Comparative Study of Nature-Inspired Algorithms

Mohammad Abdullah Tahir, Hasan Faraz Khan, Mohammad Mohsin Khan

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Mohammad Abdullah Tahir, Hasan Faraz Khan, Mohammad Mohsin Khan. Comparative Study of Nature-Inspired Algorithms. International Working Conference on Transfer and Diffusion of IT (TDIT), Dec 2020, Tiruchirappalli, India. pp.353-361, 10.1007/978-3-030-64849-7_32. hal-03701777

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Comparative study of nature-inspired algorithms

Mohammad Abdullah Tahir¹, Hasan Faraz Khan², and Mohammad Mohsin Khan³

¹Aligarh Muslim University, Aligarh, India
abdullahtahir919@gmail.com

²Aligarh Muslim University, Aligarh, India
farazkhan138@gmail.com

³Aligarh Muslim University, Aligarh, India
mkbusiness255@gmail.com

**Abstract.** Nature-inspired algorithms are problem-solving tactics and methodologies and have been gaining much recognition for their competence. These algorithms have gained massive acclaim in the last few years to solve puzzling real-world (Nondeterministic polynomial-hard and Nondeterministic polynomial-complete) problems and solve complex optimization problems and functions whose exact solution doesn't exist. These are the algorithms that are inspired by natural processes and phenomena. The nature-inspired algorithm can be categorized based on some biological processes or any other phenomena which happen in nature. So, in this paper, we have classified some popular nature-inspired algorithms such as Genetic algorithm, Simulated Annealing, harmony search, Black hole, and many more. Based on four parameters from which the first parameter is Subject from which they were inspired. The second parameter is the optimization technique i.e. Stochastic or Deterministic. The third parameter of our classification is the number of solutions they maintain i.e. population-based or trajectory-based. And the last parameter of this categorization is memory i.e. algorithm is memory-based or memory less.

**Keywords.** Nature-Inspired algorithms, stochastic algorithms, Deterministic algorithms, Memory based algorithms, Memory-less algorithms

# 1 Introduction

## 1.1 Previous Classifications

Nature-inspired computing is a discipline that develops new computing techniques by observing how nature behaves to solve existing complex problems in different environmental situations. Algorithms that are inspired by natural problems are known as Nature-Inspired Algorithms. These algorithms have gained much popularity as real-world problems are becoming more and more complex and extensively large in contrast with past computing techniques. Nature-inspired algorithms are applied
mostly to optimization problems and are used to give feasible and acceptable solu-
tions to optimization problems rather than guaranteed optimal solution within a rea-
sonable amount of time. Nature-inspired algorithms are broadly classified into four
major categories which are evolution-based, swarm intelligence based algorithms,
physics based algorithms, and human-based algorithms [1].

Evolution-based algorithms are inspired by the evolutionary behavior of natural
systems and the laws of natural evolution. In these algorithms, a set of the population
is stochastically selected and is processed over successive generations through evolu-
tionary operations. The best individuals are selected are sent through the next genera-
tion process and this process is continued until the optimal solution is obtained or the
termination criteria are reached. These algorithms are inspired by Charles Darwin
Theory [2] [3] e.g. - Genetic Algorithm (GA), Differential Evolution (DE), etc.
Swarm-based intelligence (SI), which is also known as Swarm optimization tech-
niques [4], is inspired by the collective behavior of natural swarms. The working pro-
cess of swarm-based algorithms is that they mimic the social behavior of groups on
animals. Like particle swarm optimization [5], artificial bee colony algorithm [6][7],
and ant colony optimization algorithm[8]. One of the most popular Swarm based al-
gorithms is Particle Swarm Optimization which was developed by James Kennedy
and Russell C.Eberhart. It mimics the behavior of bird flocks and fish schooling.
Physics-based nature-inspired algorithms are those algorithms that are inspired by
physical processes in nature. Some common examples of physics-based algorithms
are Simulate Annealing (SA) [9], Gravitational Search Algorithm (GSA) [10], Central
Force Optimization (CFO) [11] and Black Hole (BH) algorithm [12], etc. While Hu-
man-based nature-inspired algorithms are inspired by human behaviors and try to
imitate human characteristics. The most common example of human-based algorithms
is the Harmony Search algorithm (HS) [13]. Besides this very simple categorization,
nature-inspired algorithms are further classified into many categories based on their
working process, mathematical functions, searching methods, and capability of find-
ing optimal solutions.

