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Thus a decomposition based solution algorithm is proposed in this paper.

In view of the special structure of the model, an exact cutting-plane based solution algorithm is proposed.

The model is formulated as a combined Steiner and assignment problem, and a Lagrangian relaxation based solution algorithm is developed to solve the optimal solution.

Then, the proposed harmony search based solution algorithm is applied on the pre-selected 352 time-series to obtain the ground motion record sets compatible with design spectra.

As it is difficult to obtain precisely optimal solution to this kind of problems, a Lagrangian based solution algorithm is developed to obtain near optimal solution.

A descent-gradient-based solution algorithm is adapted to solve the model.

An efficient Lagrangian-based solution algorithm is developed, which solves large-sized instances with up to 50 service facilities and 500 customers in a few seconds.

With this, the modified link-based solution algorithm is able to generate the hybrid model-based flow pattern while inheriting the advantages of Bell's algorithm, such as easy implementation and avoidance of path enumeration/storing.

Our solution algorithm is based on a generalized graph coloring model and a randomized greedy approach.

An efficient solution algorithm is developed, based on a consistent element state determination procedure.

Finally, in order to solve the CWPRCA problem, a solution algorithm is developed based on Alternating Direction Method (ADM).