الگوریتم بهینه ‌سازی کوکو Cuckoo – COA

ABSTRACT Cuckoo Optimization Algorithm

Optimization is the process of making something better. In other words, optimization is the process of adjusting the inputs to or characteristics of a device, mathematical process, or experiment to find the minimum or maximum output or result. The input consists of variables: the process or function is known as the cost function, objective function, or fitness function; and the output is the cost or fitness [1]. There are different methods for solving an optimization problem. Some of these methods are inspired from natural processes. These methods usually start with an initial set of variables and then evolve to obtain the global minimum or maximum of the objective function. Genetic Algorithm (GA) has been the most popular technique in evolutionary computation research. Genetic Algorithm uses operators inspired by natural genetic variation and natural selection [2,3]. Another example is Particle Swarm Optimization (PSO) which was developed by Eberhart and Kennedy in 1995. This stochastic optimization algorithm is inspired by social behavior of bird flocking or fish schooling [3–5]. Ant Colony Optimization (ACO) is another evolutionary optimization algorithm which is inspired by the pheromone trail laying behavior of real ant colonies [3,6,7]. On the other hand Simulated Annealing simulates the annealing process in which a substance is heated above its melting temperature and then gradually cools to produce the crystalline lattice, which minimizes its energy probability distribution [1,8,9]. Besides these well known methods, the investigations on nature inspired optimization algorithms are still being done and new methods are being developed to continually solve some sort of nonlinear problems. In [10], making use of the ergodicity and internal randomness of chaos iterations, a novel immune evolutionary algorithm based on the chaos optimization algorithm and immune evolutionary algorithm is presented to improve the convergence performance of the immune evolutionary algorithm. The novel algorithm integrates advantages of the immune evolutionary algorithm and chaos optimization algorithm. [11] introduces a new optimization technique called Grenade Explosion Method (GEM) and its underlying ideas, including the concept of Optimal Search Direction (OSD), are elaborated. In [12] a new particle swarm optimization method based on the clonal selection algorithm is proposed to avoid premature convergence and guarantee the diversity of the population.

The main advantages of evolutionary algorithms are [3]:

(1) Being robust to dynamic changes: Traditional methods of optimization are not robust to dynamic changes in the environment and they require a complete restart for providing a solution. In contrary, evolutionary computation can be used to adapt solutions to changing circumstances.

(2) Broad applicability: Evolutionary algorithms can be applied to any problems that can be formulated as function optimization problems.

(3) Hybridization with other methods: Evolutionary algorithms can be combined with more traditional optimization techniques.

(4) Solves problems that have no solutions: The advantage of evolutionary algorithms includes the ability to address problems for which there is no human expertise. Even though human expertise should be used when it is needed and available; it often proves less adequate for automated problem-solving routines.

Considering these features, evolutionary algorithms can be applied to various applications including: Power Systems operations and control [13,19,20], NP-Hard combinatorial problems [14,15], Chemical Processes [16], Job Scheduling problems [17], Vehicle Routing Problems, Mobile Networking, Batch process scheduling, Multi-objective optimization problems [18], Modeling optimized parameters [21], Image processing and Pattern recognition problems. In this paper we introduce a new evolutionary optimization algorithm which is inspired by lifestyle of a bird family called cuckoo. Specific egg laying and breeding of cuckoos is the basis of this novel optimization algorithm. Cuckoos used in this modeling exist in two forms: mature cuckoos and eggs. Mature cuckoos lay eggs in some other birds’ nest and if these eggs are not recognized and not killed by host birds, they grow and become a mature cuckoo. Environmental features and the immigration of societies (groups) of cuckoos hopefully lead them to converge and find the best environment for breeding and reproduction. This best environment is the global maximum of objective functions. This paper illustrates how the life method of cuckoos is modeled and implemented.

Section 2 investigates the birds called cuckoo and reviews their amazing life characteristics. In Section 3, the Cuckoo Optimization Algorithm (COA) is proposed and its different parts are studied in details. The proposed algorithm is tested with some benchmark functions and also with a controller design of a Multi-Input MultiOutput (MIMO) process as a real case study in Section 4. Finally the conclusions are presented in Section 5.