1.2 History of Nature – Inspired Computing

Another reason why we use nature-inspired algorithms is the fact that these algo-
rithms are inspired by nature itself. Nature is amazing and it has always been a source
of inspiration for scientists and researchers. Besides these visible natural phenomena,
there are numerous of invisible events and marvels that our scientists are still trying to
explain. For centuries, scientists and philosophers are observing natural occurrences
and trying to emulate and adapt these processes. There are already numerous re-
searches proving that nature-inspired algorithms are much efficient and have a com-
petitive edge over deterministic methods. In today's world where real-world problems
are getting complex day-by-day and extensively large due to scientific advancements,
nature-inspired computing can be exceptionally beneficial. Real-world problems have
innumerable search spaces with countless difficulties, a large number of variables,
and multiple dimensions. These real-world problems enhance and elucidate multi-
objective functions and solve NP-hard problems. Thus, demand for resolving these
complications has engaged many scientists and researchers to come down with much faster, precise, explicitly powerful nature-inspired optimization algorithms. The revolutionary period for nature-inspired algorithms started when evolution-based algorithms came into existence. In 1950, Alan Turing proposed a machine that was inspired and emulated based on principles of evolution. 1960-1970 was the most crucial decade for the development of these algorithms. In 1963, Rechenberg and Haul-Paul Schwefel solved complex computation problems in aerospace engineering using a searching technique called evolution strategy and it was extensively acknowledged as a feasible optimization method [14]. The Genetic Algorithm was then introduced by John Holland in the early 1970s and his book "Adaptation in Natural and Artificial Systems"[15]. Genetic Algorithm is a biologically inspired computational procedure that is inspired by Darwin's theory of evolution. It shows the ability to exploit the previous information to find the optimal result or expecting off-springs. 1980-1990s were also important decades as Simulated Annealing [16] was developed by Scott Kirkpatrick, Mario P. Vechchi, and C. Daniel Gellat in 1983. In 1992, Marco Dorigo proposed his work on the Ant Colony Optimization algorithm[17]. It is a swarm intelligence based algorithm inspired by the social behavior of ant colonies. In 1995, a remarkable advancement was made when John Kennedy and Russell C. Eberhart came up with Particle Swarm Optimization (PSO). Differential Evolution [18] was developed by Rainer Storm and Kenneth Price in 1997 and it turned out to be much more efficient than the Genetic Algorithm on many aspects. Xin-She Yang developed many nature-inspired algorithms like Firefly Algorithm(2007)[19], Bat Algorithm(2010)[20], Cuckoo Search(2009)[21], and Flower Pollination Algorithm in 2012 [22]. Since the 2000's many nature-inspired algorithms were developed and many of them were modified by scientists to give better solutions. The number of these algorithms in the past two decades has risen exponentially. Even in present times, this field of nature-inspired algorithms is evolving rapidly.

## 1.3 Uses of Nature - Inspired Algorithms

Nature-inspired algorithms are implemented and used in many fields of science and engineering. The genetic Algorithm which is an evolution-based algorithm is used for Machine Learning, Deep Learning, Computer Architecture, Bayesian Inference, etc. Swarm intelligence based algorithm i.e. Ant Colony Optimization (ACO) and Particle Swarm algorithm (PSO) are used for network routing applications [23], Neural network system design, image processing etc. [24]. Firefly algorithm, Bat Algorithm, and Cuckoo Search algorithm which were developed by Xin-She Yang are also preferred in Neural Network programming, Semantic Web, Software testing, and image clustering [25][26]. Nature-inspired algorithms are immensely popular and preferred when dealing with multi-dimensional functions and complex problems where optimal solutions are required in a discrete search space.

## 1.4 Reason for Classification

In this paper, Nature-Inspired algorithms are classified into different categories on
various factors. Classification is very important because it helps us to identify and
differentiate these algorithms on the basis of their searching technique, ability to pro-
vide an optimal solution, derivation, etc. It helps in a better understanding of these
algorithms and to determine which technique to use for that specific operation and it
also allows us to understand the mechanism of algorithms easily and efficiently either
individually or in a group.

