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Inverse integer optimization with multiple observations

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Abstract

Inverse optimization is the study of imputing unknown model parameters of an optimization problem using past observed solutions to that problem. In inverse linear programming, recent work uses multiple observations as input, while inverse integer programming has, to date, mostly focused on the case of a single observed data point or the case where a given cost vector needs to be minimally perturbed in order to make observations optimal. In this paper, we propose models to impute objective function coefficients of linear integer optimization problems from multiple integer observations without any prior knowledge of the cost vector. An exact method using an extension of a cutting-plane algorithm from the literature is proposed and compared with an LP-relaxation heuristic method

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Notes

  1. For alternative applications of inverse optimization in the diet problem please see, for example, the papers by Ghobadi et al. [17], Shahmoradi and Lee [18], Ghobadi et al. [19].

  2. For a parametric perspective on the utility function estimation problem, please see the work of Keshavarz et al. [20].

  3. The datasets generated and analysed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

The authors are supported by the Natural Sciences and Engineering Research Council of Canada

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Correspondence to Daria Terekhov.

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Moghaddass, M., Terekhov, D. Inverse integer optimization with multiple observations. Optim Lett 15, 1061–1079 (2021). https://doi.org/10.1007/s11590-021-01721-4

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