## 2 Related Work  
### PIO Algorithm  
Pigeon-inspired optimization (PIO) is a new swarm intelligence algorithm based on pigeon behavior recently proposed by Professor [PERSON] [21]. By sensing the earth's magnetic field and following their familiar landmarks, pigeons can always find their way to their destinations as quickly as possible. The process of PIO algorithm can be divided into three main parts:  
(1) The population initialization  
Before algorithm execution, parameters need to be initialized. Initialization parameters include the population size \(N_{p}\), solution space dimension \(D\), map and compass factor \(R\), the total number of iterations \(N_{C}\), the number of iterations \(N_{C1}\) max and \(N_{C2}\) max for two operators, and \(N_{C1}\) max \(<N_{C2}\) max. Although PIO algorithm has a fast convergence speed, it also has a fatal shortcoming: it is easy to fall into local optimum. As you can imagine, the whole searching process is towards the optimal or the best individual; therefore, when the solution of initialization is dense, or when the optimal initial position is not in the vicinity of a truly global optimal, the error of orientation will make the space of whole other individual search mistakes along the way, and the optimal solution cannot be found. Aiming at this defect, we optimized PIO algorithm in the population initialization stage. In the process of initialization, adding chaotic mapping makes the initial sequence generated more random, and the solution space covers a wider area, which can obtain a better distribution of pigeons so that the population has diversity and convergence. (2) Map and compass section  
The main principle that pigeons use to find their destination is to sense the earth's magnetic field to create a map in their minds. At the same time, they can adjust their orientation according to the height of the sun. In the d dimensional search space, each pigeon \(P_{i}\) has two attributes: position \(X_{i}\) and speed \(V_{i}\). Pigeons use maps and compasses to update their position and speed. The updating equation of the n-th iteration is as follows:  
\[V_{i}(n)=V_{i}(n-1)e^{-Rn}+rand\big{(}X_{g}(n)-X_{i}(n-1)\big{)} \tag{1}\]  
\[X_{i}(n)=V_{i}(n)+X_{i}(n-1) \tag{2}\]  
where \(X_{g}\) is the global optimal position, which can obtain the best position in the whole search space, and \(R\) is the map and compass operator determined by the actual situation and experience, and \(rand\in[0,1]\). In the late iteration of the map and compass part of PIO algorithm, all the pigeons gradually gather together, and the optimal position of the pigeon colony only changes very little over a long period of time. In this case, the position update of pigeons is very slow, and each pigeon will slowly stop moving until it finally converges to a certain position in the search space. In this case, it will fall into local optimum. To solve the above problems, this paper proposes an improved PIO algorithm--CDPIO. Tent chaotic disturbance is introduced into iterative updating to increase the global search ability of the algorithm. Firstly, the chaotic variable \(Z_{d}\) carrier generated by the population initialization is put into the solution space to be solved, and then the chaotic disturbance of the individual is carried out according to certain rules. Finally, enhanced individual performance and better searching effect can be achieved by the simulations in Sections 4 and 5. (3) Landmark section  
Pigeons use landmarks as a tool to optimize their position as they approach their destination. Pigeons familiar with the landmark flew directly to their destination, while those unfamiliar followed them. Assuming that every pigeon could fly directly to its destination, half of the pigeons familiar with the landmark could find a nearby center that would guide them to their destination as quickly as possible. In each iteration, the number of pigeons \(N_{p}\) is reduced by half. The updated equation is as follows.