization

A two-stage R2 indicator-based evolution algorithm (TS-R2EA) was proposed in the recent years. A good balance between convergence and diversity can be achieved, due to the R2 indicator and reference vector-guided selection strategy. However, TSR2-EA is sensitive to problem geometries. In order to address this issue, a weight vector-based selection strategy is introduced, and a weight vector adaptive strategy based on population partition is proposed. In the selection strategy, each candidate solution is ranked according to the scalarizing function values in the corresponding neighbor, and the candidate solutions with good performance can be selected. In the adaptive strategy, the population is partitioned by associating each individual with its closest weight vector, and the weight vectors with a worse performance are adjusted. Similar to TS-R2EA, these strategies are combined with the R2 indicator to solve multi-objective optimization problems. The performance of proposed algorithm has been validated and compared with four related algorithms on a variety of benchmark test problems. The experimental results have demonstrated that the proposed algorithm has high competition and is less sensitive to problem geometries.