Adaptive Sampling Immune Algorithm for Multi-Objective Probabilistic Optimization

Abstract

In this paper, for a general type of multi-objective probabilistic optimization problem without any prior noisy information, which has an extensive engineering application background and needs to be solved urgently, we propose a small-population immune algorithm with adaptive sampling to solve. In the design. First, we design a small-population immune algorithm framework inspired by the response mechanism of adaptive immunity. Second, we design an adaptive sampling scheme that adaptively allocates an appropriate number of samples for each sub-objective function of all individuals in the population to estimate the objective function value. Third, based on the objective function estimates, the dominance levels of all individuals in the population and the crowding distances of individuals in each dominance level are determined. Fourth, the clone size, mutation rate, crossover distribution index, and mutation distribution index of an individual are designed to be adaptively determined based on the number of iterations, dominance level, and crowding distance. Cloning, crossover, and mutation operators are implemented for each individual, using simulated binary crossover and polynomial mutation to enhance co-evolution and facilitate information sharing and exchange among all individuals. Fifth, based on the dominance level and crowding distance, the population update strategies are designed to adaptively update the memory set with high-quality individuals and generate a new generation population with good diversity. Finally, based on three theoretical problems and two engineering problems, as well as six representative comparative algorithms, the experimental results show that the proposed algorithm is an optimizer with good competitiveness and application potential, and has few parameters, less sample consumption, strong noise suppression ability, and high search efficiency.