Optimization mechanism

In network science, the optimization mechanism is a network growth algorithm, which randomly places new nodes in the system, and connects them to the existing nodes based on a cost-benefit analysis. Depending on the parameters used in the optimization mechanism, the algorithm can build three types of networks: a star network, a random network, and a scale-free network. Optimization mechanism is thought to be the underlying mechanism in several real networks, such as transportation networks, power grid, router networks, highway, etc.

General Properties

The optimization mechanism is a model with growth, in which preferential attachment is valid under certain assumptions. As opposed to the copying model, the optimization model uses global information about the network, to connect the newly entering nodes to the existing ones, thus reducing the amount of randomness in the process. The model's mechanism is based on a cost-benefit comparison, that is for each entering node 'i', the algorithm calculates the net benefit (benefits minus costs) of connecting 'i' to each existing node, and connects node 'i' to the node which gives the highest net benefit.

Description

The costs and benefits in the optimization models can be simplified into two attributes: the distance between the new node, and the existing one; and the distance of the existing node from the central node. Thus the goal function can be written in the following form:

$C_{i}=min_{j}[\delta *d_{ij}+h_{j}]$