A new optimization method based on COOT bird natural life model

https://doi.org/10.1016/j.eswa.2021.115352Get rights and content

Highlights

  • Optimization based COOT bird movements on the water surface.

  • Designing Coot bird's movement search algorithm.

  • A new meta-heuristic algorithm for constraint problems.

  • Solving some engineering problems by the proposed algorithm.

Abstract

Recently, many intelligent algorithms have been proposed to find the best solution for complex engineering problems. These algorithms can search volatile and multi-dimensional solution spaces and find optimal answers timely. In this paper, a new meta-heuristic method is proposed that inspires the behavior of the swarm of birds called Coot. The Coot algorithm imitates two different modes of movement of birds on the water surface: in the first phase, the movement of birds is irregular, and in the second phase, the movements are regular. The swarm moves towards a group of leading leaders to reach a food supply; the movement of the end of the swarm is in the form of a chain of coots, each of coot which moves behind its front coots. The algorithm then runs on a number of test functions, and the results are compared with well-known optimization algorithms. In addition, to solve several real problems, such as Tension/Compression spring, Pressure vessel design, Welded Beam Design, Multi-plate disc clutch brake, Step-cone pulley problem, Cantilever beam design, reducer design problem, and Rolling element bearing problem this algorithm is used to confirm the applicability of this algorithm. The results show that this algorithm is capable to outperform most of the other optimization methods. The source code is currently available for public from: https://www.mathworks.com/matlabcentral/fileexchange/89102-coot-optimization-algorithm.

Introduction

Optimization is the process of finding the best answer or the global optimal point for a problem. In optimizing the problems, the optimal global point is the minimum or maximum value of a function. Optimization issues can be found in all fields of study, which makes optimization techniques an essential and important direction of study for researchers. The meta-heuristic algorithms are a kind of random algorithms which used to find an optimal response. Optimization methods and algorithms are categorized into two groups of exact algorithms and approximate algorithms. Exact algorithms are capable of finding the optimal answer in a precise manner, but they are not efficient enough for strict optimization problems and their execution time expands exponentially with the dimensions of the problems. Approximate algorithms are capable of finding good (near optimal) solutions at a short time for strict optimization problems. Approximate algorithms are divided into three categories: heuristic algorithms, meta-heuristic and hyper heuristic algorithms. The two main problems are the innovative algorithms, catching them at the local optimum points and early convergence into these points. Meta-heuristic algorithms to solve the deficit heuristic algorithms have been proposed (Spall, 2005). In fact, meta-heuristic algorithms are one of a kind of approximate optimization algorithms that have solutions for Escape from Local Optimum points and can be applied to a wide range of problems. Various categories of these algorithms have been developed in recent decades (Mahdavi et al., 2015). The capabilities of the meta-heuristic processes can be a simple, flexible, non-inference mechanism and avoid local optimums. Meta-heuristic processes are inspired by physical phenomena, animal behavior, evolutionary concepts, and human phenomena. A category of known algorithms is presented in Fig. 1. Many articles have tried to classify optimization algorithms based on their inspiration (Ertenlice and Kalayci, 2018, Hussain et al., 2018, Sotoudeh-Anvari and Hafezalkotob, 2018).

An important question arises here, when there are famous algorithms such as those mentioned above, what is needed to offer and present new algorithms. According to the NFL theorem (Blum and Roli, 2003, Wolpert and Macready, 1997), there is no optimization algorithm that can solve all optimization problems. In fact, the average performance of the optimizers is almost the same. So there are a lot of problems that are not still well solved notwithstanding the popular optimization algorithms, and offering new algorithms can solve such problems. This is the motivation of the creation of a new bird collective-behavioral based optimization algorithm called Coot to compete with current algorithms in solving problems. In this paper, a new meta-heuristic algorithm is introduced that imitates the movements of the COOT on the water.

The rest of the paper is organized as follows: Section 2 presents a literature review of previous meta-heuristic algorithms. Section 3 describes the proposed COOT algorithm. The results and discussion of the proposed algorithm, benchmark functions, and real problems are presented in Sections 4–5. Finally, Section 6 concludes this article and offers suggestions for future work.

