This paper is devoted to the numerical resolution of unit-commitment problems, with emphasis on the French model optimizing the daily production of electricity. The solution process has two phases. First a Lagrangian relaxation solves the dual to find a lower bound; it also gives a primal relaxed solution. We then propose to use the latter in the second phase, for a heuristic resolution based o...

We address a multi-item capacitated lot-sizing problem with setup times, safety stock and demand shortages. Demand cannot be backlogged, but can be totally or partially lost. Safety stock is an objective to reach rather than an industrial constraint to respect. The problem is np-hard. We propose a Lagrangian relaxation of the resource capacity constraints. We develop a dynamic programming algor...

In this paper we propose a forward-backward improvement heuristic for the variant of resource-constrained project scheduling problem aiming to maximise the net present value of a project. It relies on the Lagrangian relaxation method to generate an initial set of schedules which are then improved by the iterative forward/backward scheduling technique. It greatly improves the performance of the ...

We propose a new algorithm for unit commitment that employs a Lagrange relaxation technique with a new augmentation of the Lagrangian. The new augmentation involves a duplication of variables that allows relaxation of the coupling between generator timespanning constraints and system-wide instantaneous constraints. This framework allows the possibility of committing units that are required for ...

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 describe an optimal path design for a GMPLS network that employs the Lagrangian relaxation method, which can be used to estimate the lower bounds of a solution to a problem. This feature assists the designer of the problem to consider the accuracy of the solution obtained by the calculation when deciding whether to assign the solution to a real network in critical situations. A formulation o...

In this paper, we propose to solve the linear multicommodity flow problem using a partial Lagrangian relaxation. The relaxation is restricted to the set of arcs that are likely to be saturated at the optimum. This set is itself approximated by an active set strategy. The partial Lagrangian dual is solved with Proximal-ACCPM, a variant of the analytic center cutting plane method. The new approac...

We propose a new algorithm for unit commitment that employs a Lagrange relaxation technique with a new augmentation of the Lagrangian. The new augmentation involves a duplication of variables that allows relaxation of the coupling between generator timespanning constraints and system-wide instantaneous constraints. This framework allows the possibility of committing units that are required for ...

The solution algorithm, based on Lagrangian relaxation, a sub-gradient method and a heuristic to find the upper bound of the solution, is proposed to solve the coordinated fleet routing and flight scheduling problems. Numerical tests are performed to evaluate the proposed algorithm using real operating data from two Taiwan airlines. The test results indicate that the solution algorithm is a sig...

Analytical VLSI placement techniques achieved high solution quality and strong extensibility based on smooth approximation of placement objective and constraints. However, significant room still exist for VLSI placement to improve. We observe at least two sources of placement complexity and inaccuracy, namely, poor predictability for placement metrics and poor controllability of placement const...