Tunicate Swarm Algorithm: A new bio-inspired based metaheuristic paradigm for global optimization

https://doi.org/10.1016/j.engappai.2020.103541Get rights and content

Abstract

This paper introduces a bio-inspired metaheuristic optimization algorithm named Tunicate Swarm Algorithm (TSA). The proposed algorithm imitates jet propulsion and swarm behaviors of tunicates during the navigation and foraging process. The performance of TSA is evaluated on seventy-four benchmark test problems employing sensitivity, convergence and scalability analysis along with ANOVA test. The efficacy of this algorithm is further compared with several well-regarded metaheuristic approaches based on the generated optimal solutions. In addition, we also executed the proposed algorithm on six constrained and one unconstrained engineering design problems to further verify its robustness. The simulation 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.

Note that the source codes of the proposed TSA algorithm are available at

Introduction

To minimize or maximize a function in terms of decision variables, optimization approach plays a significant role. Many real-life problems have a large number of solution spaces, which consists of non-linear constraints. Such problems also have high computational cost along with non-convex and complicated in nature (Singh and Dhiman, 2018a, Dhiman and Kumar, 2018c, Singh and Dhiman, 2018b, Dhiman and Kaur, 2018, Singh et al., 2018b, Dhiman and Kumar, 2018a, Kaur et al., 2018, Singh et al., 2018a). Hence, for solving such problems in terms of large number of variables and constraints are very complicated tasks. Further, local optimum solutions as obtained from various classical approaches do not guarantee for the best solution. To resolve these issues, numerous metaheuristic optimization algorithms are proposed by the researchers (Dhiman et al., 2018, Dhiman and Kumar, 2019b, Dhiman and Kaur, 2019b, Dhiman and Kumar, 2019a, Dhiman et al., 2019, Dhiman, 2019c), which are found to be very efficient for solving very complex problems. However, researchers have given more emphasize in developing of metaheuristic algorithms that are computationally inexpensive, flexible, and simple by nature.

In literature, two broad categories of metaheuristics algorithms are discussed, as single solution based algorithm (SSBA) and population based algorithm (PBA) (Dhiman and Kumar, 2017). In SSBA, a solution is randomly generated and improved until the optimal solution is obtained; whereas in case of PBA, solutions are randomly evolved in a given search space and try to improve until the optimal solution is obtained. However, most of the SSBAs are unable to reach at the level of global optimum solution due the reason of generating random solution. On the other hand, PBAs are able to find the global optimum. Due to this reason, researchers have attracted towards the PBAs nowadays (Singh et al., 2019, Dhiman, 2019a, Dhiman, 2019b, Dehghani et al., 2019, Chandrawat et al., 2017, Singh and Dhiman, 2017, Dhiman and Kaur, 2017, Verma et al., 2018, Kaur and Dhiman, 2019, Dhiman and Kaur, 2019a, Dhiman and Kumar, 2019c, Garg and Dhiman, 2020).

Further PBAs are categorized, based on the theory of evolutionary algorithms (EAs), as logical behavior of physics algorithms, swarm intelligence of particles, and biological behavior of bio-inspired algorithms. Various EAs are motivated by natural processes, which include reproduction, mutation, recombination, and selection. The survival fitness of candidate in a population (i.e., a set of solutions) is the main basis of all these EAs. Algorithms that are based on the law of physics include the various rules of physics, such as electromagnetic force, gravitational force, heating and cooling of materials, and force of inertia. Algorithms that are biologically inspired mostly mimics the intelligence of swarms. Such kind of intelligence can be adopted among colonies of flocks, ants, and so on. Swarm intelligence based algorithms are very popular among the researchers due to its ease of implementation. Its also requires very less number of parameters to be adjusted. Among this category of algorithms, Particle Swarm Optimization (PSO) (Kennedy and Eberhart, 1995) and Ant Colony Optimization (ACO) (Dorigo et al., 2006) are very well-known techniques for the global optimization problems. These kind of algorithms generally mimics the social behavior of fish schooling or bird flocking, where it is assumed that each particle moves around the search space and continuous update its current position w.r.t. the global position until satisfactory solution is found.

Optimization algorithms always requires to focus on exploration and exploitation of a search space (Alba and Dorronsoro, 2005) by maintaining good balancing between them. The exploration process in an algorithm investigates the various promising regions in a search space; whereas exploitation process searches the best solutions over the promising regions (Lozano and Garcia-Martinez, 2010). Hence, to achieve the optimal solutions or near to optimal solutions, these two processes are required to be tuned enough. Having availability of large number of such optimization algorithms, there is always a question raise for the requirement of development of more optimization algorithms. Its answer lies in No Free Lunch (NFL) theorem (Wolpert and Macready, 1997), which suggests that a specific optimization algorithm does not solve every problem, because every problem has its own complexity and nature. The NFL theorem inspires the researchers to design some new optimization algorithms, which can solve various domain of specific problems.

In this study, authors introduce a novel bio-inspired metaheuristic algorithm, named as Tunicate Swarm Algorithm (TSA), is proposed for optimizing non-linear constrained problems. It is inspired by the swarm behavior of tunicate to survive successfully in the depth of ocean. The main contributions of this work are as follows:

  • A bio-inspired tunicate swarm algorithm (TSA) is proposed. The jet propulsion and swarm behaviors of tunicates are examined and mathematically modeled.

