Nonanticipative duality, relaxations, and formulations for chance-constrained stochastic programs
نویسندگان
چکیده
We propose two new Lagrangian dual problems for chance-con-strained stochastic programs based on relaxing nonanticipativity constraints. We compare the strength of the proposed dual bounds and demonstrate that they are superior to the bound obtained from the continuous relaxation of a standard mixed-integer programming (MIP) formulation. For a given dual solution, the associated Lagrangian relaxation bounds can be calculated by solving a set of single scenario subproblems and then solving a single knapsack problem. We also derive two new primal MIP formulations and demonstrate that for chanceconstrained linear programs, the continuous relaxations of these formulations yield bounds equal to the proposed dual bounds. We propose a new heuristic method and two new exact algorithms based on these duals and formulations. The first exact algorithm applies to chance-constrained binary programs, and uses either of the proposed dual bounds in concert with cuts that eliminate solutions found by the subproblems. The second exact method is a branch-and-cut algorithm for solving either of the primal formulations. Our computational results indicate that the proposed dual bounds and heuristic solutions can be obtained efficiently, and the gaps between the best dual bounds and the heuristic solutions are small.
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ورودعنوان ژورنال:
- Math. Program.
دوره 162 شماره
صفحات -
تاریخ انتشار 2017