*3.2. Multi-Objective Grey Wolf Optimizer*

Two new components were integrated into MOGWO for performing multi-objective optimization: an archive of the best non-dominated solutions and a leader selection strategy of alpha, beta, and gamma solutions. The archive is needed for storing non-dominated Pareto solutions through the course of iterations. The archive controller has dominant sorting rules for entering new solutions and for archive states. The size of the archive is closely related to the number of objective functions, which is named segments or hypercubes. Figure 3a shows the archive of three hypercubes with the non-dominated solutions for the t-iteration.

The second component is a leader selection, which chooses the least crowded hypercube of the search space and offers available non-dominated solutions from the archive (Figure 3b). In case there are only two solutions, the third one can be taken from the second least crowded hypercube.

**Figure 3.** Two modules of MOGWO: (**a**) the archive, which consists of three hypercubes, and (**b**) the leader selection mechanism.

Generally, it can be said that the archive stores the best solutions for each objective function. It saves them not only as alpha, beta, and gamma agents, but also with the segment priorities, which are defined by the number of total solutions. Thus, the global best solution can be chosen among the local ones in the archive. This selection mechanism in MOGWO prevents the picking of the same leaders. In other words, it avoids stagnation in local optimal points. Figure 4 shows the full algorithm of MOGWO.

MOGWO finds application in cloud computing for virtual machine placement [47], medicine for preventing cervical cancer by scanning images [48], wind power for speed forecasting [49], and energy-efficient scheduling [50]. However, it has not been used in the robotic field up to this time.
