Keywords:

1 Introduction

Nature is incessantly reckoned as a source of inspiration for human community in diverse ambit. Numbers of optimization algorithms have been developed stirred by the optimization approaches espoused by the nature [1]. These methods are often entitled as nature inspired meta-heuristics impersonating certain triumphant distinctiveness of the nature. In spite of the verity that the preeminent strategy is yet to be discovered, or may not be present at all, this suite of techniques have transpired remarkably in the last two decades [2]. They are often considered as astonishingly proficient in solving difficult and challenging real-world optimization problems, which may even sometimes required to deal with NP hard problems. They have the knack to portray and resolve intricate relationships from essentially extremely simple initial conditions and rules with modest or no knowledge of the search space. The span of this area is certainly enormous leading to an innovative era in next generation computing, modeling and algorithm engineering. An immense literature of nature inspired approaches exists to decipher imposing range of problems [3].

A group of algorithms of this vast research area is inspired by biological mechanisms occurring in the nature and its components and are fall under the umbrella of bio-inspired meta-heuristics. Bio inspired algorithms are going to be a new-fangled transformation in computer science. The key feature is the equilibrium between solution diversity and solution speed. Ideally, the aim is to find the global best solution with the minimum computing effort. This study is an attempt to compare the broad sub-categories of bio-inspired intelligence methods via three well-known and well-established algorithms, Ant Colony Optimization (ACO) [4], Biogeography Based Optimization (BBO) [5] and Genetic Algorithm (GA) [6] based on assorted aspects. Study is supported by exploiting six benchmark functions available for global optimization. In addition to this a better taxonomy is suggested for the wide range of nature inspired intelligence algorithms based on their source of inspiration.

The rest of the paper is organized as follows. Section 2 highlights the taxonomy of the nature inspired techniques focusing more towards bio-inspired approaches. The next section presents the brief overview of the three approaches, ACO, BBO and GA used in the study. The comparison of these algorithms based on various aspects will be carried out in Sect. 4. Section 5 illustrates the experiments performed using the six benchmark functions. Analysis of the results obtained, are also presented in the same section. The last section is dedicated to the conclusion with some suggestions for the future work.

2 Taxonomy of Nature Inspired Meta-heuristics

The vast literature of Nature inspired techniques (NIT) successfully marked the presence of more than 40 innovative algorithms under this category [2]. Numerous researchers have tried to classify them based on assorted facets. It is truly an exigent errand to categorize these algorithms analytically. The most recent taxonomy recommended by Yang [3] considered the higher level grouping of these techniques based on broad source of inspiration areas of biology, physics or chemistry. He has also conveyed that from the set theory point of view, SI-based algorithms are a subset of bio-inspired algorithms, which itself is a subset of nature-inspired algorithms. This relationship can be easily represented as [2],

$$ Swarm\,Intelligence\, Based\, Algorithms\, \subset Bio-Inspired\, Algorithms\, \subset Nature Inspired Algorithms$$

He has further specified that some algorithms do not fall under bio inspired category but still they are developed by mimicking certain physical and/or chemical laws. Thus they are specified under a sub category of NIT satisfying the following relation [2].

$$ Physics\,\& \,Chemistry\,Based\,Algorithms\,\left\{{\begin{array}{*{20}l} {\notin \,Bio-inspired\,Algorithm} \hfill \\ {\subset \,Nature\,Inspired\,Algorithm} \hfill \\ \end{array}} \right. $$

Inspired by the above statements, we have proposed a taxonomy based on the source of inspiration as illustrated in Fig. 1. Initially the broad categories of bio-inspired methods are evolutionary techniques and swarm intelligence mechanisms. However, it has been identified that methods inspired by human mechanisms also spur a large number of approaches, which are nothing but the bio-inspired methods. Recently few approaches have been developed which have proved their competence in this pool but unable to find its place in any of these categories. Hence, in the taxonomy we have proposed a new sub-category associating the methods inspired by adopting some of the ecological mechanisms. A recent addition to this category is Biogeography Based optimization. This paper is an attempt to compare the three broad categories—Swarm Intelligence methods, Evolutionary techniques and Ecology based approaches via three algorithms namely ACO, GA and BBO that fall under these groups respectively. This comparison is an effort in support of the addition of a new subcategory under bio-inspired methods. The Swarm Intelligence methods and Evolutionary techniques have been chosen because the Ecology based techniques are thought of having the competencies of both these categories.

Fig. 1
figure 1

Taxonomy of nature inspired meta-heuristics based on the source of information

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3 Brief Overview of ACO, BBO and GA Algorithms

This section discusses three main algorithms selected for comparison with their generalized pseudo codes.

3.1 Ant Colony Optimization

ACO is one of the most booming swarm based algorithms proposed by Dorigo in 1999 [4]. It is inspired by the foraging behavior of ants and based on the phenomena known as stigmergy. The most fascinating facet of the collaborative behavior of numerous ant species is their knack to locate the shortest paths between the ants’ nest and the food sources by tracing pheromone trails: stronger the pheromone trail, higher its desirability. The pseudo code [4] is illustrated below.

