The Benders Dual Decomposition Method

AbstractMany methods that have been proposed to solve large-scale MILP problems rely on the use of decomposition strategies. These methods exploit either the primal or dual structures of the problems by applying the Benders decomposition or Lagrangian dual decomposition strategy, respectively. In “The Benders Dual Decomposition Method,” Rahmaniani, Ahmed, Crainic, Gendreau, and Rei propose a new and high-performance approach that combines the complementary advantages of both strategies. The authors show that this method (i) generates stronger feasibility and optimality cuts compared with the classical Benders method, (ii) can converge to the optimal integer solution at the root node of the Benders master problem, and (iii) is capable of generating high-quality incumbent solutions at the early iterations of the algorithm. The developed algorithm obtains encouraging computational results when used to solve various benchmark MILP problems.Many methods that have been proposed to solve large-scale mixed integer linear programing (MILP) problems rely on decomposition techniques. These methods exploit either the primal or the dual structure of the problem, yielding the Benders decomposition or Lagrangian dual decomposition methods. We propose a new and high-performance approach, called Benders dual decomposition (BDD), which combines the complementary advantages of both methods. The development of BDD is based on a specific reformulation of the Benders subproblem, where local copies of the master variables are introduced in the proposed subproblem formulation and then priced out into the objective function. We show that this method (i) generates stronger feasibility and optimality cuts compared with the classical Benders method, (ii) can converge to the optimal integer solution at the root node of the Benders master problem, and (iii) is capable of generating high-quality incumbent solutions at the early iterations of the algorithm. We report encouraging computational results on various benchmark MILP problems.