Diffusion Model-Based Multiobjective Optimization for Gasoline Blending Scheduling (2402.14600v1)
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.
- C. W. Nam, “World economic outlook for 2022 and 2023,” in CESifo Forum, vol. 23, pp. 50–51, München: ifo Institut-Leibniz-Institut für Wirtschaftsforschung an der Universität München, 2022.
- P. A. C. Castillo, P. M. Castro, and V. Mahalec, “Global optimization of nonlinear blend-scheduling problems,” Engineering, vol. 3, no. 2, pp. 188–201, 2017.
- S. Y. Ivanov and A. K. Ray, “Multiobjective optimization of industrial petroleum processing units using Genetic algorithms,” Procedia Chemistry, vol. 10, pp. 7–14, 2014.
- Y. Hou, N. Wu, Z. Li, Y. Zhang, T. Qu, and Q. Zhu, “Many-objective optimization for scheduling of crude oil operations based on NSGA-III with consideration of energy efficiency,” Swarm and Evolutionary Computation, vol. 57, p. 100714, 2020.
- Y. Tian et al., “Evolutionary large-scale multi-objective optimization: A survey,” ACM Computing Surveys (CSUR), vol. 54, no. 8, pp. 1–34, 2021.
- X. Ma et al., “A multiobjective evolutionary algorithm based on decision variable analyses for multiobjective optimization problems with large-scale variables,” IEEE Transactions on Evolutionary Computation, vol. 20, no. 2, pp. 275–298, 2016.
- J. Li and I. Karimi, “Scheduling gasoline blending operations from recipe determination to shipping using unit slots,” Industrial & Engineering Chemistry Research, vol. 50, no. 15, pp. 9156–9174, 2011.
- D. Panda and M. Ramteke, “Preventive crude oil scheduling under demand uncertainty using structure adapted genetic algorithm,” Applied Energy, vol. 235, pp. 68–82, 2019.
- F. Bayu, D. Panda, M. A. Shaik, and M. Ramteke, “Scheduling of gasoline blending and distribution using graphical genetic algorithm,” Computers & Chemical Engineering, vol. 133, p. 106636, 2020.
- J. Sohl-Dickstein, E. Weiss, N. Maheswaranathan, and S. Ganguli, “Deep unsupervised learning using nonequilibrium thermodynamics,” in International Conference on Machine Learning, pp. 2256–2265, PMLR, 2015.
- A. Ramesh, P. Dhariwal, A. Nichol, C. Chu, and M. Chen, “Hierarchical text-conditional image generation with clip latents,” arXiv preprint arXiv:2204.06125, 2022.
- P. Dhariwal and A. Nichol, “Diffusion models beat GANs on image synthesis,” Advances in Neural Information Processing Systems, vol. 34, pp. 8780–8794, 2021.
- R. Rombach, A. Blattmann, D. Lorenz, P. Esser, and B. Ommer, “High-resolution image synthesis with latent diffusion models,” in Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 10684–10695, 2022.
- W. Harvey, S. Naderiparizi, V. Masrani, C. Weilbach, and F. Wood, “Flexible diffusion modeling of long videos,” arXiv preprint arXiv:2205.11495, 2022.
- Z. Kong, W. Ping, J. Huang, K. Zhao, and B. Catanzaro, “Diffwave: A versatile diffusion model for audio synthesis,” arXiv preprint arXiv:2009.09761, 2020.
- A. Q. Nichol and P. Dhariwal, “Improved denoising diffusion probabilistic models,” in International Conference on Machine Learning, pp. 8162–8171, PMLR, 2021.
- X. Liu, D. H. Park, S. Azadi, G. Zhang, A. Chopikyan, Y. Hu, H. Shi, A. Rohrbach, and T. Darrell, “More control for free! image synthesis with semantic diffusion guidance,” in Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision, pp. 289–299, 2023.
- B. Jing, G. Corso, J. Chang, R. Barzilay, and T. Jaakkola, “Torsional diffusion for molecular conformer generation,” arXiv preprint arXiv:2206.01729, 2022.
- E. Hoogeboom, V. G. Satorras, C. Vignac, and M. Welling, “Equivariant diffusion for molecule generation in 3D,” in International Conference on Machine Learning, pp. 8867–8887, PMLR, 2022.
- T. Xie, X. Fu, O.-E. Ganea, R. Barzilay, and T. Jaakkola, “Crystal diffusion variational autoencoder for periodic material generation,” arXiv preprint arXiv:2110.06197, 2021.
- S. Luo, Y. Su, X. Peng, S. Wang, J. Peng, and J. Ma, “Antigen-specific antibody design and optimization with diffusion-based generative models,” bioRxiv, pp. 2022–07, 2022.
- Z. Sun and Y. Yang, “DIFUSCO: Graph-based diffusion solvers for combinatorial optimization,” arXiv preprint arXiv:2302.08224, 2023.
- S. Burer and A. N. Letchford, “Non-convex mixed-integer nonlinear programming: A survey,” Surveys in Operations Research and Management Science, vol. 17, no. 2, pp. 97–106, 2012.
- A. Creswell, T. White, V. Dumoulin, K. Arulkumaran, B. Sengupta, and A. A. Bharath, “Generative adversarial networks: An overview,” IEEE signal processing magazine, vol. 35, no. 1, pp. 53–65, 2018.
- Y. LeCun, “The MNIST database of handwritten digits,” http://yann. lecun. com/exdb/mnist/, 1998.
