We present a Lagrangian decomposition approach for the Knapsack Constrained Maximum Spanning Tree problem yielding upper bounds as well as heuristic solutions. This method is further combined with an evolutionary algorithm to a sequential hybrid approach. Thorough experimental investigations, including a comparison to a previously suggested simpler Lagrangian relaxation based method, document t...

The subgradient method is used frequently to optimize dual functions in Lagrangian relaxation for separable integer programming problems. In the method, all subproblems must be solved optimally to obtain a subgradient direction. In this paper, the surrogate subgradient method is developed, where a proper direction can be obtained without solving optimally all the subproblems. In fact, only an a...

Whereas CP methods are strong with respect to the detection of local infeasibilities, OR approaches have powerful optimization abilities that ground on tight global bounds on the objective. An integration of propagation ideas from CP and Lagrangian relaxation techniques from OR combines the merits of both approaches. We introduce a general way of how linear optimization constraints can strength...

The analytic center cutting plane method (ACCPM) is one of successful methods to solve nondifferentiable optimization problems. In this paper, ACCPM is used to accelerate Lagrangian relaxation procedure for solving a vehicle routing problem with time windows (VRPTW). First, a basic cutting plane algorithm and its relationship with a column generation technique is clarified. Then, the proposed m...

We study optimization for collaborative multi-agent planning in factored Markov decision processes (MDPs) with shared resource constraints. Following past research, we derive a distributed planning algorithm for this setting based on Lagrangian relaxation: we optimize a convex dual function which maps a vector of resource prices to a bound on the achievable utility. Since the dual function is n...

Dynamic lot sizing problem is one of the significant problem in industrial units and it has been considered by  many researchers. Considering the quantity discount in  purchasing cost is one of the important and practical assumptions in the field of inventory control models and it has been less focused in terms of stochastic version of dynamic lot sizing problem. In  this paper, stochastic dyn...

We discuss a Lagrangian-relaxation-based heuristics for dealing with feature selection in a standard L1 norm Support Vector Machine (SVM) framework for binary classification. The feature selection model we adopt is a Mixed Binary Linear Programming problem and it is suitable for a Lagrangian relaxation approach. Based on a property of the optimal multiplier setting, we apply a consolidated nons...

A new exact solution algorithm is proposed for the Degree-Constrained Minimum Spanning Tree Problem. The algorithm involves two combined phases. The first one contains a Lagrangian Relaxand-Cut procedure while the second implements a Branch-and-Cut algorithm. Both phases rely on a standard formulation for the problem, reinforced with Blossom Inequalities. An important feature of the proposed al...

We present a new evolutionary algorithm to solve the 0-1 multidimensional knapsack problem.We tackle the problem using duality concept, differently from traditional approaches. Ourmethod is based on Lagrangian relaxation. Lagrangemultipliers transform the problem, keeping the optimality as well as decreasing the complexity. However, it is not easy to find Lagrange multipliers nearest to the cap...