A new discovery of transition rules for cellular automata by using cuckoo search algorithm

Abstract

This paper presents an intelligent approach to discover transition rules for cellular automata (CA) by using cuckoo search (CS) algorithm. CS algorithm is a novel evolutionary search algorithm for solving optimization problems by simulating breeding behavior of parasitic cuckoos. Each cuckoo searches the best upper and lower thresholds for each attribute as a zone. When the zones of all attributes are connected by the operator 'And' and linked with a cell status value, one CS-based transition rule is formed by using the explicit expression of 'if-then'. With two distinct advantages of efficient random walk of Lévy flights and balanced mixing, CS algorithm performs well in both local search and guaranteed global convergence. Furthermore, the CA model with transition rules derived by CS algorithm (CS-CA) has been applied to simulate the urban expansion of Nanjing City, China. The simulation produces encouraging results, in terms of numeric accuracy and spatial distribution, in agreement with the actual patterns. Preliminary results suggest that this CS approach is well suitable for discovering reliable transition rules. The model validation and comparison show that the CS-CA model gets a higher accuracy than NULL, BCO-CA, PSO-CA, and ACO-CA models. Simulation results demonstrate the feasibility and practicability of applying CS algorithm to discover transition rules of CA for simulating geographical systems.

A grey wolf optimizer–cellular automata integrated model for urban growth simulation and optimization

“…These urban growth rules mainly have two forms: formulaic and non‐formulaic. For the former, the urban growth rules are defined via mathematical equations involving parameter estimation problems (Cao, Tang, Shen, & Wang, ). For the latter, the urban growth rules indicate complex nonlinear relationships between spatial variables and urban growth in the form of “if–then” statements.…”

“…These algorithms derive from the burst collective intelligence of simple agent groups (Bonabeau, Dorigo, & Theraulaz, ) and are often inspired by natural swarm behaviors of social animals, such as ants, birds, fish, and fireflies. A variety of SI algorithms have been employed to derive the transition rules, such as particle swarm optimization (Feng, Liu, Tong, Liu, & Deng, ; Liao et al, ), ant colony optimization (Liu, Li, Liu, He, & Ai, ; Liu, Li, Yeh, He, & Tao, ), simulated annealing (Feng & Liu, ), artificial bee colony (Yang, Tang, Cao, & Zhu, ), cuckoo search (Cao et al, ), and bat algorithms (Cao, Bennett, Shen, & Xu, ).…”

Calibration of cellular automata models using differential evolution to simulate present and future land use

“…The model generated smaller residuals in fitting CA transition rules and better spatial patterns of land use compared with an LR method. Swarm intelligence methods such as particle swarm optimization (PSO), ant colony optimization (ACO), and artificial bee colony (ABC) are typical metaheuristics that have been applied to CA modeling of land use and urban expansion (Cao, Tang, Shen, & Wang, ; Feng, Liu, Tong, Liu, & Deng, ; Li, Lao, Liu, & Chen, ; Naghibi, Delavar, & Pijanowski, ; Yang, Zheng, & Lv, ). These metaheuristics showed better accuracy and spatial distribution in simulating land use change when integrated into CA models.…”

Urban Growth Modeling Using Cellular Automata with Multi-Temporal Remote Sensing Images Calibrated by the Artificial Bee Colony Optimization Algorithm

“…Cao et al used the cuckoo search algorithm to discover transition rules for CA. They showed that the CA model calibrated by that cuckoo search algorithm had greater accuracy than that of other swarm models such as the ACO-CA model [63]. …”