1.5 Basis of Classification

In this paper, algorithms are classified into Four major parameters which are
optimization technique, population, and the number of solutions, subjects they are
inspired from. Based on optimization, it is categorized into two categories which are
Stochastic optimization and Deterministic optimization [27]. Stochastic
Optimization generates and uses random variables. Stochastic optimization
algorithms have expansive applications in problems in mathematics, computation
techniques, and engineering. Deterministic global optimization focuses on finding
global solutions to optimization problems. The next parameter is population-based
against single solution based search [28]. Population-based algorithms execute a
search with various initial points. Single solution method focus on modifying and
enhancing an individual solution. The third parameter focuses on the source of
inspiration and the subject from which they are derived. Besides the broad
classification that we already have, it further classifies these algorithms based on the
subject like biological evolution, chemical processes, physics-based, music-based
and swarm behavior or social psychology. As per our knowledge, we have further
distributed this paper in section 2 and section3. In section 2 we have described the
drawbacks of the previous classifications which have been proposed earlier. Then in
section 3, we proposed our classification. Following which section 4 concludes this
paper with some related future work.

## 2 Drawbacks

Nothing is perfect, everything lacks something in it. As time passes by new issues
and new problems arise. And thus, people keep working to turn it into the best possi-
ble version of it. Nature-inspired algorithms are developed to solve problems or to
find a better solution to a problem. Today we have lots of Nature-inspired algorithms
available to solve a particular problem. But how we are going to decide which would
be the best algorithm to solve that problem. Though it is found that in some cases or
circumstances one algorithm performs better than the other or Vice – Versa. It mainly
depends on the problem, dimensions of the problem, inputs, variables, and many other
factors that decide the success of the algorithm. So there is no universal algorithm that outperforms the other algorithms [29]. A best available algorithm must be effective in terms of performance and efficiency in terms of resources such as computation cost and time allowed to come up with the solution. These are important factors in deciding what algorithm to use.

While we were studying for our research work we have gone through a lot of books and research papers and we have found that a lot of researchers have classified Nature-inspired algorithms only based on their subject namely, swarm intelligence, physical or chemical-based algorithms, and evolutionary algorithms.[30] In our classification, we have also classified Nature-Inspired Algorithms based on their subject, nature of optimization, number of solutions, and also on the basis of memory, and in each category, we have arranged the list of Nature-Inspired Algorithms in their Chronological order.

# 3 Classification

Here we classify Natural Inspired Algorithm according to different categories which are described below one by one.

* **Inspired Subject:** In this category, we classify algorithms according to their subject from which they are inspired. Like the Gravitational Search algorithm which is inspired by Physics.

* **Number of Solutions:** In this category, we have two sub-Categories:

- **Trajectory-Based NIA:** In this Category, we put those algorithms which use the single agent/particle/solution which get better upon iteration. And in the trajectory-based method, the initial agent/particle/solution is randomly selected.

- **Population-Based NIA:** In this category, we put those algorithms which use the set of agent/particle/solutions which also result in obtaining the number of a solution in a particular iteration. A population-based algorithm selects the best solution among the number of solutions generated in the iterations. This is called elitism.

* **Based on optimization:** In this category also we have two sub-categories:

- **Deterministic Algorithms:** These algorithms follow a certain procedure and provide the same solution on different runs.

- **Stochastic Algorithms:** These algorithms possess randomness and provide different solutions on a different run. The main advantage of stochastic algorithms is the ability to explore several regions of the search space. That is the reason they can escape from the local optima to reach the global optimum.

* **Based on Memory:** In this category also we have two sub-categories:
- **Memory-Based Algorithms:** Memory-based algorithms approach the problem by functioning over the entire dataset. The memory-based approach uses data to compute the similarity between items. These memory-based algorithms calculate the similarity between previously analyzed items and produce a prediction by taking the weighted average of all the ratings.

- **Memory-less Algorithms:** Memory-less algorithms operate on an individual problem and its dataset to find an optimal solution rather than comparing and predicting results from previously compiled solutions.

