**Introduction**

The bear smell search algorithm (BSSA) imitates both dynamic behaviors of bear based on sense of smell mechanism and the way bear moves in the search of food in thousand miles farther. According to the comprehensive study of animal’s behavior and their senses in nature it can be concluded that the bear’s sense of smell is stronger than other available intrinsic senses in nature [1]. Bear is one of the most well-known and superior hunter in the nature. Bear’s olfactory bulb is several times larger than other animals, while its main task is sending of smell information from the nose to the brain. The reason of this the Bear’s ability to find the prey in a short time based on its strong smell sense in a large search space [2]. Since bears cannot see food at far distances, the mathematical model based on the sense of smell suggests a powerful way to ﬁnd the targeted. The olfactory and neuron behavior of smell mechanism is evaluated and modeled mathematically

The BSSA algorithm is evaluated on many benchmark functions to show its performance on different types of local and global search spaces. Generally, various problems like economics, engineering, etc. have some important control variables so that their proper value directly affects on system output [3]. For that reason, the exact setting and getting a proper solution require an expert designer while it may be boring, time-consuming and progression details. As a result, it is reasonable to convert them as an optimization model that they can solve by the intelligence algorithms. In the Bear smell search algorithm the classical methods are used a linear structure with a smooth form to ﬁnd the best solution.

**2. Inspiration of BSSA**

The Bear smell search algorithm was developed based on the hunting ability of bears to use their smell sense. Among all animals, bears have inconceivable sense of smell due to their huge olfactory bulbs that manage the sense of different odors. Since the olfactory bulb is a neural model of the vertebrate forebrain, it can make a strong exploration and exploitation for optimization [4]. According to the odors value, bear moves the next location. Therefore, this algorithm is to predict the quality of an odor from a set of odorant components taking into account, their interaction is a difficult problem, while it is easily done by bear’s sense of smell mechanism which finds its inspiration from the superior hunting behavior of bears and their ability to sense the odor of prey even from miles away. To demonstrate and evaluate the BSSA ability, numerous types of benchmark functions and four engineering problems such as iteration, overlapping, decomposition and integration, and convergence are employed to compare the obtained results of BSSA with other available optimization methods with several analyzed indices such as pair-wise test and the statistical analysis. The numerical results revealed that BSSA presents competitive and greater results compared to other optimization algorithms.

**3. Bear Smell Search Algorithm (BSSA)**

Bears are thought to have the most robust sense of smell of any animal on earth. A bear’s sense of smell is 7 times better than a blood hounds or 2,100 times better than a human. Bears acute sense of smell evolved in order to help them find food, mates, keep track of their cubs and avoid danger, particularly between competing individuals. Except for mother bears, bears are territorial animals that need to range widely to find enough food to sustain themselves. A bear’s sense of smell is so acute that they can detect animal carcasses upwind and from a distance of 20 miles away [5]. Bears have an incredible sense of smell because the area of their brain that manages the sense of smell, called the olfactory bulb is at least 5 times larger than the same area in human brains even though a bear’s brain is one third the size. Bears also have highly developed noses that contain hundred of tiny muscles and let them manipulate them with the same dexterity as people’s fingers. The surface area inside their 9 inch noses also has hundreds of times more surface area and receptors than a human’s.

This algorithm is based on the ability of bear, as a superior hunter in the nature, for finding prey, which is taken from the smell sense of bear and its movement to the odor source. Various behaviors of bear within the search environment are mathematically modeled within the optimization approach [6]. The effectiveness of the algorithm will continue with large steps in order to enhance the search ability and for the last stage (when the algorithm approaches the optimal solution) the steps will be smaller to increase the resolution of search around the optimal solution.

According to the review, the bear has the best sense of smell of all terrestrial mammals. Black bears have been observed to travel 18 miles in a straight line to a food source, while grizzlies can find a carcass when it’s underwater and polar bears can smell a seal through 3 feet of ice. At ﬁrst, suppose that bear’s nose absorbed different odors so that each one shows a position for moving because everything has a special smell in the environment. Note that many of them are named as the local solution. The particular odor of desired food is the ﬁnal solution [7]. In facts, the olfactory bulb is main part of this process. Since bears have the larger olfactory bulb compared to other organisms, it makes the great smell of sense. The olfactory bulb receives odor and transmits their information by olfactory tract to the brain [8]. Also, it has the simplest structure between all of the senses causing the simplicity of its cortical model, its signal-processing role and its initial condition phylogenetically. Note that this is a positive point in the BSSA algorithm

Olfactory search strategies are interesting because of their relevance to animal behavior. Here we analyze the statistical physics aspects of the problem and propose an efficient strategy for olfactory search. The algorithm combines the maximum likelihood inference of the source position with an active search. Our approach provides the theoretical basis for the design of olfactory robots and the quantitative tools for the analysis of the observed olfactory search behavior of bears.

Bears in each position moves with the speed toward stronger odor particles to become closer to the prey [9]. Thus, corresponding to the position, where each speed vector has components in each dimension as;

P= P^{1}_{, }P^{2 }, P^{3} …Piwhere i= 1, 2, 3 …n (1)

Bear follows the odor and direction of prey movement is adjusted based on the odor intensity. Also, by increasing the concentration of the odors, the speed of bear increases. From optimization viewpoint, we can mathematically model this type of movement that should be maximized, illustrating the direction that the objective function increases by the highest rate:

Where OF is the Objective function of indicating prey smell, is the speed of bear corresponding to the odor sense of smell and is the time interval if , for each components then t= {1< i< n}.The particular odor of desired food is the ﬁnal solution and considered as the global solution[10]. Since bear receives n odors in breathing time, the initial breathing function of cycle, denote the odor components. Based on this the mathematic formulation as

Where exhale, inhale are a constant value for the inhalation and exhalation time, respectively. In the optimization process, the overall time of a cycle of breathing is the same of odor and according to exhalation and inhalation times.