  • BEGIN

    • SET parameters, INITIALIZE and LOCATE individuals of the population randomly in search space. Also INITIALIZE pheromone values

    • REPEAT UNTIL (TERMINATION CONDITION is satisfied)

      • EVALUATE the fitness of each ant solution

      • FOR each individual

        • UPDATE individual’s knowledge, position and pheromone values by using the knowledge of other individuals

      • END LOOP

    • END LOOP

  • END

3.2 Biogeography Based Optimization

BBO is a global optimization algorithm developed by Simon in 2008 [5]. It is inspired by mathematical models of biogeography. Each possible solution corresponds to an island and their features that characterize habitability are termed as suitability index variables (SIV). The fitness of each solution is called its habitat suitability index (HSI) and depends on many features of the habitat. High-HSI solutions tend to share their features with low by emigrating solution features to other habitats. Low-HSI solutions accept a lot of new features from high-HSI solutions by immigration from other habitats. Immigration and emigration tend to improve the solutions and thus evolve a solution to the optimization problem [6]. The pseudo code [5] is discussed below.

  • BEGIN

    • FOR each Habitat Hi

      • FOR each Habitat feature s

        • Select Habitat Hi with probability proportional to λi (immigration rate)

          • If Habitat Hi is selected

            • Select Hj with probability proportional to μi (emigration rate)

          • If Hj is selected

            •         Hi (s) ← Hj (s)

      • END LOOP

      •   Next Habitat feature

      •   Mutate Hi (Based on mutation probability)

    • END LOOP

  • END

3.3 Genetic Algorithms

GA is an evolutionary based stochastic optimization algorithm with a global search potential proposed by Holland [7]. GA is inspired by the evolutionary ideas of natural selection. They follow the principles of Charles Darwin Theory of survival of the fittest. Population of solution (chromosome) is initialized randomly. Based on the fitness function, the best chromosomes are selected into the mating pool, where cross over and mutation are carried out to obtain new set of solutions (offspring). The three principal genetic operators in GA involve selection, crossover, and mutation. The pseudo code [7] of the algorithm is as follows,

  • BEGIN

    •    INITIALIZE population of n chromosomes with random candidate solutions

    •    EVALUATE each candidate with the fitness function f(x)

      • REPEAT UNTIL (TERMINATION CONDITION is satisfied)

        •        SELECT two parent chromosomes based on the fitness values

        •        CROSSOVER pair of parents to form new offspring using crossover probability

        •        MUTATE the resulting offspring with mutation probability

        •        EVALUATE the new candidates using f(x)

        •        SELECT individuals for next generation based on the survival of fittest

      • END LOOP

  • END

4 Comparison of Bio-inspired Techniques

This section highlights the comparative study carried out for the three broad categories of bio-inspired techniques—Swarm Intelligence methods [8, 9], Evolutionary techniques [10] and Ecology based approaches. For this we have selected three well-known and well-established algorithms, Ant Colony Optimization, Genetic Algorithm and Biogeography Based Optimization one from each group and compare them on the basis of various characteristic [11, 12]. Table 1 illustrates the summarized details of the assessment.

Table 1 Comparison of ACO, BBO and GA based on various factors
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5 Experiments and Analysis

The six benchmark functions [13] have been used to compare the three algorithms on various nodes as represented in the Table 2 with their properties.

Table 2 List of Benchmark functions used for comparison
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Each algorithm is run for the above mentioned six benchmark functions for 50 generations considering 20 probable solutions in one generation. The results obtained have been illustrated in Table 3 with their initial and final best and mean minimum. To analyze the flow of convergence, i.e., the search strategy, initial point is considered as same for each of the algorithm.

Table 3 Illustrating the graphs of each of the algorithm with their initial and final best and mean minimum values
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The Table 3 shows that the BBO converges quite fast towards the solution as compared to the other two algorithms. Also, the trend followed by the BBO is quite similar to GA in some functions. However, the ACO convergence strategy is totally different. The next Table 4 shows the results obtained by 100 monte carlo simulations run for 100 generations. Results clearly state that BBO outperforms the other two methods in finding the solutions. Also, the average time taken by each of the algorithm during the monte carlo simulations has been specified in the Table 5. It shows that the time taken by BBO algorithm is least followed by GA and ACO.

Table 4 BEST values obtained by 100 monte carlo simulations run for 100 generations
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Table 5 Average CPU time taken by each of the algorithm during the 100 monte carlo simulations
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6 Conclusion

The last two decades has experienced an astonishing growth in the nature inspired meta-heuristics. Its frontiers have been expanding in multiple directions resulting in the development of novel nature inspired computing techniques at rapid pace. This paper presents a comparative study of ACO, BBO and GA-the three bio-inspired mechanisms based on the various characteristics and six well-known benchmark functions. The paper validates the better performance of BBO which combines the features of swarm techniques and evolutionary approach, thereby re-enforcing our belief to keep it under separate category of ecology based algorithms. A more detailed comparison can be carried out by considering different combinations of parameters involved. More techniques can be used for comparison purpose to further support the statement.