<table><caption>Table 1. Classification table consisting of three parameters</caption><thead><tr><th>Name</th><th>Inspired Subject</th><th>Population based</th><th>Trajectory based</th><th>Stochastic</th><th>Deterministic</th></tr></thead><tbody><tr><td>Simulated Annealing</td><td>Physics</td><td>-</td><td>✓</td><td>✓</td><td>-</td></tr><tr><td>Stochastic diffusion search</td><td>Physics</td><td>✓</td><td>-</td><td>✓</td><td>-</td></tr><tr><td>Harmony Search</td><td>Physics</td><td>✓</td><td>-</td><td>✓</td><td>-</td></tr><tr><td>Electro magnestism Optimization</td><td>Physics</td><td>✓</td><td>-</td><td>✓</td><td>-</td></tr><tr><td>Big Bang Crunch</td><td>Physics</td><td>✓</td><td>-</td><td>✓</td><td>-</td></tr><tr><td>River Formation Dynamics</td><td>Physics</td><td>✓</td><td>-</td><td>✓</td><td>-</td></tr><tr><td>Central Force Intelligent Water Drop</td><td>Physics</td><td>✓</td><td>-</td><td>-</td><td>✓</td></tr><tr><td>Gravitational Search</td><td>Physics</td><td>✓</td><td>-</td><td>✓</td><td>-</td></tr><tr><td>Charged System Search</td><td>Physics</td><td>✓</td><td>-</td><td>✓</td><td>-</td></tr><tr><td>Spiral Optimization</td><td>Physics</td><td>✓</td><td>-</td><td>✓</td><td>-</td></tr><tr><td>Black hole Vibrating particle System</td><td>Physics</td><td>✓</td><td>-</td><td>✓</td><td>-</td></tr><tr><td>Chemical Reaction Optimization</td><td>Chemistry</td><td>✓</td><td>-</td><td>-</td><td>✓</td></tr><tr><td>ARCO Artificial Immune System</td><td>Chemistry</td><td>✓</td><td>-</td><td>✓</td><td>-</td></tr><tr><td>Biology</td><td>Biology</td><td>✓</td><td>-</td><td>✓</td><td>-</td></tr><tr><td>Genetic</td><td>Biology</td><td>✓</td><td>-</td><td>✓</td><td>-</td></tr></tbody></table>
<table><caption>**Table 2.** Classification Table consisting of Memory parameter</caption><tr><td>Taboo Search</td><td>Biology</td><td>-</td><td>✓</td><td>-</td><td>✓</td></tr><tr><td>Memetic Search</td><td>Biology</td><td>✓</td><td>-</td><td>✓</td><td>-</td></tr><tr><td>Differential Evolution</td><td>Biology</td><td>✓</td><td>-</td><td>✓</td><td>-</td></tr><tr><td>Flower Pollination</td><td>Biology</td><td>✓</td><td>-</td><td>✓</td><td>-</td></tr><tr><td>Invasive Weed</td><td>Biology</td><td>✓</td><td>-</td><td>✓</td><td>-</td></tr><tr><td>Krill Herd</td><td>Biology</td><td>✓</td><td>-</td><td>✓</td><td>-</td></tr><tr><td>Dendritic Cell</td><td>Biology</td><td>✓</td><td>-</td><td>✓</td><td>-</td></tr><tr><td>Deterministic Dendritic Cell</td><td>Biology</td><td>✓</td><td>-</td><td>-</td><td>✓</td></tr><tr><td>Brainstorm</td><td>Biology</td><td>✓</td><td>-</td><td>-</td><td>✓</td></tr><tr><td>Ant Colony</td><td>Social Psychology</td><td>✓</td><td>-</td><td>✓</td><td>-</td></tr><tr><td>Particle Swarm</td><td>Social Psychology</td><td>✓</td><td>-</td><td>✓</td><td>-</td></tr><tr><td>Shuffles Frog leaping</td><td>Social Psychology</td><td>✓</td><td>-</td><td>✓</td><td>-</td></tr><tr><td>Bee Algorithm</td><td>Social Psychology</td><td>✓</td><td>-</td><td>✓</td><td>-</td></tr><tr><td>Artifical Bee Colony</td><td>Social Psychology</td><td>✓</td><td>-</td><td>✓</td><td>-</td></tr><tr><td>Firefly Algorithm</td><td>Social Psychology</td><td>✓</td><td>-</td><td>✓</td><td>-</td></tr><tr><td>Cuckoo Search</td><td>Social Psychology</td><td>✓</td><td>-</td><td>✓</td><td>-</td></tr><tr><td>Fish School</td><td>Social Psychology</td><td>✓</td><td>-</td><td>✓</td><td>-</td></tr><tr><td>Atmosphere Clouds model</td><td>Ecology</td><td>✓</td><td>-</td><td>✓</td><td>-</td></tr><tr><td>Biogeography Based Optimization</td><td>Geography</td><td>✓</td><td>-</td><td>✓</td><td>-</td></tr></table>

