This paper proposes an augmented Lagrange Hopfield network (ALHN) for combined heat and power economic dispatch (CHPED) problem. The ALHN method is the continuous Hopfield neural network with its energy function based on augmented Lagrangian relaxation. In the proposed ALHN, the energy function is augmented by Hopfield terms from Hopfield neural network and penalty factors from augmented Lagran...

Due to the process of network convergence, the variety of types of traffic transmitted over a single medium increases steeply. This phenomenon can be handled by the existing networking structure although the protocols that are used and, especially, the underlying routing protocols need to be improved. The problem of finding the shortest path on the Internet can no longer be easily defined as th...

Trigeneration is a booming power production technology where three energy commodities are simultaneously produced in a single integrated process. Electric power, heat (e.g. hot water) and cooling (e.g. chilled water) are three typical energy commodities in the trigeneration system. The production of three energy commodities follows a joint characteristic. This paper presents a Lagrangian relaxa...

This paper proposes an augmented Lagrangian Hopfield network (ALHN) for combined heat and power economic dispatch (CHPED) problem. The ALHN is the continuous Hopfield neural network based on augmented Lagrangian relaxation as its energy function. In the proposed ALHN, its energy function is augmented by Hopfield terms from Hopfield neural network and penalty factors from augmented Lagrangian re...

Maximum a-posteriori (MAP) estimation is an important task in many applications of probabilistic graphical models. Although finding an exact solution is generally intractable, approximations based on linear programming (LP) relaxation often provide good approximate solutions. In this paper we present an algorithm for solving the LP relaxation optimization problem. In order to overcome the lack ...

The paper deals with the economic dispatch problem for a district heating system. The distribution network is modeled with a number of nodes and arcs, implying that time delays and restrictions in distribution capacity can be considered. A solution algorithm for the corresponding nonlinear optimization problem is proposed. The method is based on Lagrangian relaxation and exploits the relations ...

In this paper we consider the single machine scheduling problem with precedence constraints to minimize the total weighted tardiness of jobs. This problem is known to be strongly NP-hard.A solution methodology based on Lagrangian relaxation is developed to solve it. In this approach, a hybrid backward and forward dynamic programming algorithm is designed for the Lagrangian relaxed problem, whic...

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. Experimental investigations, including a comparison to a previously suggested simpler Lagrangian relaxation based method, document the advant...