**1. Introduction**

A novel bio-inspired metaheuristic algorithm, named as Tunicate Swarm Algorithm, is simplified for optimizing non-linear constrained problems [1]. It is inspired by the swarm behavior of tunicate to survive successfully find the location of food source in the depth of ocean [2]. This fact has motivated to develop a new population based metaheuristic algorithm with the hope to solve several problems which are hard to solve with existing optimization techniques [3]. The results demonstrate that TSA generates better optimal solutions in comparison to other competitive algorithms and is capable of solving real case studies having unknown search spaces.

**2. Foraging behavior of Tunicate**

The fundamental inspiration of this algorithm includes jet propulsion and swarm behaviors of the tunicate. Thus the tunicate is associated with two foraging behavior they are as follows;

**Jet Propulsion:**Jet propulsion is the propulsion by the backward ejection of a high-speed jet of gas or liquid.**Swarm intelligence:**Swarm intelligence (SI) is the collective behavior of decentralized, self-organized systems, natural or artificial.

**3. Structure of Tunicate**

Tunicates are cylindrical-shaped which are open at one end and closed at the other each tunicate is a few millimeters in size. Tunicates commonly called sea squirts are a group of marine animals that spend most of their lives attached to docks, rocks or the undersides of boats [3]. They look like small colored blobs and it is built like a barrel. Most tunicates live with the posterior or lower end of the barrel attached firmly to a fixed object and have two openings projecting from the other. Tunicates are plankton feeders [4]. They live by drawing seawater through their bodies. Water enters the oral siphon, passes through a sieve- like structure, the branchial basket that traps food particles and oxygen.

**4. Inspiration of TSA**

Tunicate has an ability to find the location of food source in sea. Two behaviors of tunicate are employed for finding the food source those behaviors are jet propulsion and swarm intelligence there is a common gelatinous tunic in each tunicate which is helpful to join all of the individuals [5]. However, each tunicate individually draws water from the surrounding sea and producing jet propulsion by its open end through atrial siphons. Tunicate is only animal to move around the ocean with such fluid jet like propulsion. This propulsion is powerful to migrate the tunicates vertically in ocean [6]. Tunicates are often found at depth of 500–800 m and migrate upwards in the upper layer of surface water at night. The size of a tunicate varies from a few centimeters to more than 4m .The most interesting fact of tunicate is their jet propulsion and swarm behaviors which is the main motivation of the tunicate swarm algorithm.

**5. Mathematical Model and optimization of TSA**

When the swarm behavior will update the positions of other search agents about the best optimal solution. The mathematical modeling of this behavior is described as below;

Where Q_{ min }and Q_{ max} are the maximum and minimum speed to make social interaction between the tunicate each other [7]. After avoiding the conflict between neighbours the search agents are move towards the direction of best neighbour.

TSA requires the time complexity for the jet propulsion and swarm behavior for better exploration and exploitation. Hence the total time complexity of TSA algorithm is defined as

TSA = O (Max_{ iterations} * n* d * N) (8)

Where n defines the population size, d defines the dimension and N defines the jet propulsion and swarm behaviors of tunicate for the best optimum food source.

**6. Advantages of TSA**

**7. Flowchart of TSA**

**8. Pseudo code of TSA**

**9. Application of TSA**

TSA algorithm is tested on constrained and unconstrained engineering design problems. They are as follow below;

- Pressure vessel design problem [8]
- Welded beam design problem [9].
- Tension/ compression spring design problem [10].
- 25-bar truss design problem [11].
- Displacement of loaded structure design problem [12].
- Rolling element bearing design problem [13].

**Reference**

[1]. Esslinger T (1978) Studies in the Lichen Family Physciaceae. IV. Awasthia, a New Genus from the Himalayas. The Bryologist 81:445. Doi: 10.2307/3242252

[2]. Alba E, Dorronsoro B (2005) The Exploration/Exploitation Tradeoff in Dynamic Cellular Genetic Algorithms. IEEE Transactions on Evolutionary Computation 9:126-142. doi: 10.1109/tevc.2005.843751

[3]. Berrill N (1950) Budding and development in Salpa. Journal of Morphology 87:553-606. doi: 10.1002/jmor.1050870308

[4]. Camp C, Bichon B (2004) Design of Space Trusses Using Ant Colony Optimization. Journal of Structural Engineering 130:741-751. doi: 10.1061/(asce)0733-9445(2004)130:5(741)

[5]. Yue C, Liang J, Lang B, Qu B (2017) Two-hidden-layer extreme learning machine based wrist vein recognition system. Big Data & Information Analytics 2:59-68. doi: 10.3934/bdia.2017008

[6]. Brest J, Bošković B, Greiner S et al. (2006) Performance comparison of self-adaptive and adaptive differential evolution algorithms. Soft Computing 11:617-629. doi: 10.1007/s00500-006-0124-0

[7]. DEHGHANİ M, MONTAZERİ Z, DEHGHANİ A, MALİK O (2020) GO: Group Optimization. GAZI UNIVERSITY JOURNAL OF SCIENCE 33:381-392. doi: 10.35378/gujs.567472

[8]. Dhiman S, Kumar A, Dhiman M (2016) COMPARATIVE STUDY OF KUMARI SWARASA AND KANYASARA IN THE MANAGEMENT OF KASHTARTAVA. International Journal of Research in Ayurveda & Pharmacy 7:36-39. doi: 10.7897/2277-4343.075191

[9]. Dhiman G, Guo S, Kaur S (2018) ED-SHO: A framework for solving nonlinear economic load power dispatch problem using spotted hyena optimizer. Modern Physics Letters A 33:1850239. doi: 10.1142/s0217732318502395

[10]. Kaur N, Kaur J, Dhiman A (2018) Embodying Identity Experienced By Breast Cancer Patients Survivals Undergoing Chemotherapy . Nursing and Midwifery Research Journal, doi: 10.33698/nrf0234

[11]. Dhiman G, Garg M (2020) MoSSE: a novel hybrid multi-objective meta-heuristic algorithm for engineering design problems. Soft Computing. doi: 10.1007/s00500-020-05046-9

[12]. Dhiman G (2019) MOSHEPO: a hybrid multi-objective approach to solve economic load dispatch and micro grid problems. Applied Intelligence 50:119-137. doi: 10.1007/s10489-019-01522-4

[13]. Dhiman G, Kumar V (2019) Seagull optimization algorithm: Theory and its applications for large-scale industrial engineering problems. Knowledge-Based Systems 165:169-196. doi: 10.1016/j.knosys.2018.11.024

👍