Survey on data science with populationbased algorithms
 Shi Cheng^{1}Email author,
 Bin Liu^{2}Email author,
 T. O. Ting^{3},
 Quande Qin^{4},
 Yuhui Shi^{3} and
 Kaizhu Huang^{3}
Received: 28 December 2015
Accepted: 7 April 2016
Published: 1 July 2016
Abstract
This paper discusses the relationship between data science and populationbased algorithms, which include swarm intelligence and evolutionary algorithms. We reviewed two categories of literature, which include populationbased algorithms solving data analysis problem and utilizing data analysis methods in populationbased algorithms. With the exponential increment of data, the data science, or more specifically, the big data analytics has gained increasing attention among researchers. New and more efficient algorithms should be designed to handle this massive data problem. Based on the combination of populationbased algorithms and data mining techniques, we understand better the insights of data analytics, and design more efficient algorithms to solve realworld big data analytics problems. Also, the weakness and strength of populationbased algorithms could be analyzed via the data analytics along the optimization process, a crucial entity in populationbased algorithms.
Keywords
Background
With the amount of data growing constantly and exponentially, the current data processing tasks are beyond the computing ability of traditional computational models. The data science, or more specifically, the big data analytics, has attracted more and more attention among researchers. The data are easily generated and gathered, while the volume of data is increasing very quickly. It exceeds the computational capacity of current systems to validate, analyze, visualize, store, and extract information. To analyze these massive data, there are several kinds of difficulties, such as the large volume of data, dynamical changes of data, data noise, etc. New and efficient algorithms should be designed to handle massive data analytics problems.
Swarm intelligence and evolutionary algorithms are two sets of search and optimization techniques [1–3]. To search a problem domain, a swarm intelligence algorithm processes a population of individuals. Different from traditional singlepoint based algorithms such as hillclimbing algorithms, each swarm intelligence algorithm is a populationbased algorithm, which consists of a set of points (population of individuals). Each individual represents a potential solution to the problem being optimized. The population of individuals is expected to have high tendency to move towards better and better solution areas along iteration through cooperation and competition among themselves.
In this paper, we present the analysis of the relationship from data science to populationbased algorithms, which include swarm intelligence and evolutionary algorithms. Swarm intelligence/evolutionary algorithms could be applied to optimize the data mining problems or to handle data directly. In populationbased algorithms, individuals move through a solution space and search for solution(s) for the data mining task. The algorithm could be utilized to optimize the data mining problem, e.g., the parameter tuning. The swarm intelligence algorithm could be directly applied to the data samples, e.g., subset data extraction. With the swarm intelligence, more effective methods can be designed and utilized in the massive data analytics problem.
In populationbased algorithms, every solution is spread in the search space. Each solution is also a data point; the distribution of solutions can be utilized to reveal the landscape of a problem. Data analysis techniques have been exploited to design new swarm intelligence/evolutionary algorithms, such as brain storm optimization algorithm [4, 5] and estimation of distribution algorithms [6]. In this paper, the populationbased algorithms indicate the evolutionary computation algorithms and swarm intelligence algorithms. There are several existing solutions at the same time, and massive information is generated over iterations. Thus, the big data analytics could be utilized to analyze the process of optimization. For nonpopulation based techniques, such as neural networks, a large number of parameters are tuned in different layers, which may also be analyzed by data analytics techniques.
There are three key challenges in big data problems, the data modeling, computing model, and implementation platform. The mainstream of big data research includes computing model, such as deep learning [7], MapReduce [8], and Platform, such as Hadoop [9], and Apache Spark. The aim of this paper is to provide a comprehensive review of the optimization of populationbased algorithms on data science and on the analysis of data science method for populationbased algorithms. The remaining of the paper is organized as follows. “Data science” Section reviews the basic concepts of data science methods. “Populationbased algorithms” Section reviews the general concepts of swarm intelligence and evolutionary algorithms and in particular, four algorithms, which are particle swarm optimization (PSO), ant colony optimization (ACO), brain storm optimization (BSO), and fireworks algorithm (FWA). “Data science with swarm intelligence and evolutionary algorithms” Section reviews the swarm intelligence and evolutionary algorithms utilized to optimize data science methods and data analysis methods utilized to analyze swarm intelligence algorithms are reviewed. A realworld application on freight prediction and recommendation system is introduced in “Freight prediction and recommendation system” Section. The key challenges and future directions of data science with populationbased algorithms are discussed in “Key challenges and future directions” Section, followed by conclusions in “Conclusions” Section.
