In this paper

an adaptive sampling immune optimization algorithm is proposed to solve the nonlinear multi-objective probabilistic optimization problem in noisy environments. In the whole design of the algorithm

we develop an evolutionary framework with small population inspired by the clonal selection principle. The approach for estimating objective value is designed by adaptively determining the sample size of an individual. The population is divided into multilevel non-dominated sub-populations for co-evolution by the traditional fast non-dominated sorting approach. The simulation binary crossover with dynamic crossover distribution index is designed to enhance the information exchanges among all sub-populations. Polynomial mutation and uniform mutation with dynamic mutation distribution index

and adaptive mutation probability are designed to enhance the capability of global and local exploration. Finally

based on three theoretical test questions

energy consumption optimization of sea-rail intermodal transportation and nine representative comparison algorithms

the numerical experiment results show that the algorithm has significant search efficiency

superior search effect and good stability.