Double cycling is an efficient tool to increase the efficiency of quay crane (QC) in container terminals. In this paper, an optimization model for double cycling is developed to optimize the operation sequence of multiple QCs. The objective is to minimize the makespan of the ship handling operation considering the ship balance constraint. To solve the model, an algorithm based on Lagrangian rel...

Lagrangian relaxation has been used extensively in the design of approximation algorithms. This paper studies its strengths and limitations when applied to Partial Cover. We show that for Partial Cover in general no algorithm that uses Lagrangian relaxation and a Lagrangian Multiplier Preserving (LMP) α-approximation as a black box can yield an approximation factor better than 4 3 α. This match...

Lagrangian relaxation has been used extensively in the design of approximation algorithms. This paper studies its strengths and limitations when applied to Partial Cover. We show that for Partial Cover in general no algorithm that uses Lagrangian relaxation and a Lagrangian Multiplier Preserving (LMP) α-approximation as a black box can yield an approximation factor better than 4 3 α. This match...

Lagrangian relaxation has been used extensively in the design of approximation algorithms. This paper studies its strengths and limitations when applied to Partial Cover. We show that for Partial Cover in general no algorithm that uses Lagrangian relaxation and a Lagrangian Multiplier Preserving (LMP) α-approximation as a black box can yield an approximation factor better than 4 3 α. This match...

Lagrangian relaxation has been used extensively in the design of approximation algorithms. This paper studies its strengths and limitations when applied to Partial Cover. We show that for Partial Cover in general no algorithm that uses Lagrangian relaxation and a Lagrangian Multiplier Preserving (LMP) α-approximation as a black box can yield an approximation factor better than 4 3 α. This match...

In this paper, we consider the working VP and backup VP routing problems jointly and employ the integer programming based approach to maximize the system resource utilization and the network survivability. The VP planning problem is formulated as a nonlinear combinatorial optimization problem. The objective function minimizes the resource usage while maximizing the network survivability. By pro...

For a given iterate generated by the augmented Lagrangian or the Lagrangian relaxation based method, we derive estimates for the distance to the primal solution of the underlying optimization problem. The estimates are obtained using some recent contributions to the sensitivity theory, under appropriate first or second order sufficient optimality conditions. The given estimates hold in situatio...

We present a branch-and-bound (bb) algorithm for the multiple sequence alignment problem (MSA), one of the most important problems in computational biology. The upper bound at each bb node is based on a Lagrangian relaxation of an integer linear programming formulation for MSA. Dualizing certain inequalities, the Lagrangian subproblem becomes a pairwise alignment problem, which can be solved ef...

We present a branch-and-bound (bb) algorithm for the multiple sequence alignment problem (MSA), one of the most important problems in computational biology. The upper bound at each bb node is based on a Lagrangian relaxation of an integer linear programming formulation for MSA. Dualizing certain inequalities, the Lagrangian subproblem becomes a pairwise alignment problem, which can be solved ef...

-In this paper a Lagrangean decomposition technique for solving the scheduling problem for Hot Charged Rolling (HCR) in the continuous casting process which involves sequencing and grouping. This Lagrangian relaxation algorithm is proposed that incorporate two sets of constraints into the objective function after applying the variable splitting technique. The relaxed problem has a special struc...