To conclude, we have proposed an olfactory search algorithm designed to function of turbulent prey. The efficiency of the BSSA algorithm derives from the implemented strategy, which resembles the observed olfactory search behavior of moths [11]. These results clearly show that the BSSA has better convergence with least iteration. It can be obvious that BSSA is a fast and reliable algorithm even if it was not successful in a few indices. In contrast, the BSSA method can ﬁnd better and actual solution well and fast, while other methods still have a signiﬁcance gap to the actual solution [12].

**5. Flowchart of BSSA**

**6. BSS Algorithm**

**7. Application of BSSA**

- Statistical Analysis [16].
- Power System [17].
- Process Control [18].
- Engineering Design Problem [19].
- Load Frequency Control [20].

**8. Advantages of BSSA**

- Performed in time varying control parameters [13].
- Obtaining the simple and efficient model.
- Investigated for four engineering problems [14].
- Comparative study is done using statistical analysis and convergence rate analysis [15].
- Analysis for the glomercular activity.
- Better convergence with least iteration.

**Reference**

[1] Ghasemi-Marzbali A (2020) A novel nature-inspired meta-heuristic algorithm for optimization: bear smell search algorithm. Soft Computing. doi: 10.1007/s00500-020-04721-1

[2] Gromiha M, Harini K, Sowdhamini R, Fukui K (2012) Relationship between amino acid properties and functional parameters in olfactory receptors and discrimination of mutants with enhanced specificity. BMC Bioinformatics. doi: 10.1186/1471-2105-13-s7-s1

[3] Nagel KI (2018) Elementary sensory-motor transformations underlying olfactory navigation in walking fruit-flies. E Life 7:e37815. doi:10.7554/eLife.37815 pmid: 30129438

[4] Wilson RI (2016) Behavior reveals selective summation and max pooling among olfactory processing channels. Neuron 91:425–438. doi:10.1016/j.neuron.2016.06.011 pmid: 27373835

[5] Shraiman BI (2002) olfactory search at high Reynolds number. Proc Natl Acad Sci U S A 99:12589–12593. doi:10.1073/pnas.192393499 pmid: 12228727

[6]Sirohi R, Singh A, Tarafdar A, Shahi NC (2018) Application of genetic algorithm in modeling and optimization of cellulase production. Biores Technol 270:751–754

[7] Atema J(1996) Eddy chemo taxis and odor landscapes: exploration of nature with animal sensors. Biol Bull 191:129–138. doi: 10.2307/1543074 pmid: 29220222

[8] Abedinia O, Amjady N, Shayanfar HA, Ghasemi A (2012) Optimal congest management based VEPSO on electricity market. Int J Tech Phys Probl Eng (IJTPE) 4(2):56–62

[9] Yamazaki K, Beauchamp GK, Singer A, Bard J, Boyse EA (1999) Odor types: their origin and composition. Proc Natl Acad Sci USA 96(4):1522–1525

[10] Bansal JC, Gopal A, Nagar AK (2018) Stability analysis of artificial bee colony optimization algorithm. Swarm Evolut Comput 41:9–19

[11] Dillon JS, Dhillon JS, Kothari DP (2009) Economic-emission load dispatch using binary successive approximation-based evolutionary search. IET Gener Transm Distrib 3

[12].Baker TC (1990) upwind flight and casting flight: complementary phasic and tonic systems used for location of sex pheromone sources by male moth. In Proceedings of the 10th International Symposium on Olfaction and Taste (Døving ED, ed), pp 18–25. Oslo: Graphic Communication System.

[13]Alimoradi MR, Kashan AH (2018) a league championship algorithm equipped with network structure and backward Q-learning for extracting stock trading rules. Appl Soft Comput 68:478–493

[14]Cerdà V, Cerdà JL, Idris AM (2016) Optimization using the gradient and simplex methods. Talanta 148:641–648

[15] Chuanwen J, Yuchao M, Chengmin W (2006) PID controller parameters optimization of hydro-turbine governing systems using deterministic-chaotic-mutation evolutionary programming (DCMEP). Energy Convers Manag 47(9–10):1222–1230

[14] Dos Santos Júnior JG, do MonteLima JPS (2018) Particle swarm optimization for 3D object tracking in RGB-D images. Comput Graph 78:167–180

[16] García S, Molina D, Lozano M, Herrera F (2009) A study on the use of non-parametric tests for analyzing the evolutionary algorithms’ behavior: a case study on the CEC’2005 Special Session on Real Parameter Optimization. J Heuristics 15:617

[17] Ghasemi A (2013) A fuzzified multi objective interactive honey bee mating optimization for environmental economic power dispatch with valve point effect. Int J Electr Power Energy Syst 49:308–321

[18] Rashedi E, Rashedi E, Nezamabadi-pour H (2018) A comprehensive survey on gravitational search algorithm. Swarm Evolut Comput 41:141–158

[19] Shayeghi H, Ghasemi A (2012) optimal design of power system stabilizer using improved ABC algorithm. Int J Tech Phys Probl Eng (IJTPE) 4(3):24–31

[20] Valipour K, Ghasemi A (2017) Using a new modified harmony search algorithm to solve multi-objective reactive power dispatch in deterministic and stochastic models. J Artif Intell Data Min 5(1):89–100