<table><thead><tr><th>Name</th><th>Memory based</th><th>Memory-less</th></tr></thead><tbody><tr><td>Artifical Bee Colony</td><td>✓</td><td>-</td></tr><tr><td>Firefly Algorithm</td><td>-</td><td>✓</td></tr><tr><td>Jumper Firefly Algorithm</td><td>✓</td><td>-</td></tr><tr><td>Memetic Search</td><td>-</td><td>✓</td></tr><tr><td>Simulated Annealing</td><td>-</td><td>✓</td></tr><tr><td>Blackhole</td><td>✓</td><td>-</td></tr></tbody></table>
<table><tr><td>Bat Algorithm</td><td>✓</td><td>-</td></tr><tr><td>Particle Swarm</td><td>✓</td><td>-</td></tr><tr><td>Cuckoo Search</td><td>✓</td><td>-</td></tr><tr><td>Chemical Reaction Optimization</td><td>✓</td><td>-</td></tr><tr><td>Artificial Immune System</td><td>✓</td><td>-</td></tr><tr><td>Harmony Search</td><td>✓</td><td>-</td></tr><tr><td>Central Force</td><td>✓</td><td>-</td></tr><tr><td>Differential Evolution</td><td>✓</td><td>-</td></tr><tr><td>Dragon Fly Algorithm</td><td>-</td><td>✓</td></tr><tr><td>Taboo Search</td><td>✓</td><td>-</td></tr><tr><td>Accelerated PSO</td><td>✓</td><td>-</td></tr><tr><td>Bacterial Foraging</td><td>✓</td><td>-</td></tr><tr><td>Glowworm Swarm Algorithm</td><td>-</td><td>✓</td></tr><tr><td>Big Bang Crunch</td><td>-</td><td>✓</td></tr><tr><td>Gene Expression</td><td>✓</td><td>-</td></tr><tr><td>Roach Infestation Algorithm</td><td>✓</td><td>-</td></tr><tr><td>Gravitational Search</td><td>-</td><td>✓</td></tr><tr><td>Gravitational Local Search</td><td>-</td><td>✓</td></tr></table>

## 4 Conclusion and Future Works

As the provenance of innovation of nature-inspired algorithms are very contrasting and distinct so it is indisputable that algorithms are also varying in their nature. Hence in this paper, we classify the existing nature-inspired algorithms like genetic algorithm, Cuckoo search, Bat algorithm, Central force algorithm, Differential evolution, Genetic programming, and many other natural inspired algorithms based on four parameters. This can be a very informative source to choose the appropriate algorithm for the problem and also to form a base for further higher research.

It might be notable that the classification is not unique. But this paper seems to be effective for the researchers and also for the common people who don't have prior knowledge about these algorithms. It is very hard to find the appropriate algorithm for the problem because there is a huge number of nature-inspired algorithms are present out there. So the main motive of the paper is to help the researcher to find the appropriate algorithm from the ocean of these algorithms. So they can solve the real-world optimization problem more effectively. As we all know that the development of nature-inspired algorithms for optimization is arising rapidly and has seen enormous growth in the past few decades.

In the future, we try to add on more parameters in the classification of nature-inspired algorithms i.e. objective function of the algorithm. But this classification
can be broadened to freshly originated nature-inspired algorithms and also can be practiced for alteration and modifying already existing nature-inspired algorithms.

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