Section snippets

Related works

In recent years, optimization has become a popular research field and an economical way to find an optimal solution to complex problems. According to Fig. 1, we have divided the optimization algorithms into four categories based on the type of inspiration: Swarm Based Algorithms, which include Particle Swarm Optimization (PSO) (Eberhart & Kennedy, 2002), Firefly Algorithm (FFA) (X.-S. Yang, 2010), Ant Colony Optimization (ACO) (Colorni et al., 1991), Artificial Bee Colony (ABC) (Basturk &

Description

the Coots are small water birds that are members of the rail family, Rallidae. They constitute the genus Fulica, the name being the Latin for “coot” (Paillisson & Marion, 2001). Coots have prominent frontal shields or other decoration on the forehead, with red to dark red eyes and colored bills. Many, but not all, have white on the under the tail. The literature on American coot behavior includes extensive work on breeding, habitat and migratory behavior (Randler, 2005, Varo and Amat, 2008,

COOT algorithm performance on the classical functions

In this section, the COOT algorithm is evaluated in 13 criteria functions (with 30, 100, and 500 dimention). These are classical functions that have been used by many researchers (Mirjalili, 2016, Saremi et al., 2017). We selected these test functions to compare our results with the results of the current meta-heuristic algorithms. These standard functions are shown in Table 1, Table 2, where Dim represents the function dimensions, Range is the boundary of the search space of the function, and

The function of the COOT algorithm on engineering problems

There are eight limited problems in engineering design used by many researchers: Tension/compression spring, welded beam, pressure vessel designs, Multi-plate disc clutch brake, Step-cone pulley problem, Cantilever beam design, reducer design problem, Rolling element bearing problem. These problems have several constraints of equality and inequality, so the COOT algorithm must be equipped with a constraint control method so that it can also optimize constraint problems. The results of COOT is

Conclusion

In this paper, a new swarm-based optimization algorithm was suggested that inspired regular and irregular movements of birds called Coot on the surface of the water. Unique features such as swarm leadership by a leading group and chain movement at the end of the swarm are the main motive for creating this optimization algorithm. In order to evaluate the algorithm in terms of exploration and exploitation, 13 test functions (with 30, 100, and 500 dimention) including 7 single-modal test functions

CRediT authorship contribution statement

Iraj Naruei: Investigation, Validation, Writing - original draft. Farshid Keynia: Conceptualization, Data curation, Methodology, Supervision, Writing - review & editing.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Iraj Naruei born in Zahedan, Iran in 1986. He received his B.Sc. in computer engineering from Hatef University in 2010 and his M.Sc. in software engineering from the Islamic azad University of Zahedan Branch in 2010. Since September 2017, he has been working on his Ph.D. degree at the University of Kerman in software engineering. His current major research areas include Optimization Algorithms and Soft Computing.

References (90)

  • H. Eskandar et al.

    Water cycle algorithm – A novel metaheuristic optimization method for solving constrained engineering optimization problems

    Computers & Structures

    (2012)
  • A.A. Ewees et al.

    Improved grasshopper optimization algorithm using opposition-based learning

    Expert Systems with Applications

    (2018)
  • A.H. Gandomi et al.

    Krill herd: A new bio-inspired optimization algorithm

    Communications in Nonlinear Science and Numerical Simulation

    (2012)
  • N. Ghorbani et al.

    Exchange market algorithm

    Applied Soft Computing

    (2014)
  • S. Gupta et al.

    Multi-objective design optimisation of rolling bearings using genetic algorithms

    Mechanism and Machine Theory

    (2007)
  • X. Han et al.

    Novel fruit fly optimization algorithm with trend search and co-evolution

    Knowledge-Based Systems

    (2018)
  • A. Hatamlou

    Black hole: A new heuristic optimization approach for data clustering

    Information Sciences

    (2013)
  • Q. He et al.

    An effective co-evolutionary particle swarm optimization for constrained engineering design problems

    Engineering Applications of Artificial Intelligence

    (2007)
  • A.A. Heidari et al.

    Harris hawks optimization: Algorithm and applications

    Future Generation Computer Systems

    (2019)
  • E.H. Houssein et al.

    Lévy flight distribution: A new metaheuristic algorithm for solving engineering optimization problems

    Engineering Applications of Artificial Intelligence

    (2020)
  • F. Huang et al.

    An effective co-evolutionary differential evolution for constrained optimization

    Applied Mathematics and Computation

    (2007)
  • M. Jaderyan et al.