Data science
Currently, data science or data analytics is a popular topic in computer science and statistics. It concerns with a wide variety of data processing tasks, such as data collection, data management, data analysis, data visualization, and realworld applications.
Definition

Prediction: To predict the response/output of future input variables;

Inference: To deduce the association among response variables and input variables.
From the perspective of computer science research, the data science is more practical. The phrase “data mining” is often used to indicate the data science tasks. The process of converting raw data into useful information, termed as knowledge discovery in databases (KDD). Data mining, which is data analysis process of knowledge discovery, attempts to discover useful information (or patterns) in large data repositories [11].
Tasks
In short, the data science field includes many subfields, such as data classification, data clustering, association analysis, and anomaly detection. The data classification and data clustering are two different kinds of basic problems, essential approaches in data mining research.
Classification
Data classification is a problem that finds the correct category (or categories) for objects (i.e., data) when a set of categories (subject, topics) and a collection of data set are given. Data categorization can be considered as a mapping function denoted as \(f: \mathcal {D} \rightarrow \mathcal {C}\), which is from the object space \(\mathcal {D}\) onto the set of classes \(\mathcal {C}\). The objective of a classifier is to obtain an accurate categorization results or predictions with high confidence.
The massive data processing needs to handle many kinds of unstructured or semistructured data; in some cases, these data need to be transformed into structured data. Each data record with many attributes or features is transformed as a vector with many dimensions. The dimension of the feature space is equal to the number of different attributes that appear in the data set. Different weights can be assigned to each feature. The methods of assigning weights to the features may vary. The simplest is the binary method in which the feature weight is either one – if the corresponding feature is present in the data – or zero otherwise [12, 13]. Recall and precision are two metrics to evaluate the classification results. Both metrics consider the categorized objects and relevant objects together.
Data clustering
The data clustering analysis is a technique that divides data into several groups (clusters). The goal of clustering is to classify objects being similar (or related) to one another in the same cluster and put objects being distant from each other in different clusters [14].
Clustering is the process of grouping similar objects together. From the perspective of machine learning, the clustering analysis is sometimes termed as unsupervised learning. There are N points in the given input, \(\mathcal {D} = \{\mathbf {x}_{i}\}_{i = 1}^{N}\), the “interesting and/or useful pattern” can be obtained through similarity calculation among points [15].
Data Science with Statistics
Statistics is defined as a set of tools such as probability theory, real analysis, measure theory, asymptotic theory, decision theory, Markov chains, martingales, ergotic theory, etc., [16]. In contrast with data mining, the subject of statistics emphasizes much more on mathematical validation. In the field of statistics, the goal of data analysis is to explain data with relevant models, whereas the data mining or machine learning research is more interested in prediction with accuracy and thus does not concern much on the model’s interpretability.
In this big data era, there is a big demand to improve traditional statistical data analysis tools, which were used to study observations of instances of particular phenomena. A big data research paradigm claims for analyzing multisource heterogeneous data in a theoretically sound and consistent way. To face challenges arising from big data analytics problem, we need to integrate advanced techniques in disciplines like metaheuristics based optimization into the statistical toolbox.
As metaheuristics based optimization advocates naturally inspired strategy, whereas statistics stresses mathematical validation, a fusion of them can bring in a lot of new opportunities in proposing new models or algorithms. Some existing trials in fusion of statistics and optimization include the Bayesian simulation scheme mixed with computational intelligence [17], the sequential Monte Carlo optimization methods [18], sequential Monte Carlo simulated annealing [19], sequential Monte Carlo samplers [20], population modelbased optimization with sequential Monte Carlo [21], estimation of distribution algorithms [6], etc.
We argue that one of the most promising directions in combining metaheuristics and statistics is to handle the curse of dimensionality in highdimension data analysis or optimization problems.
Two Examples of Applications
Massive data are generated in our daily life. With the data analytics techniques and swarm intelligence methods, more effective applications or systems can be designed to solve realworld problems. The intelligent transportation system and wireless sensor networks are two typical examples of massive data analytics applications.
