Expensive many-objective evolutionary optimization guided by two individual infill criteria

Recently, surrogate-assisted multi-objective evolutionary algorithms have achieved much attention for solving computationally expensive multi-/many-objective optimization problems. An effective infill sampling strategy is critical in surrogate-assisted multi-objective evolutionary optimization to assist evolutionary algorithms in identifying the optimal non-dominated solutions. This paper proposes a Kriging-assisted many-objective optimization algorithm guided by two infill sampling criteria to self-adaptively select two new solutions for expensive objective function evaluations to improve history models. The first uncertainty-based criterion selects the solution for expensive function evaluations with the maximum approximation uncertainty to improve the chance of discovering the optimal region. The approximation uncertainty of a solution is the weighted sum of approximation uncertainties on all objectives. The other indicator-based criterion selects the solution with the best indicator value to accelerate exploiting the non-dominated optimal solutions. The indicator of an individual is defined by the convergence-based and crowding-based distances in the objective space. Finally, two multi-objective test suites, DTLZ and MaF, and three real-world applications are applied to test the performance of the proposed method and four compared classical surrogate-assisted multi-objective evolutionary algorithms. The results show that the proposed algorithm is more competitive on most optimization problems.