(392i) Data-Driven Chance-Constrained Mixed Integer Nonlinear Bilevel Optimisation Via Copulas: Application to Integrated Planning and Scheduling Problems

In real-world applications, many optimisation problems are inherently difficult to find feasible solutions due to the lack of exact information, the presence of noisy data distributions, and parameter uncertainties. As a result, data-driven optimisation approaches are increasingly adopted to efficiently explore solution spaces and identify improved outcomes. Chance constraint programming (CCP) is an optimisation approach that ensures stochastic constraints are met with a predetermined probability of satisfaction amongst all possible scenarios (Li et al. 2008; Calfa et al. 2015). Numerous studies have successfully integrated specifically with various optimisation problems (Bianco et al. 2019). Copulas are data-driven coupling functions that capture the dependence structure between multiple univariate marginal distributions under certain correlations. Incorporating copula formulations into CCP makes it possible to better model dependencies between variables under different scenarios when underlying data exhibits complex distributions or non-trivial dependencies, such as correlated risks or non-linear relationships, thereby improving the accuracy of decision-making in optimisation problems with the presence of uncertain parameters. In recent years, the integration of copula and CCP has shown significant promise (Chen et al., 2015; Hosseini et al., 2020; Khezri and Khodayifar, 2023).

In this work, we present a copula-based chance-constrained optimisation framework designed to achieve good efficiency and accuracy in estimating demand levels for integrated planning and scheduling problems. Our approach ensures feasible decision-making within a defined risk threshold. We validated this framework within the context of data-driven optimisation, leveraging the DOMINO framework (Beykal et al., 2020; Nikkhah et al., 2025), which is a data-driven grey-box algorithm for addressing generic constrained bilevel optimisation problems. Our experiments demonstrate that the proposed approach is capable of identifying robust solutions that result in higher joint satisfaction rates for products and near-optimal performance, all while significantly reducing computational time compared to exact methods and other simulation-based software. The efficiency and effectiveness of our approach are further validated through a number of case studies across a range of optimisation problems.

References

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Acknowledgements

Financial support from the UK EPSRC grants EP/V051008/1 and EP/W003317/1, U.S. National Institutes of Health (NIH) grant P42 ES027704, and ACS Petroleum Research Fund Doctoral New Investigator Grant PRF # 66086-DNI9 is gratefully acknowledged