# Binary Cockroach Swarm Optimization for Combinatorial Optimization Problem
## 1 Introduction  
Evolutionary Computation (EC) encompasses all population-based algorithms. Algorithms are constructed on a set of multiple solution candidates (which are referred to as a population) and are iteratively refined [1]. EC involves meta-heuristic optimization algorithms whose origins are found in biological systems. One of the classes of EC is Evolutionary Algorithms (EA), which are generic population-based algorithms that make use of biological evolution mechanisms (such as reproduction, mutation, recombination and selection). Examples of EA algorithms includes Genetic Algorithm (GA), which models genetic evolution; Genetic Programming (GP), which is based on GA, but with individual programs represented as trees; Evolutionary Programming (EP), which is derived from the simulation of adaptive behavior in evolution; Evolutionary Strategies (ES), which are geared towards modeling the strategic parameters that control variation in evolution; and Differential Evolution (DE), which is similar to GA, but differs in the reproduction mechanisms used. Another class of EC is the Swarm Intelligence (SI) techniques. This class is population-based, where an individual population is initialized randomly, and each individual represents a potential solution. Individuals are simple agents that follow simple rules that mimic social and cognitive insect and animal behavior moving in search patterns to find optimal. Examples include: particleswarm optimization, which mimics the social behavior of birds [2]; ant colony optimization, which mimics the social behavior of ants [3]; Roach Infestation Optimization (RIO) [4] and Cockroach Swarm Optimization (CSO) [5], which mimic the social foraging behavior of cockroaches. Both EA and SI algorithms belong to the EC family, but use different approaches for searching. Recently, cockroach-based algorithms were introduced into the SI community [4; 5]; cockroach swarm algorithms were shown to be inspired by the emergent social behavior of cockroaches. Cockroaches obtain local information via interaction with peers and the immediate environment, on which their decision making is based. Cockroach habits include: swarming, chasing, dispersing, hungering and ruthlessness. The CSO algorithm that was originally introduced by [PERSON] and [PERSON] [5] and its variants have been shown in the literature including [5; 6; 7; 8; 9; 10; 11] as efficient in solving global optimization problems. According to the literature, the CSO algorithm and variants show competitive results in instances where they were applied to some optimization problems and compared to PSO. The application of CSO reported in the literature include: Solving benchmark functions [5; 6]; [PERSON] et al. applied CSO to the Traveling Salesman Problem (TSP) [7]; and [PERSON] and [PERSON] applied CSO to the Vehicle Routing Problem [8]. Additionally, [PERSON] et al. enhanced the ability of CSO in solving multi-dimensional space function problems by the introduction of the stochastic constriction factor, and this enables the algorithm to avoid explosion in regions outside of the search space. It also enhances local and global searches of the algorithm, even as a cockroach is able to exploit its local neighborhood and explore the whole search region [9]. [PERSON] and [PERSON] presented an Improved Cockroach Swarm Optimization (ICSO) algorithm by introducing a hunger component, which is described by the Partial Differential Equation (PDE) for the migration method [10]. [PERSON] and [PERSON] proposed a cockroach genetic algorithm for estimating the parameters of the biological system in showing a net interactive effect of systems biology (S-system) where cockroach behavior was imitated and embedded into an advanced genetic algorithm to increase exploration and exploitation abilities [11]. Many optimization problems, such as sensor management, routing and scheduling, have their decision variables in a binary format [12].