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Approximating a linear multiplicative objective in watershed management optimization
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DOI：10.1016/j.ejor.2022.06.006.png)
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摘要
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Implementing management practices in a cost-efficient manner is critical for regional efforts to reduce the amount of pollutants entering the Chesapeake Bay. We study the problem of selecting a subset of practices that minimizes pollutant load-subject to budgetary and environmental constraints-as simu-lated in a widely used regulatory watershed model. Mimicking the computation of pollutant load in the regulatory model, we formulate this problem as a continuous optimization model with a linear mul-tiplicative objective function and linear constraints. To lay the groundwork for incorporating additional stakeholder requirements in the future, especially those that would require integer variables, we present and study a continuous linear optimization model that approximates the nonlinear model. The linear model, which requires an exponential number of variables, arises naturally as an alternative model for the same underlying physical process. We examine the theoretical behavior of these optimization models and investigate restrictions of the linear model to handle its large number of variables. Through extensive computational tests on real and randomly generated instances, we demonstrate that the linear model and its restrictions provide optimal solutions close to those of the nonlinear model in practice, despite poor approximation properties in the worst case. We conclude that the linear model-together with our ap-proach to handling its large number of variables-provides a viable framework from which to extend the optimization model to better meet the needs of the Chesapeake Bay watershed management stakehold-ers. (c) 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )
Keyword:
Nonlinear programming
Linear programming
OR in environment and climate change
Watershed management
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6
论文数:
2.2W
被引数:
6.4W
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