This paper presents a novel biologically inspired metaheuristic algorithm called sevenspot ladybird optimization (SLO). The SLO is inspired by recent discoveries on the foraging behavior of a sevenspot ladybird. In this paper, the performance of the SLO is compared with that of the genetic algorithm, particle swarm optimization, and artificial bee colony algorithms by using five numerical benchmark functions with multimodality. The results show that SLO has the ability to find the best solution with a comparatively small population size and is suitable for solving optimization problems with lower dimensions.
In recent years, heuristic algorithms have gained popularity because of their ability to find nearoptimal solutions to problems unsolved by analytical methods within reasonable computation time due to the multimodality or high dimensionality of their objective functions [
Researchers continue to develop many metaheuristic algorithms. Some of the most successful metaheuristic algorithms include genetic algorithm (GA) [
Metaheuristic algorithms are widely used in different fields and problems, such as manufacturing [
This paper introduces a novel biologically inspired metaheuristic algorithm called sevenspot ladybird optimization (SLO). SLO is inspired by the foraging behavior of a sevenspot ladybird. This paper presents the basic concepts and main steps of the SLO and demonstrates its efficiency. The performance of the SLO is compared with some popular metaheuristic algorithms, such as GA, PSO, and ABC, by using five different dimensional classical benchmark functions, as given in [
In general, all the metaheuristic algorithms have something in common in the sense that they are populationbased search methods. These methods move from a set of points (population) to another set of points in a single iteration with likely improvement using a combination of deterministic or probabilistic rules. The most remarkable difference of these metaheuristic algorithms lies in the updating rules. The GA is inspired by the principles of genetics and evolution and mimics the reproduction behavior observed in biological populations. The GA employs the principal of “survival of the fittest” in its search process to select and generate individuals that are adapted to their environment. In PSO, instead of using genetic operators, each particle adjusts its “flying” according to its own flying experience and its companions’ flying experience [
The rest of this paper is organized as follows. Section
The sevenspot ladybird (Figure
Sevenspot ladybird.
Recent studies have shown that sevenspot ladybirds are more social than we believe them to be [
The life history of the sevenspot ladybird.
Sevenspot ladybirds are effective predators of aphids and other homopteran pests, and, thus, their foraging behaviors have been extensively studied [
Diagram illustrating how a ladybird might perceive its environment and forage for resources.
In Figure
Sevenspot ladybirds locate their prey via extensive search and then switch to intensive search after feeding. While searching for its prey, a sevenspot ladybird holds its antennae parallel to its searching substratum and its maxillary palpi perpendicular to the substratum. The ladybird vibrates its maxillary palpi and turns its head from side to side. The
How sevenspot ladybirds decide when to leave a patch for another, also known as
This section describes the proposed sevenspot ladybird optimization (SLO) algorithm, which simulates the foraging behavior of sevenspot ladybirds to solve multidimensional and multimodal optimization problems. The main steps of the SLO are as follows.
Suppose that the search space (environment) is a
Suppose that each sevenspot ladybird is treated as a point in a
If
For each particle, evaluate the optimization fitness in a
The current fitness evaluation of each ladybird was compared with the fitness value of its best historical position (
The current best fitness evaluation of all the ladybirds in a patch was compared with the fitness value of their previous best position (
The current best fitness evaluation of all the ladybirds in the population was compared with the fitness value of their previous best position (
In the SLO, if a position does not improve in a predetermined number of cycles, then a new position is produced in the patch where
If the abandoned position is
The position of a ladybird is updated associated with its previous movement. If a ladybird has done extensive search, then the position of the ladybird is changed as follows:
In (
From equations above, we can see that the velocity updating rule is composed of three parts. The first part, known as
If the termination condition is satisfied, that is, the SLO has achieved the maximum iteration number, then the SLO is terminated; otherwise, it returns to Step
In the field of heuristic computation, it is common to compare different algorithms using a set of test functions. However, the effectiveness of an algorithm against another algorithm cannot be measured by the number of problems that it solves better [
The first function is the Griewank function whose value is 0 at its global minimum
The second function is the Rastrigin function whose value is 0 at its global minimum
The third function is the Rosenbrock function whose value is 0 at its global minimum
The fourth function is the Ackley function whose value is 0 at its global minimum
The fifth function is the Schwefel function whose value is 0 at its global minimum
The common control parameters for the algorithms include population size and number of maximum generation. In the experiments, maximum generations were 750, 1000, and 1500 for Dimensions 5, 10, and 30, respectively, and the population size was 50. Other control parameters of the algorithms and the schemes used in [
The settings for the used GA scheme presented in [
PSO equations can be expressed as follows:
The control parameters of the ABC algorithm are as follows: the maximum number of cycles is equal to the maximum number of generation and the colony size is equal to the population size, that is, 50, as presented in [
In SLO, each dimension is divided into two equal parts, and thus, 2^{D} patches are generated. In each patch, the initial population of ladybirds is set to 20. The parameter
In this paper, all the experiments were repeated 30 times with different random seeds. The best and mean function values of the solutions found using the algorithms for different dimensions were recorded. Tables
Results of the Griewank function.
Algorithm  Dimension  Mean  Best  SD 