- S. Liu, Q. Lin, J. Li, and K. C. Tan, “A survey on learnable evolutionary algorithms for scalable multiobjective optimization,” IEEE Transactions on Evolutionary Computation, vol. 27, no. 6, pp. 1941–1961, 2023.
- S. Wang, A. Zhou, G. Zhang, and F. Fang, “Learning regularity for evolutionary multiobjective search: A generative model-based approach,” IEEE Computational Intelligence Magazine, vol. 18, no. 4, pp. 29–42, 2023.
- C. M. Bishop, M. Svensén, and C. K. I. Williams, “GTM: The generative topographic mapping,” Neural Computation, vol. 10, no. 1, pp. 215–234, 1998.
- Y. Sun, G. G. Yen, and Z. Yi, “Improved regularity model-based EDA for many-objective optimization,” IEEE Transactions on Evolutionary Computation, vol. 22, no. 5, pp. 662–678, 2018.
- D. P. Kingma and M. Welling, “Auto-encoding variational bayes,” arXiv preprint arXiv:1312.6114, 2013.
- L. Dinh, D. Krueger, and Y. Bengio, “Nice: Non-linear independent components estimation,” arXiv preprint arXiv:1410.8516, 2014.
- C. He, S. Huang, R. Cheng, K. C. Tan, and Y. Jin, “Evolutionary multiobjective optimization driven by generative adversarial networks (GANs),” IEEE Transactions on Cybernetics, vol. 51, no. 6, pp. 3129–3142, 2021.
- Z. Wang, H. Hong, K. Ye, G.-E. Zhang, M. Jiang, and K. C. Tan, “Manifold interpolation for large-scale multiobjective optimization via generative adversarial networks,” IEEE Transactions on Neural Networks and Learning Systems, vol. 34, no. 8, pp. 4631–4645, 2023.
- Z. Liang, Y. Zhu, X. Wang, Z. Li, and Z. Zhu, “Evolutionary multitasking for optimization based on generative strategies,” IEEE Transactions on Evolutionary Computation, vol. 27, no. 4, pp. 1042–1056, 2023.
- J. Ji, Y. Guo, X. Yang, R. Wang, and D. Gong, “Generative adversarial networks-based dynamic multi-objective task allocation algorithm for crowdsensing,” Information Sciences, vol. 647, p. 119472, 2023.
- C. A. Floudas and X. Lin, “Continuous-time versus discrete-time approaches for scheduling of chemical processes: a review,” Computers & Chemical Engineering, vol. 28, pp. 2109–2129, 2004.
- D. Kingma, T. Salimans, B. Poole, and J. Ho, “Variational diffusion models,” Advances in neural information processing systems, vol. 34, pp. 21696–21707, 2021.
- O. Ronneberger, P. Fischer, and T. Brox, “U-net: Convolutional networks for biomedical image segmentation,” in Medical Image Computing and Computer-Assisted Intervention–MICCAI 2015: 18th International Conference, Munich, Germany, October 5-9, 2015, Proceedings, Part III 18, pp. 234–241, Springer, 2015.
- K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition,” in Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 770–778, 2016.
- K. Deb, “An efficient constraint handling method for genetic algorithms,” Computer methods in applied mechanics and engineering, vol. 186, no. 2-4, pp. 311–338, 2000.
- K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Transactions on Evolutionary Computation, vol. 6, no. 2, pp. 182–197, 2002.
- H. Zille, H. Ishibuchi, S. Mostaghim, and Y. Nojima, “A framework for large-scale multiobjective optimization based on problem transformation,” IEEE Transactions on Evolutionary Computation, vol. 22, no. 2, pp. 260–275, 2018.
- R. Wang, Z. Zhou, H. Ishibuchi, T. Liao, and T. Zhang, “Localized weighted sum method for many-objective optimization,” IEEE Transactions on Evolutionary Computation, vol. 22, pp. 3–18, 2018.
- H. Xu, W. Zeng, D. Zhang, and X. Zeng, “MOEA/HD: A multiobjective evolutionary algorithm based on hierarchical decomposition,” IEEE Transactions on Cybernetics, vol. 49, pp. 517–526, 2019.
- K. Deb, M. Goyal, et al., “A combined genetic adaptive search (GeneAS) for engineering design,” Computer Science and informatics, vol. 26, pp. 30–45, 1996.
- J. Ma, H. Xu, J. Jiang, X. Mei, and X.-P. Zhang, “DDcGAN: A dual-discriminator conditional generative adversarial network for multi-resolution image fusion,” IEEE Transactions on Image Processing, vol. 29, pp. 4980–4995, 2020.
- Jazzbin et al., “Geatpy: The genetic and evolutionary algorithm toolbox with high performance in python,” 2020.
- L. While, P. Hingston, L. Barone, and S. Huband, “A faster algorithm for calculating hypervolume,” IEEE Transactions on Evolutionary Computation, vol. 10, pp. 29–38, 2006.
- Q. Zhang and H. Li, “MOEA/D: A multiobjective evolutionary algorithm based on decomposition,” IEEE Transactions on evolutionary computation, vol. 11, pp. 712–731, 2007.
- J. Knowles, “A summary-attainment-surface plotting method for visualizing the performance of stochastic multiobjective optimizers,” in 5th International Conference on Intelligent Systems Design and Applications (ISDA’05), pp. 552–557, IEEE, 2005.