Improving the reliability of implicit averaging methods using new conditional operators for robust optimization

In the field of robust optimization, the robustness of a solution is confirmed using a robustness indicator. In the literature, such an indicator uses explicit or implicit averaging techniques. One of the main drawbacks of the implicit averaging techniques is unreliability since they only use the sampled points generated by an optimization algorithm. In this paper, we propose a set of conditional operators for comparing solutions based on the number of sampled solutions in their neighbourhoods, thereby making reliable decisions during the process of robust optimization. This technique is integrated into the Particle Swarm Optimization (PSO) to update GBEST and PBESTs reliably, and the designed robust PSO algorithm is applied to a number of case studies. A set of extensive experiments shows that the proposed technique prevents an algorithm that relies on implicit averaging technique from making risky decisions and thus proven beneficial in finding robust solutions.