Lagrangian relaxation based Feasible Solution Algorithm

Lagrangian relaxation is widely and efficiently applied to solve large scale integer programming problems. One of the most challenging issues for Lagrangian relaxation based approaches is to obtain a good feasible solution based on the optimal dual solution. In this paper, a Feasible Solution Algorithm in Largrangian relaxation framework is proposed to systematically obtain a feasible solution. The basic idea is to gradually add relaxed constraints back into the subproblems which are then solved successively. The numerical testing results show that this method can not only alleviate dual solution oscillation and zigzag phenomena but also can achieve fast converge and obtain feasible solutions.