3.2.1. Encoding Mechanism

The encoding mechanism is essential, and the theoretical principle of IGA is implemented based on it. Traditional encoding mechanisms include the binary, the floating, the integer, and the symbol. The binary mechanism provides convenient encoding and decoding operations when solving discrete or continuous optimization problems. The floating mechanism provides results with high precision when solving continuous optimization problems with multidimensional functions. The integer mechanism is usually employed for solving combinatorial optimization problems such as the Traveling Salesman Problem [40]. The symbol mechanism contributes to the combination of GA and other algorithms. In IGA, the integer encoding mechanism is employed for the waypoint sequence, while the binary encoding mechanism is employed for the sequence of joint configurations and the special value corresponding with the cubic coefficients of the arguments, which is sketched in Figure 5.

**Figure 5.** Encoding mechanisms of each chromosome.

#### A. First Part of Each Chromosome

In MTTP, the end effector is constrained to visit a set of predefined waypoints, and each waypoint is limited to being visited once. According to binary encoding, the random selection of the crossover and mutation mechanisms may lead to alphabet repetition, thus conflicting with the requirement of only visiting each waypoint once. Integer encoding is the best choice, where *N* positive integers correspond with *N* waypoints.