    Virulence optimization algorithm

    Applied Soft Computing

    (2016)
  • M. Jahangiri et al.

    Interactive autodidactic school: A new metaheuristic optimization algorithm for solving mathematical and structural design optimization problems

    Computers & Structures

    (2020)
  • S. Kaur et al.

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

    Engineering Applications of Artificial Intelligence

    (2020)
  • A. Kaveh et al.

    Water evaporation optimization: A novel physically inspired optimization algorithm

    Computers & Structures

    (2016)
  • A. Kaveh et al.

    A novel meta-heuristic optimization algorithm: Thermal exchange optimization

    Advances in Engineering Software

    (2017)
  • A. Kaveh et al.

    A new meta-heuristic method: Ray optimization

    Computers & Structures

    (2012)
  • K.S. Lee et al.

    A new structural optimization method based on the harmony search algorithm

    Computers & Structures

    (2004)
  • P. Liu et al.

    Multi-leader PSO (MLPSO): A new PSO variant for solving global optimization problems

    Applied Soft Computing

    (2017)
  • S. Mahdavi et al.

    Metaheuristics in large-scale global continues optimization: A survey

    Information Sciences

    (2015)
  • D. Manjarres et al.

    A survey on applications of the harmony search algorithm

    Engineering Applications of Artificial Intelligence

    (2013)
  • S. Mirjalili

    Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm

    Knowledge-Based Systems

    (2015)
  • S. Mirjalili

    SCA: A sine cosine algorithm for solving optimization problems

    Knowledge-Based Systems

    (2016)
  • S. Mirjalili et al.

    Salp Swarm Algorithm: A bio-inspired optimizer for engineering design problems

    Advances in Engineering Software

    (2017)
  • S. Mirjalili et al.

    The whale optimization algorithm

    Advances in Engineering Software

    (2016)
  • S. Mirjalili et al.

    Grey wolf optimizer

    Advances in Engineering Software

    (2014)
  • S. Ouadfel et al.

    Enhanced crow search algorithm for feature selection

    Expert Systems with Applications

    (2020)
  • J.-M. Paillisson et al.

    Interaction between coot (Fulica atra) and waterlily (Nymphaea alba) in a lake: The indirect impact of foraging

    Aquatic Botany

    (2001)
  • C. Randler

    Coots Fulica atra reduce their vigilance under increased competition

    Behavioural Processes

    (2005)
  • R.V. Rao et al.

    Teaching–learning-based optimization: A novel method for constrained mechanical design optimization problems

    Computer-Aided Design

    (2011)
  • E. Rashedi et al.

    GSA: A gravitational search algorithm

    Information Sciences

    (2009)
  • H. Salimi

    Stochastic Fractal Search: A powerful metaheuristic algorithm

    Knowledge-Based Systems

    (2015)
  • S. Saremi et al.

    Grasshopper optimisation algorithm: Theory and application

    Advances in Engineering Software

    (2017)
  • P. Savsani et al.

    Passing vehicle search (PVS): A novel metaheuristic algorithm

    Applied Mathematical Modelling

    (2016)
  • P.R. Singh et al.

    Modified Spider Monkey Optimization based on Nelder-Mead method for global optimization

    Expert Systems with Applications

    (2018)
  • Cited by (237)

    View all citing articles on Scopus

    Iraj Naruei born in Zahedan, Iran in 1986. He received his B.Sc. in computer engineering from Hatef University in 2010 and his M.Sc. in software engineering from the Islamic azad University of Zahedan Branch in 2010. Since September 2017, he has been working on his Ph.D. degree at the University of Kerman in software engineering. His current major research areas include Optimization Algorithms and Soft Computing.

    Farshid Keynia was born in Kerman, Iran. He received the B.Sc. degree in Electrical Engineering from S. B. University, Kerman, Iran, in 1996, and the M.Sc. degree in Electrical Engineering from Semnan University, Semnan, Iran, in 2001. He is received the Ph.D. degree at the Electrical Engineering Department of Semnan University, Semnan, Iran, in 2010. His researches focus on Electricity Market Faetures, short-term and mid-term price and load forecasting in deregulated electricity markets, and feature selection and classification algorithms. He also work on meta heuristic multi optimization methods.

    View full text