Optimizing insuring critical path problem under uncertainty based on GP-BPSO algorithm

This study considers a novel class of bi-level fuzzy random programming problem about insuring critical path. In this study, each task duration is assumed as a fuzzy random variable and follows the known possibility and probability distributions. Because there doesn’t exist an effective way to solve the problem directly, we first reduce the chance constraint to two equivalent random subproblems under two kinds of different risk attitudes. Then, we may use sample average approximation (SAA) method for reformulating the equivalent random programming subproblems as their approximation problems. Since the approximation problems are also hard to be solved, we explore a hybrid genotype phenotype binary particle swarm optimization algorithm (GP-BPSO) for resolving two equivalent subproblems, where dynamic programming method (DPM) is used for finding the solution in the lower-level programming. At last, a series of simulation examples are performed for demonstrating the validity of the hybrid GP-BPSO compared with the hybrid BPSO algorithm.