# Border Collie Optimization (BOC): Algorithm mimicking the Sheep Herding Styles of Border Collie Dogs used for Solving Real World Optimization Problem

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1. Introduction

The Border collie is often considered to be the brightest dog from other breeds that are considered to have higher cognitive skill levels [1]. It is known that dogs, like people, have different levels of intelligence [2]. Intelligence is determined by the ability of the dog to learn, which generally means the ability to associate sounds or motions with objects or actions [3].

2. Inspiration

The herding style of the Border Collie dogs and the ability to judge a situation and to take adaptive decisions has inspired to develop BOC algorithm based on their behavior Border Collies which is the best herding dogs of all time [4]. Border Collies adopt a different approach for herding mainly follow three herding techniques, as demonstrated in Figure below

3. Mathematical Model of Herding Techniques of Border Collie

In Border Collie Optimization, a population of three dogs and sheep is considered [5]. The distance covered and direction of the sheep and dogs are controlled by velocity, acceleration and time. The velocity of all the three dogs is calculated as

3.1 Gathering

The sheep which are nearer to the first dog they are chosen based on their fitness values (F).

G indicates that the sheep is nearer to the first dog. Velocity of the sheep is updated using the following equation

Where  is directly influenced by the velocity of the lead dog at time and  is the present position location of the sheep to be gathered [6].

3.2 Stalking

The equations for the velocity Updation of the stalked sheep are presented below.

3.3 Eyeing

Eyeing is implemented, when in consecutive iterations, the fitness of an individual does not improve the equation is represented as below;

The dog with least fitness is considered because it is assumed that this dog is closest to the sheep. The positions of the sheep are updated using the following equations, when the sheep belong to the gathering and stalking groups [8].

Where  indicates the time required the sheep to move the position. In case of sheep which are eyed, the below mentioned equation is used,

If the fitness of the sheep doesn’t improve in five consecutive steps, the sheep is considered to be stuck in local optima. Then this sheep is eyed by the dog to get it back on track.

4. Systems and methods for Data Driven optimization of Dog

A system for training a dog [9]. The system includes a test for determining a profile of the dog. The system also includes a products database and a training database. The databases are developed by identifying optimum training products and training protocols based on dog profiles [10].

5. Pseudo Code of BOC

6. Detection dog search methods: How to plan and implement an efficient and effective search pattern

Before handling detection dogs on projects, prospective handlers should understand and be able to effectively implement training and handling based on the concepts to be effectively trained in scent detection work [11].The detection dogs must extend into physiological, cultural, legal, and scientifically established domains [12].

7. Advantages of BOC

8. Application of BOC

Reference

[1]P. Bedford, “Collie eye anomaly in the border collie”, Veterinary Record, vol. 111, no. 2, pp. 34-35, 1982. Available: 10.1136/vr.111.2.34.

[2]J. Brooks, “Board on the job: public-pension governance in the United States (US) states”, Journal of Public Policy, vol. 39, no. 1, pp. 1-34, 2017. Available: 10.1017/s0143814x17000241.

[3]S. Mirjalili, S. Mirjalili and A. Lewis, “Grey Wolf Optimizer”, Advances in Engineering Software, vol. 69, pp. 46-61, 2014. Available: 10.1016/j.advengsoft.2013.12.007.

[4]X. Yang, “Review of meta-heuristics and generalized evolutionary walk algorithm”, International Journal of Bio-Inspired Computation, vol. 3, no. 2, p. 77, 2011. Available: 10.1504/ijbic.2011.039907.

[5]A. Ewees, M. Abd Elaziz, M. Al-Qaness, H. Khalil and S. Kim, “Improved Artificial Bee Colony Using Sine-Cosine Algorithm for Multi-Level Thresholding Image Segmentation”, IEEE Access, vol. 8, pp. 26304-26315, 2020. Available: 10.1109/access.2020.2971249.

[6]F. Xie, F. Li, C. Lei, J. Yang and Y. Zhang, “Unsupervised band selection based on artificial bee colony algorithm for hyperspectral image classification”, Applied Soft Computing, vol. 75, pp. 428-440, 2019. Available: 10.1016/j.asoc.2018.11.014.

[7]A. Kaveh and S. Talatahari, “A novel heuristic optimization method: charged system search”, Acta Mechanica, vol. 213, no. 3-4, pp. 267-289, 2010. Available: 10.1007/s00707-009-0270-4.

[8]H. Salimi, “Stochastic Fractal Search: A powerful metaheuristic algorithm”, Knowledge-Based Systems, vol. 75, pp. 1-18, 2015. Available: 10.1016/j.knosys.2014.07.025.

[9]X. Chen, Y. Liu, X. Li, Z. Wang, S. Wang and C. Gao, “A New Evolutionary Multiobjective Model for Traveling Salesman Problem”, IEEE Access, vol. 7, pp. 66964-66979, 2019. Available: 10.1109/access.2019.2917838.

[10]Zong Woo Geem, Joong Hoon Kim and G. Loganathan, “A New Heuristic Optimization Algorithm: Harmony Search”, SIMULATION, vol. 76, no. 2, pp. 60-68, 2001. Available: 10.1177/003754970107600201.

[11]D. Karaboga and B. Basturk, “A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm”, Journal of Global Optimization, vol. 39, no. 3, pp. 459-471, 2007. Available: 10.1007/s10898-007-9149-x.

[12]J. Bansal, H. Sharma, S. Jadon and M. Clerc, “Spider Monkey Optimization algorithm for numerical optimization”, Memetic Computing, vol. 6, no. 1, pp. 31-47, 2014. Available: 10.1007/s12293-013-0128-0.

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