Integrating $$\varepsilon $$ ε -dominance and RBF surrogate optimization for solving computationally expensive many-objective optimization problems

Multi-objective optimization of computationally expensive, multimodal problems is very challenging, and is even more difficult for problems with many objectives (more than three). Optimization methods that incorporate surrogates within iterative frameworks, can be effective for solving such problems by reducing the number of expensive objective function evaluations that need to be done to find a good solution. However, only a few surrogate algorithms have been developed that are suitable for solving expensive many-objective problems. We propose a novel and effective optimization algorithm, $$\varepsilon $$ ε -MaSO, that integrates $$\varepsilon $$ ε -dominance with iterative Radial Basis Function surrogate-assisted framework to solve problems with many expensive objectives. $$\varepsilon $$ ε -MaSO also incorporates a new strategy for selecting points for expensive evaluations, that is specially designed for many-objective problems. Moreover, a bi-level restart mechanism is introduced to prevent the algorithm from remaining in a local optimum and hence, increase the probability of finding the global optimum. Effectiveness of $$\varepsilon $$ ε -MaSO is illustrated via application to DTLZ test suite with 2 to 8 objectives and to a simulation model of an environmental application. Results on both test problems and the environmental application indicate that $$\varepsilon $$ ε -MaSO outperforms the other two surrogate-assisted many-objective methods, CSEA and K-RVEA, and an evolutionary many-objective method Borg within limited budget.