Multi-dual decomposition solution for risk-averse facility location problem

We consider the risk-averse uncapacitated facility location problem under stochastic disruptions. By the Conditional-value-at-risk, we control the risks at each individual customer, while previous works usually control the entire networks. We show that our model provides more reliable solutions than previous ones. The resulting formulation is a mixed-integer nonlinear programming. In response, we develop a multi-dual decomposition algorithm based on the augmented Lagrangian and classic penalty function. A class of decomposed unconstrained subproblems are then solved by an iterative approach not relying on Lagrange multipliers and differentiability. Our experiments show that the algorithm performs well even for some larger problems.