SLO  5 



10 




30 




 
GA  5 



10 




30 




 
PSO  5 



10 




30 




 
ABC  5 



10 




30 



Results of the Rastrigin function.
Algorithm  Dimension  Mean  Best  SD 

SLO  5 



10 




30 




 
GA  5 



10 




30 




 
PSO  5 



10 




30 




 
ABC  5 



10 




30 



Results of the Rosenbrock function.
Algorithm  Dimension  Mean  Best  SD 

SLO  5 



10 




30 




 
GA  5 



10 




30 




 
PSO  5 



10 




30 




 
ABC  5 



10 




30 



Results of the Ackley function.
Algorithm  Dimension  Mean  Best  SD 

SLO  5 



10 




30 




 
GA  5 



10 




30 




 
PSO  5 



10 




30 




 
ABC  5 



10 




30 



Results of the Schwefel function.
Algorithm  Dimension  Mean  Best  SD 

SLO  5 



10 




30 




 
GA  5 



10 




30 




 
PSO  5 



10 




30 




 
ABC  5 



10 




30 



Convergence characteristics of the Griewank function with
Convergence characteristics of the Griewank function with
Convergence characteristics of the Griewank function with
Convergence characteristics of the Rastrigin function with
Convergence characteristics of the Rastrigin function with
Convergence characteristics of the Rastrigin function with
Convergence characteristics of the Rosenbrock function with
Convergence characteristics of the Rosenbrock function with
Convergence characteristics of the Rosenbrock function with
Convergence characteristics of the Ackley function with
Convergence characteristics of the Ackley function with
Convergence characteristics of the Ackley function with
Convergence characteristics of the Schwefel function with
Convergence characteristics of the Schwefel function with
Convergence characteristics of the Schwefel function with
According to the best function values obtained using the different algorithms with
From the results, we can see that the SLO does not obtain better result along with the growing dimensions. Considering the No Free Lunch Theorem [
This paper investigated the foraging behaviors of sevenspot ladybirds and proposed a novel biologically inspired metaheuristic algorithm called SLO. The SLO, GA, PSO, and ABC algorithms were tested on five numerical benchmark functions with multimodality to validate the performance of SLO. The simulated results show that SLO has the ability to find the best solution and is suitable for solving optimization problems with lower dimensions. In this paper, the ABC algorithm outperformed all other algorithms, but according to the No Free Lunch Theorem [
The authors are grateful to the editor and the anonymous referees for their insightful and constructive comments and suggestions, which have been very helpful for improving this paper. This research was supported by the National Natural Science Foundation of China (Grant no. 51375389) and the National High Technology Research and Development Program of China (863 Program) no. 2011AA09A104.