A grid-based adaptive multi-objective differential evolution algorithm

Differential evolution is an excellent optimizer for single objective optimization problems. To extend its use for multi-objective optimization problems with promising performance, this paper proposes a grid-based adaptive multi-objective differential evolution algorithm. The main feature of the proposed algorithm is its dynamical adjustment of convergence and diversity by exploiting the feedback information during the evolutionary process. In the algorithm, the objective space is divided into grids according to the nondominated solutions in the population. Based on the grid, three indexes including grid fitness, grid density, and grid-objective-wise standard deviation are defined to measure individual rank, individual density, and population search status quo, respectively. Afterwards, three main components of the algorithm, i.e., parents selection, parameter control, and population update, are implemented based on grid index values. To validate algorithm performance, comprehensive experiments are carried out on thirty-one benchmark problems. The results show that the proposed algorithm outperforms nine state-of-the-art competitors in terms of three performance metrics. Also, the effectiveness of three components and the sensitivity of two design parameters in the algorithm are empirically quantified.