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Wang et al. Intell Robot 2023;3(4):538-64 I http://dx.doi.org/10.20517/ir.2023.30 Page 23 of 27

Figure 15. Best fitness under different iteration steps using different optimization algorithms.

particle swarm optimization [10] (ME-PSO) and a motion-encoded genetic algorithm [15] (ME-GA) are chosen
as the comparison group of the direct motion-encoding method as these are commonly used to solve similar
problems in recent research. Secondly, to test the proposed priority-encoding method, these optimization
algorithms have been rewritten with corresponding encoding methods and denoted as PE-PSO and PE-GA,
respectively. In addition, to compare with more optimization algorithms, a differential evolution (DE) algo-
rithm [28] and an artificial bee colony (ABC) algorithm [29] are chosen and rewritten with priority-encoding
methods, which are PE-DE and PE-ABC.

In order to match the parameters used by IGAFA in the second experiment, the parameters in GA are set
to = 0.7 and = 0.3, and the PSO, DE and ABC have the same population size as IGAFA. Figure 15
shows the best fitness under different iteration steps using different optimization algorithms. The result shows
that the fitness optimized by ME-PSO or ME-GA is significantly higher than the fitness using the indirect
priority-encoding method proposed in this paper, which indicates that the direct motion-encoding method
is not appropriate when dealing with the proposed optimization problem. The fundamental reason is that
the direct motion-encoding method cannot guarantee the legitimacy of its descendants, and it is difficult to
achieve convergence of the optimal solution during the optimization. Each bit in the encoding has a significant
influence on the results, and the optimization is inefficient under a large solution space.

Among the algorithms that use the priority-encoding method, traditional PE-GA has the slowest optimization
speed. By comparison, PE-PSO, PE-DE and PE-ABC have faster optimization speeds in the early stage due
to their characteristics being close to random-search. However, in the later stage, considering the continuity
problem of the solution, the optimization speed significantly decreases. As an improved algorithm for GA,
priority-encoded IGAFA optimizes the evolution direction while retaining the excellent genes of its parents,
making the evolution process closer to the encoding characteristics, thus maintaining good optimization effi-
ciencyin themiddleandlaterstagesoftheoptimizationprocess. Itprovesthatthefine-adjustmentmechanism
proposed in this paper has efficient optimization performance when dealing with priority-encoding methods.

In order to further compare the influence on the target search process when using different optimization algo-
rithms, PE-GA and ME-PSO are selected as typical optimization algorithms representing priority-encoding
method and motion-encoding method, respectively.

Table 5 shows the average execution time with different and . The result indicates that ME-PSO has
a shorter execution time because of the defect of illegal descendant, and IGAFA has a longer execution time