INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTERS IN SIMULATION Implementation and performance of an object-oriented software system for cuckoo search algorithm Nebojsa Bacanin Modern metheuristic algorithms (typically high-level Abstract—Evolutionary computation (EC) algorithms have been strategies which guide an underlying subordinate heuristic to successfully applied to hard optimization problems. In this very efficiently produce high quality solutions and increase their active research area one of the newest EC algorithms is a cuckoo performance) can be applied to both problem domains [2]. search (CS) metaheuristic for unconstrained optimization problems They include population based, iterative based, stochastic, which was developed by Yang and Deb in MATLAB software. This paper presents our software implementation of CS algorithm which deterministic and other approaches. we called CSApp. CSApp is an object-oriented system which is fast, Population based algorithms are working with a set of robust, scalable and error prone. User friendly graphical user solutions and trying to improve them. By the nature of interface (GUI) enables simple adjustment of algorithm’s control phenomenon simulated by the algorithm, population based parameters. The system was successfully tested on standard algorithms can be divided into two groups: evolutionary benchmark functions for unconstrained problems with various algorithms (EA) and swarm intelligence based algorithms. The number of parameters. CSApp software, as well as experimental results are presented in this paper. most prominent representative of the first group is genetic algorithms (GA). GA is a method for moving a population of Keywords—Cuckoo search, Metaheuristic optimization, Software candidate solutions through fitness landscape using nature system, Nature inspired algorithms. inspired operators: selection, crossover and mutation. But, second group of algorithms is of our particular interest in this I. INTRODUCTION paper. ANY practical, real life, problems belong to a class of Researchers` attention has been attracted by the collective M intractable combinatorial (discrete) or numerical intelligent behavior of insects or animal groups such as flocks optimization problems because they are often highly nonlinear. of birds, schools of fish, colonies of ants or bees and groups of Optimization, or mathematical programming, refers to other animals/insects. The aggregate behavior of insects or choosing the best element from some set of available animals is called swarm behavior and the branch of artificial alternatives. This means solving problems in which one seeks intelligence which deals with the collective behavior of to minimize or maximize a real function by systematically swarms through complex interactions of individuals without choosing the values of real or integer variables from an centralized supervision component is referred to as swarm allowed set of values. This formulation, using a scalar, real- intelligence. Swarm intelligence has some advantages such as valued objective function, is probably the simplest example. scalability, fault tolerance, adaptation, speed, modularity, The generalization of optimization theory and techniques to autonomy, and parallelism [3]. other formulations comprises a large area of applied Key factors for optimizing capability of swarm intelligence mathematics. systems are self-organization and division of labor. In such In order to solve such problems, many methods for self-organized system, each component (agent) may respond continuous optimization and heuristics for discrete problems efficiently to local stimuli individually, but they also can act were developed. Fitness landscape for such problems is together to accomplish global task via labor division. Entire multimodal because of its nonlinear nature. Subsequently, system is fully adaptive to internal and external changes. Four local search algorithms such as hill-climbing and its basic properties on which self-organization rely are: positive modifications are not suitable, only global algorithms can feedback, negative feedback, fluctuations and multiple obtain optimal solutions [1]. interactions [4]. Positive feedback refers to a situation when and individual recruits other individuals (agents) by some directive. For example, positive feedback is when bees dance Manuscript received December 25, 2011. in order to lead other bees to a specific food source site. The research was supported by the Ministry of Science, Republic of Serbia, Project No. III-44006 Negative feedback retracts individuals from bad solution for N. Bacanin is with the Faculty of Computer Science, Megatrend the problem. Fluctuations are random behaviors of individuals University, Belgrade, Serbia, e-mail: [email protected] in order to explore new states, such as random flights of scouts Issue 1, Volume 6, 2012 185 INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTERS IN SIMULATION in a bee swarm. Multiple interactions are the basis of the tasks Improved version of the PSO algorithm is particle swarm to be carried out by certain rules. inspired evolutionary algorithm (PS-EA) which is a hybrid A lot of swarm intelligence algorithms have been model of EA and PSO. PS-EA incorporates PSO with developed. For example, ant colony optimization (ACO) is a heuristics of EA in the population generator and mutation technique that is quite successful in solving many operator while retaining the workings of PSO. combinatorial optimization problems. The inspiring source of Recently, a novel metaheuristic search algorithm has been ACO was the foraging behavior of real ants which enables developed by Yang and Deb [5]. It is called cuckoo search them to find shortest paths between food sources and their (CS) algorithm. It has been shown that it is very promising nests. While working from their nests to food source, ants algorithm which could outperform existing algorithms such as deposit a substance called pheromone. Paths that contain more PSO. pheromone concentrations are chosen with higher probability In this paper, we will present our implementation of CS by ants than those that contain lower pheromone algorithm. In order to see its robustness and efficiency, we concentrations. Thus, ants exchange information indirectly by developed object-oriented CS software, named CSApp, for depositing pheromones. This system is called stigmergy, and it solving combinatorial and numeric optimization problems in is common among many insect societies. JAVA programming language. This software will be in detail The core philosophy of ACO algorithm involves the presented in this paper as well as testing results on four movement of an ant colony through different locations which standard benchmark functions with varying parameters. is directed by two local decision policies: pheromone trails and its attractiveness. This algorithm uses two more mechanisms in II. CUCKOO BEHAVIOR order to balance exploitation – exploration tradeoff. These are Cuckoos are special because they have many characteristics trail evaporation and daemon actions. First mechanism reduces that differentiate them from other birds. Their major all trail values over time and decreases possibility of getting distinguishing feature is aggressive reproduction strategy. stuck in local optima. The daemon actions are used to bias a Some species such as the Ani and Guira cuckoos lay their eggs search process from non-local perspective. in communal nests, though they may remove others’ eggs to Artificial bee colony algorithm (ABC) models intelligent increase the hatching probability of their own eggs [6]. behavior of honey bee swarm. This algorithm produces Cuckoos are brood parasites. They use a kind of klepto- enviable results in optimization problems. Here, a possible parasitism which involves the use and manipulation of host solution to a problem represents a food source (flower). Nectar individuals, either of the same (intraspecific brood-parasitism) amount of flower designates the fitness of a solution. There are or different species (interspecific brood-parasitism) to raise the three types of artificial bees (agents): employed, onlookers and young of the brood parasite. Brood parasitism in which host scouts [3]. They all work together in order to gain optimal birds do not behave friendly against intruders, and throw alien solution (find appropriate food source). Employed and eggs away is called nest takeover. On the other hand, less onlooker bees conduct exploitation process by generating aggressive hosts will simply abandon its nest and build a new neighborhood solution of a chosen solution. Solution which nest at other location or will help care for young that are not cannot be improved by employed and onlooker bees within their own, at the expense of their own reproduction. This type certain number of trials are considered to be exhausted and of bird parasitism is known as cooperative breeding. they are abandoned. Abandoned solutions are replaced with Some parasite cuckoo species lay eggs that, to the human randomly generated solutions. This is exploration process and eye, appear to mimic the appearance of the eggs of their it is guided by scout bee. favorite hosts, which hinders discrimination and removal of Besides ABC, there are also other algorithms which their eggs by host species. This cuckoos` feature increases simulate behavior of bees, such as: bee colony optimization their fertility by reducing the probability of their eggs being (BCO) and chaotic bee swarm