  • The proposed TSA is implemented and tested on 74 benchmark test functions (i.e., classical, CEC-2015, and CEC-2017).

  • The performance of the proposed TSA algorithm is compared with state-of-the-art metaheuristics.

  • The efficiency of TSA algorithm is examined for solving the engineering design problems.

The rest of this paper is organized as follows: Section 2 presents the main inspiration and justification of the proposed algorithm. The proposed TSA algorithm is described in Section 3. The experimentation and simulations are presented in Section 4. Section 5 describes the applications of TSA on real-life engineering problems. Finally, the conclusion and future work is given in Section 6.

Section snippets

Inspiration

Tunicates are bright bio-luminescent, producing a pale blue–green light that can be seen more than many metres away. Tunicates are cylindrical-shaped which are open at one end and closed at the other (Berrill, 1950). Each tunicate is a few millimeters in size. There is a common gelatinous tunic in each tunicate which is helpful to join all of the individuals. However, each tunicate individually draws water from the surrounding sea and producing jet propulsion by its open end through atrial

Tunicate swarm algorithm (TSA)

In this section, the inspiration and mathematical modeling of the proposed algorithm are described in detail.

Experimental results and discussions

This section describes the simulation and experimentation of TSA on seventy-four standard benchmark test functions. The detailed description of these benchmark test functions are discussed below. Further, the results are analyzed and compared with well-known metaheuristics.

TSA for engineering design problems

TSA algorithm is tested on six constrained and one unconstrained engineering design problems. These problems are pressure vessel, speed reducer, welded beam, tension/compression spring, 25-bar truss, rolling element bearing, and displacement of loaded structure.

Conclusion and future scope

In this paper, we presented a bio-inspired based bio-inspired metaheuristic algorithm called Tunicate Swarm Algorithm (TSA). The fundamental inspiration of this algorithm includes the jet propulsion and swarm behaviors of tunicate. The proposed algorithm is experimented on a set of seventy-four benchmark test functions belonging to classical, CEC-2015 and CEC-2017 test suite. The statistical results proved the effectiveness of TSA towards attaining global optimal solutions having better

CRediT authorship contribution statement

Satnam Kaur conceptualize the data and write the paper, Lalit K. Awasthi proposed the methodology, A.L. Sangal simulate the software, and Gaurav Dhiman investigate the proposed algorithm.

Acknowledgment

The corresponding author, Dr. Gaurav Dhiman, would like to thanks to the goddess SHRI MATA VAISHNO DEVI for her divine blessings on him.

References (55)

  • MirjaliliS. et al.

    Grey wolf optimizer

    Adv. Eng. Softw.

    (2014)
  • RashediE. et al.

    GSA: A gravitational search algorithm

    Inf. Sci.

    (2009)
  • SinghP. et al.

    A hybrid fuzzy time series forecasting model based on granular computing and bio-inspired optimization approaches

    J. Comput. Sci.

    (2018)
  • SinghP. et al.

    Uncertainty representation using fuzzy-entropy approach: Special application in remotely sensed high-resolution satellite images (rshrsis)

    Appl. Soft Comput.

    (2018)
  • AlbaE. et al.

    The exploration/exploitation tradeoff in dynamic cellular genetic algorithms

    IEEE Trans. Evol. Comput.

    (2005)
  • AwadN. et al.

    Problem Definitions and Evaluation Criteria for the Cec 2017 Special Session and Competition on Single Objective Bound Constrained Real-Parameter Numerical OptimizationTechnical Report

    (2016)
  • BerrillJ.

    The Tuniccafa

    (1950)
  • BichonC.V.C.B.J.

    Design of space trusses using ant colony optimization

    J. Struct. Eng.

    (2004)
  • BrestJ. et al.

    Single objective real-parameter optimization: algorithm jso

  • ChandrawatR.K. et al.

    An analysis of modeling and optimization production cost through fuzzy linear programming problem with symmetric and right angle triangular fuzzy number

  • ChenQ. et al.

    Problem Definitions and Evaluation Criteria for Cec 2015 Special Session on Bound Constrained Single-Objective Computationally Expensive Numerical OptimizationTechnical Report

    (2014)
  • DavenportJ. et al.

    ’fiery bodies’ - are pyrosomas an important component of the diet of leatherback turtles?

    Br. Herpetol. Soc. Bull.

    (1991)
  • DehghaniM. et al.

    Bosa: Binary orientation search algorithm

    Int. J. Innov. Technol. Explor. Eng.

    (2019)
  • DhimanG.

    Esa: a hybrid bio-inspired metaheuristic optimization approach for engineering problems

    Eng. Comput.

    (2019)
  • DhimanG.

    Multi-Objective Metaheuristic Approaches for Data Clustering in Engineering Application (S)

    (2019)
  • DhimanG.

    Moshepo: a hybrid multi-objective approach to solve economic load dispatch and micro grid problems

    Appl. Intell.

    (2019)
  • DhimanG. et al.

    Ed-sho: A framework for solving nonlinear economic load power dispatch problem using spotted hyena optimizer

    Modern Phys. Lett. A

    (2018)
  • Cited by (795)

    View all citing articles on Scopus

    No author associated with this paper has disclosed any potential or pertinent conflicts which may be perceived to have impending conflict with this work. For full disclosure statements refer to https://doi.org/10.1016/j.engappai.2020.103541.

    View full text