Then some of the typical algorithms were introduced,such as algorithms based on problem decomposition,Lagrangian relaxation/decomposition and intelligent optimization algorithms.

Collaborative planning in supply chains based on Lagrangian relaxation and genetic algorithm;

Fuzzy subgradient algorithm for solving Lagrangian relaxation dual problem;

Novel fault localization approach based on Lagrangian relaxation and subgradient method;

Coordination method for multi-plants supply chain production planning based on Lagrange relaxation algorithm;

Self-adaptive Lagrange relaxation algorithm for aggregated multicast;

An algorithm based on Lagrange relaxation for delay-constrained multicast routing;

Firstly,Lagrange relaxation algorithm was applied to obtain several Pareto optima which were exploited to divide the search space into several domains.

Market deregulation makes transmission networks running near the edge of security limit, so it is particularly important to consider network security constraints in unit commitment and the Lagrangian relaxation method based on dual principle is an effective way to solve this problem.

At first stage, an augmented Lagrangian relaxation method is deve loped to obtain a preparatory job-shop scheduling.

We explore the use of Lagrangian Relaxation to the model, by which the complex scheduling problem can be decomposed into subproblems and solved effectively.