Further, inefficiency in logistics can be realized still, if a rectangular coordinate system is considered for the logistic in MLP, where the coordinates of locations for machines are changed but relative positions relationships are maintained.

Basic MLP Model under Rectangular Coordinate System

Firstly, a transformation of the rectangular coordinate geometry into a series of local polar coordinate systems is devised as depicted in Figure 2, in which the first local polar coordinate system is set as in Figure 1; thus, every geometric center of machines is set as a local polar origin, and their local polar axes are directed as x-axis.

In order to illustrate the superiority of improved ACO algorithm under local polar coordinate system, a comparative experiment is performed between GA and ACO and improved ACO are considered under rectangular coordinate system.

The experimental results of 40000 generations are shown in Figure 8, where genetic algorithm is adopted under rectangular coordinate system.

Furthermore, an experiment is conducted by employing the regular ACO algorithm under rectangular coordinate system, and it was noticeable that the trait is trapped into the local optimal value.