The Value of Randomized Strategies in Distributionaliy Robust Risk-Averse Network Interdiction Problems

Utsav Sadana; Erick Delage

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The Value of Randomized Strategies in Distributionaliy Robust Risk-Averse Network Interdiction Problems

机译：The Value of Randomized Strategies in Distributionaliy Robust Risk-Averse Network Interdiction Problems

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Conditional value at risk (CVaR) is widely used to account for the preferences of a risk-averse agent in extreme loss scenarios. To study the effectiveness of randomization in interdiction problems with an interdictor that is both risk- and ambiguity-averse, we introduce a distributionaliy robust maximum flow network interdiction problem in which the interdictor randomizes over the feasible interdiction plans in order to minimize the worst case CVaR of the maximum flow with respect to both the unknown distribution of the capacity of the arcs and the interdictor's own randomized strategy. Using the size of the uncertainty set, we control the degree of conservatism in the model and reformulate the interdictor's distributionaliy robust optimization problem as a bilinear optimization problem. For solving this problem to any given optimality level, we devise a spatial branch-and-bound algorithm that uses the McCormick inequalities and reduced reformulation linearization technique to obtain a convex relaxation of the problem. We also develop a column-generation algorithm to identify the optimal support of the convex relaxation, which is then used in the coordinate descent algorithm to determine the upper bounds. The efficiency and convergence of the spatial branch-and-bound algorithm is established in numerical experiments. Further, our numerical experiments show that randomized strategies can have significantly better performance than optimal deterministic ones.

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《INFORMS journal on computing》 |2023年第1期|216-232|共17页
作者
Utsav Sadana; Erick Delage;
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作者单位

GERAD, Montreal, Quebec H3T 1J4, Canada, Desautels Faculty of Management, McGill University, Montreal, Quebec H3A 1G5, Canada;

GERAD, Montreal, Quebec H3T 1J4, Canada, Department of Decision Sciences, HEC Montreal, Montreal, Quebec H3T 2A7, Canada;

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正文语种英语
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network interdiction; conditional value at risk; distributionaliy robust optimization; spatial branch and bound; column generation;

The Value of Randomized Strategies in Distributionaliy Robust Risk-Averse Network Interdiction Problems

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