In the outer level of the model, we optimize the horizontal alignment and in the inner level of the model a vertical alignment optimization problem considering earthwork allocation is solved for a fixed horizontal alignment.
The primal optimization problem has been decomposed into subproblems where resource allocation and power allocation are solved in an iterative manner.
When the SUs are assigned to the spectrum holes, the second part of the procedure: power allocation, is solved by the Gradient Projection Method (GPM) [31] instead of using PI-algorithm and the Lagrangian multiplier method.
To demonstrate how these methods work, the well-known redundancy allocation problem was solved as a multiple objective problem by using the NSGA genetic algorithm to initially find the Pareto optimal solutions, and then, the two proposed methods are applied to prune the Pareto set.
Finally, the optimal power allocation problem was solved by the Lagrangian dual method.
More recently, the resource allocation problem was solved for a point-to-point single user system with power splitting receiver in ergodic fading channels [16].
In this paper, a power allocation problem was solved for a SWIPT system in K-user interference channels using the framework of game theory.
The Pareto-Optimal Allocation problem was solved with dynamic programming by Sitarz [ 19].
Power allocation problem in CDMA was solved by the PSO in [22] where a few constraint handlings were investigated and extensive studies on the parameters of PSO were given.