Intelligent transportation system
The traffic problem is arising in many cities now. Many factors affect the traffic and transportation system, e.g., the number of vehicles, weather, accident occurrence, etc., and the traffic information changes in real time. The purpose of intelligent transportation is to build more rapid, safe, and more efficient traffic and transportation system by constructing the intelligent vehicles and road environment [22, 23]. In the intelligent transportation system, there are multiple objectives that ought to be satisfied. For instance, in the case of rapid transportation, environmental pollution, transportation scheduling: there are multiobjective conflicting objectives arising to achieve the predefined goal.
The intelligent transportation problem can be modeled as a largescale, dynamical, and multiobjective optimization problem. The traditional methods have difficulties to solve this problem. Swarm intelligence has been proven to be an effective method in solving these problems [24] as no gradient information is necessary to find a feasible solution.
Wireless sensor network
Based on the wireless sensor networks, the physical world is turning to be a kind of information system [25]. Different sensors are connected to form a network; information is transferred in this network by communication techniques. The information on the physical surroundings is available easily from sensors in the network. These sensor networks and communication techniques have constructed a new paradigm, which is called the internet of things [25, 26].
The wireless sensor networks have been applied to many realworld problems, such as environmental surveillance, transportation monitoring, engineering surveying, and industrial control, just to name a few [27]. Massive data will be generated from the longterm and/or largescale wireless sensor network system. The goal of data analysis is to make the fastest possible revelation toward the “useful” information. Data mining techniques are effective ways to handle these data, and to obtain “useful” information [28, 29].
Populationbased algorithms
Many realworld applications can be represented as optimization problems where algorithms are required to have the capability to search for the optimum. Most traditional methods can only be applied to continuous and differentiable functions [5]. The metaheuristic algorithms are proposed to solve the problem, which the traditional methods cannot solve or, at least, be difficult to solve. Recently, kind of metaheuristic algorithms, termed as swarm intelligence (SI) and evolutionary algorithm (EA), are attracting more and more attentions from researchers.
Swarm intelligence and evolutionary algorithms are collections of populationbased searching techniques [1]. To search a problem domain, an SI or EA algorithm processes a population of individuals. Each individual represents a potential solution of the problem being optimized. In EA or SI, an algorithm maintains and successively improves a collection of potential solutions until some stopping condition is met. The solutions are initialized randomly in the search space, and are guided toward the better and better areas through the interaction among solutions.

A population of individuals (potential solutions) is utilized in the search process.

The “fitness” information, i.e., the “quality” of solutions, instead of function derivatives or other related knowledge are directly used in the search.

The probabilistic, rather than deterministic, update rules are used to improve the “quality” of solutions.
As a general principle, the expected fitness of a solution returned should improve as the search method is given more computational resources in time and/or space. More desirable, in any single run, the quality of the solution returned by the method over iterations should improve monotonically – that is, the fitness of the solution at time t+1 should be no worse than the fitness at time t, i.e., f i t n e s s(t+1)≤f i t n e s s(t) for minimization problems. The general procedure of swarm intelligence/evolutionary algorithms is given in Algorithm 1.
There exist many swarm intelligence algorithms; among them most common ones are the particle swarm optimization (PSO) algorithm [30], which was originally designed for solving continuous optimization problems, and the ant colony optimization (ACO) algorithm, which was originally designed for discrete optimization problems [31]. The Brain Storm Optimization (BSO) algorithm and Fireworks algorithms (FWA) are two recently proposed swarm intelligence algorithms that are based on the convergence and divergence of solutions. Both BSO and FWA algorithms have the same operators: divergence operator and convergence operator; but two operators are utilized in different sequence.
Particle swarm optimization
Particle Swarm Optimization (PSO), which is one of the swarm intelligence techniques, was invented by Eberhart and Kennedy in 1995 [30, 32]. It is a populationbased stochastic algorithm modeled on the social behaviors observed in flocking birds. Each particle, representing a solution, flies through the search space with a velocity that is dynamically adjusted according to its own and its companion’s historical behaviors. The particles tend to fly toward better and better search areas over the course of the search process [1, 33].
In the particle swarm optimization problem, a particle not only learns from its own experience, but also learns from its companions. It indicates that a particle’s ‘moving position’ is determined by its own experience and its neighbors’ experience [34]. The general procedure of PSO algorithm is given in Algorithm 2.
