Insight Centre for Data Analytics - Conference Items
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Item A fully Bayesian approach to bilevel problems(Springer Nature, 2024-10-16) Dogan, Vedat; Prestwich, Steven; O’Sullivan, Barry; Science Foundation IrelandThe mathematical models of many real-world decision-making problems contain two levels of optimization. In these models, one of the optimization problems appears as a constraint of the other one, called follower and leader, respectively. These problems are known as bilevel optimization problems (BOPs) in mathematical programming and are widely studied by both classical and evolutionary optimization communities. The nested nature of these problems causes many difficulties such as non-convexity and disconnectedness for traditional methods, and requires a huge number of function evaluations for evolutionary algorithms. This paper proposes a fully Bayesian optimization approach, called FB-BLO. We aim to reduce the necessary function evaluations for both upper and lower level problems by iteratively approximating promising solutions with Gaussian process surrogate models at both levels. The proposed FB-BLO algorithm uses the other decision-makers’ observations in its Gaussian process model to leverage the correlation between decisions and objective values. This allows us to extract knowledge from previous decisions for each level. The algorithm has been evaluated on numerous benchmark problems and compared with existing state-of-the-art algorithms. Our evaluation demonstrates the success of our proposed FB-BLO algorithm in terms of both effectiveness and efficiency.Item A hybrid Bayesian approach for pessimistic bilevel problems with a new formulation(2024) Dogan, Vedat; Prestwich, Steven D.; O'Sullivan, Barry; Science Foundation IrelandIn many real-world problems, finding the optimal decision for a decision-maker depends on another decision-maker’s response, and it is called bilevel optimization in mathematical programming. It contains two levels of optimization problems while one appears as a constraint of another one called follower and leader, respectively. In many real-world scenarios, the lower level has multiple global optima and the upper level needs to make worst-case assumptions about the decision of the lower level, called the pessimistic case of the bilevel problem. Various approaches have been implemented over the years to solve generic bilevel problems, but few of them could be extended to pessimistic cases. In this short paper, we first propose a new formulation for the pessimistic case. In this way, we take advantage of the hierarchical structure of bilevel problems to make the results more accurate for pessimistic cases. Then, we implement a black-box approach to solve the pessimistic upper level problem to decrease the necessary function evaluations. The performance of the problem is examined by solving a test benchmark problem from the literature.Item A fully Bayesian approach to bilevel problems(2024) Dogan, Vedat; Prestwich, Steven D.; O'Sullivan, Barry; Science Foundation IrelandThe mathematical models of many real-world decision-making problems contain two levels of optimization. In these models, one of the optimization problems appears as a constraint of the other one, called follower and leader, respectively. These problems are known as bilevel optimization problems (BOPs) in mathematical programming and are widely studied by both classical and evolutionary optimization communities. The nested nature of these problems causes many difficulties such as non-convexity and disconnectedness for traditional methods, and requires a huge number of function evaluations for evolutionary algorithms. This paper proposes a fully Bayesian optimization approach, called FB-BLO. We aim to reduce the necessary function evaluations for both upper and lower level problems by iteratively approximating promising solutions with Gaussian process surrogate models at both levels. The proposed FB-BLO algorithm uses the other decision-makers’ observations in its Gaussian process model to leverage the correlation between decisions and objective values. This allows us to extract knowledge from previous decisions for each level. The algorithm has been evaluated on numerous benchmark problems and compared with existing state-of-the-art algorithms. Our evaluation demonstrates the success of our proposed FB-BLO algorithm in terms of both effectiveness and efficiencyItem Approximating a global objective by solving repeated sub-problems for an oven scheduling problem(ModRef 2024, 2024-09-02) Simonis, Helmut; Science Foundation IrelandIn this paper we describe results for an oven scheduling problem studied during the European ASSISTANT project. This is a multi-stage scheduling problem arising in the production of rotor assemblies for compressors, provided by one of the industrial partners in the consortium. The main resource type is a set of identical ovens, which are used to heat-treat components in different ways. The process for one product may require multiple consecutive steps using these ovens, with specific temperature and process requirements at each step. Multiple tasks of different orders can be processed together in the same oven, if the temperature and process parameters for the tasks are identical. Processing multiple tasks together is more energy efficient, but typically forces some tasks to wait until all scheduled items are available, possibly impacting product quality and creating delays for the orders. The main difference to the oven scheduling problem studied in the literature is that we are not just trying to find an optimal solution to the short-term, detailed scheduling problem, but rather are interested in how selecting different parameters and constraints for the short-term scheduling problem affects the overall long-term, global objective of minimizing energy use, while maintaining the quality of products. Turning ovens off and then on again is considered bad for energy and maintenance reasons, we therefore try to minimize the number of shutdown events over the full planning horizon, while dealing with demand fluctuations over time. Information about jobs to be scheduled is only available within a limited time horizon, we therefore cannot solve the overall problem as one global optimization problem. Results indicate that we obtain a good overall schedule with a simple detailed scheduling model.Item Modelling choices for the Roadef 2022 challenge(Association for Constraint Programming, 2024-09-02) Simonis, Helmut; Science Foundation IrelandThis paper describes our approach to modelling and solving the Roadef 2022 Challenge, a trans portation planning problem introduced by Renault. We describe a high-level decomposition of the problem, and the models for different stages, focussing on a MIP main problem which decides when in time stacks of items should be transported. We present a lower bound on the number of trucks required to deliver all stacks in time, and show how the lower bounds on individual placement problems can be incorporated as cuts in the main MIP model.