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G-2024-78

Learning and modeling implicit constraints in optimization models through decision trees

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Planners in different industries use optimization software for decision-making. In numerous practical applications, these optimization tools are often not readily adjustable or configurable by end users due to limited knowledge, resources, or the required investment to consistently make such customizations. As a result, planners frequently adjust the solutions obtained from software based on implicit internal operational rules and preferences to make them feasible in practice. These practices may differ across various business units and subsidiaries. One can leverage data-driven methods to learn and embed implicit side constraints in a mixed integer linear program (MILP) to ensure that such rules can be learned and systematically incorporated into optimization models. These implicit constraints can be created from machine learning models trained using previously implemented solutions. To this end, we extend a data-driven constraint customization framework in the literature developed to extract constraints in the form of a traditional linear regression model to the case when constraints take the form of decision trees. This allows us to learn and incorporate implicit constraints in a non-linear or logical form. To demonstrate the value of this framework, experiments were conducted on the knapsack and nurse rostering problems where various combinations of hidden operational rules were simulated. The solutions obtained by our proposed solution framework suggest that it can effectively adjust the solutions based on the constraints extracted from historical solutions. The implicit constraints that take the form of decision trees generally outperform those based on linear regression models, mainly when part of the decision model comprises discrete variables.

, 16 pages

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