Diffusion Model-Based Multiobjective Optimization for Gasoline Blending Scheduling

TL;DR

This work presents DMO, a diffusion-model-based framework for multiobjective optimization of gasoline blending scheduling, addressing the joint challenges of nonlinearity, integer constraints, and large decision spaces. DMO generates feasible, high-quality schedules by gradually transforming Gaussian noise into feasible scheduling representations while guiding objective improvement via gradient descent, and it outputs a Pareto front through standardized post-processing. Empirical results on real refinery data show that DMO consistently outperforms state-of-the-art MOEAs in efficiency and solution stability across small to large-scale problems, with notable gains in hypervolume as problem size grows. The method leverages GPU-accelerated CNNs (U-Net) to handle image-like scheduling data and demonstrates strong potential for extension to other scheduling and combinatorial optimization problems, albeit with considerations for selection mechanisms to prune non-Pareto solutions. Overall, DMO offers a scalable, flexible approach that couples generative diffusion with direct objective optimization for practical industrial scheduling tasks.

Abstract

Gasoline blending scheduling uses resource allocation and operation sequencing to meet a refinery's production requirements. The presence of nonlinearity, integer constraints, and a large number of decision variables adds complexity to this problem, posing challenges for traditional and evolutionary algorithms. This paper introduces a novel multiobjective optimization approach driven by a diffusion model (named DMO), which is designed specifically for gasoline blending scheduling. To address integer constraints and generate feasible schedules, the diffusion model creates multiple intermediate distributions between Gaussian noise and the feasible domain. Through iterative processes, the solutions transition from Gaussian noise to feasible schedules while optimizing the objectives using the gradient descent method. DMO achieves simultaneous objective optimization and constraint adherence. Comparative tests are conducted to evaluate DMO's performance across various scales. The experimental results demonstrate that DMO surpasses state-of-the-art multiobjective evolutionary algorithms in terms of efficiency when solving gasoline blending scheduling problems.

Figures (10)

• Figure 1: A schematic diagram of a gasoline blending unit. The components from different tanks are blended in varying proportions using the blenders to produce different grades of gasoline. These grades of gasoline are then transferred to product tanks to fulfill customer orders.
• Figure 2: Examples of the Gantt charts. The colored areas indicates that an oil component tank is transferring oil to product tank $j$ (vertical coordinate) during this specific period (horizontal coordinate). The shades of blue indicate the flow of oil transportation. (a) A feasible schedule. (b) An unfeasible schedule.
• Figure 3: Illustration of how diffusion models operate on the MNIST handwritten digit database.
• Figure 4: The overall flowchart of DMO.
• Figure 5: The architecture of U-Net in DMO. The symbol CAT denotes the concatenation of the given inputs in the channel dimension. A "+" in a circle indicates the direct summation of the given inputs.