The analytic center cutting plane method (ACCPM) is one of successful methods to solve nondifferentiable optimization problems. In this paper ACCPM is used for the first time in the vehicle routing problem with time windows (VRPTW) to accelerate lagrangian relaxation procedure for the problem. At first the basic cutting plane algorithm and its relationship with column generation method is clari...

An improved Lagrangian relaxation (LR) solution to the thermal unit commitment problem (UCP) is proposed in this paper. The algorithm is characterized by: (1) a new Matlab function to determine the optimal path of the dual problem, (2) new initialization procedure of Lagrangian multipliers, based on both unit and time interval classification, (3) a flexible adjustment of Lagrangian multipliers,...

Nowadays, a rapid growth in the rate of life expectancy can be seen especially in the developed countries. Accordingly, the population of elderlies has been increased. By another point of view, the number of hospitals, retirement homes along with medical staffs has not been grown with a same rate. Hence, Home Health Care (HHC) operations including a set of nurses and patients have been develope...

In this paper, a step fixed charge transportation problem is developed where the products are sent from the sources to the destinations in existence of both unit and step fixed-charges. The proposed model determines the amount of products in the existing routes with the aim of minimizing the total cost (sum of unit and step fixed-charges) to satisfy the demand of each customer. As the problem i...

This paper presents an enhanced merit order (EMO) and augmented Lagrange Hopfield network (ALHN) for unit commitment (UC). The EMO method is a merit order based heuristic search for unit scheduling and ALHN is a continuous Hopfield network based on augmented Lagrange relaxation for economic dispatch problem. First, generating units are sorted in ascending average production cost and committed t...

For solving the multicommodity flow problems, Lagrangian relaxation based algorithms are fast in practice. The time-consuming part of the algorithms is the shortest path computations in solving the Lagrangian dual problem. We show that an A* search based algorithm is faster than Dijkstra’s algorithm for the shortest path computations when the number of demands is relatively smaller than the siz...

This paper presents Chemo-tactic PSO-DE (CPSO-DE) optimization algorithm combined with Lagrange Relaxation method (LR) for solving Unit Commitment (UC) problem. The proposed approach employs Chemo-tactic PSO-DE algorithm for optimal settings of Lagrange multipliers. It provides high-quality performance and reaches global solution and is a hybrid heuristic algorithm based on Bacterial Foraging O...

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...