Distribution Shape of Objective Function-Oriented Probabilistic Constrained Multi-Objective Stochastic Optimization with Its Application to an Ironmaking Process in a Blast Furnace

In this paper, a distribution shape of the objective function-oriented probabilistic constrained multi-objective stochastic optimization for industrial processes is proposed. First, to effectively reduce the impact of randomness in the optimization process, each objective function is regarded as a random variable. The uncertainties embedded within the objective function are quantified through the probability density function (PDF) shape, thereby transforming the traditional constrained multi-objective optimization problem into a probabilistic constrained multi-objective optimization problem focusing on the distribution shape of the objective function. Second, a multi-objective differential evolution (MODE) algorithm generated from a Cauchy–Gaussian mixture distribution is designed. A linear decay mechanism is employed to adjust the distribution weights to achieve a balance between global exploration and local exploitation. Finally, the numerical simulations and the experiments based on industrial data further confirm the effectiveness of the proposed method. Compared with the conventional mean-based multi-objective optimization method, the proposed method reduces the average PDF-tracking errors for the two objectives by 6.31% and 44.10% in the numerical example, and by 3.40% and 2.55% in the offline industrial case study.