Ant colony optimization
Ant Colony Optimization (ACO) is another type of swarm intelligence, which takes inspiration from the foraging behavior of some ant species [2, 31]. These ants deposit a chemical called pheromone on the ground, and other ants tend to choose routes with strong pheromone concentration. When an ant finds a short route, the signal of pheromone can mark some favorable path that should be followed by other members of the colony. Ant colony optimization exploits a similar mechanism for solving optimization problems.
In the ant colony optimization problem, a group of artificial ants will build many solutions to an optimization problem at the same time, and the search information is exchanged on their quality (fitness) via a communication scheme. The general procedure of ACO algorithm is given in Algorithm 3.
Brain storm optimization
The brain storm optimization (BSO) algorithm was proposed in 2011 [4, 5], which is a young and promising algorithm in swarm intelligence. It is based on the collective behavior of human being, that is, the brainstorming process [4, 5]. The solutions in BSO are converging into several clusters. The best solution of the population will be kept if the newly generated solution at the same index is not better. New individuals can be generated based on the mutation of one or two individuals in clusters. The exploitation ability is enhanced when the new individual is close to the best solution so far. While the exploration ability is enhanced when the new individual is randomly generated, or generated by individuals in two clusters. The procedure of BSO algorithm is given in Algorithm 4.
Fireworks algorithm
Fireworks algorithm (FWA) is a swarm intelligence optimization method that mimics the explosion process of fireworks [35–37]. The procedure of fireworks algorithm is given in Algorithm 5. There are four operators/strategies in FWA, which are explosion operator, mutation operator, mapping strategy, and selection strategy, respectively.
The most important factor, which affects a swarm intelligence/evolutionary algorithm’s performance may be its ability of exploration and exploitation [34]. Exploration means the ability of a search algorithm to explore different areas of the search space to have the high probability to find good promising solutions. Exploitation, on the other hand, means the ability to concentrate the search around a promising region to refine a candidate solution. A good optimization algorithm should optimally balance the two conflicted objectives.
Data science with swarm intelligence and evolutionary algorithms
Generally, there are two kinds of approaches that apply populationbased algorithms as data science techniques [38]. The first category consists of techniques where individuals of a swarm move through a solution space and search for solution(s) for the data mining task. This is a search approach; the swarm intelligence is applied to optimize the data mining problem, e.g., the parameter tuning. In the second category, swarms move data instances that are placed on a lowdimensional feature space to reach a suitable clustering or lowdimensional mapping solution of the data. This is a data organizing approach; the swarm intelligence is directly applied to the data samples, e.g., dimensionality reduction of the data.
The data science could also be utilized in the swarm intelligence/evolutionary algorithms or other optimization techniques. The most common application is to utilize the data analysis methods to improve the optimization techniques. The classification and clustering algorithms could be embedded into optimization algorithms to enhance the population diversity or to accelerate the convergence of solutions. The optimization techniques are also benefited from data visualization methods. For the multi/manyobjective optimization problems, several solutions are distributed on Pareto front, which may have three or higher dimensions. A clear illustration on the solutions could help the decision makers have a good understanding on the solved problems.
Populationbased algorithms in data science
The applications of populationbased algorithms solved problems in data science
Particle swarm optimization
Since the invention of the PSO algorithm in 1995, it has attracted many attentions in the swarm intelligence research community. Around 650 PSO application papers were analyzed in 2008; all applications were categorized into 26 classes, such as clustering and classification, control, design [47]. Several classes of applications could be regarded as PSO solving problems in data science, for example, approximately 29 papers (4.3 %) are categorized into clustering, classification, and data mining; 2.9 % of the papers on applications were utilized to solve problems with prediction and forecasting; and the applications on modeling and financial may also be related to the data science. PSO variants are also utilized to solve different problems in data science.
Clustering A method, named particle swarm clustering (PSC) algorithm, was proposed to solve data clustering problems [42]. A set of particles in the input data space is generated by the PSC algorithm, and the particles are moved so that they could become the prototypes representing the natural clusters of the original data [42]. In [43], PSO was utilized to solve the variable weighting problem in projected clustering of highdimensional data.
Association rules mining A PSO variant based on the notion of rough patterns, named rough PSO algorithm (RPSOA), has used rough values defined with upper and lower intervals that represent a range or set of values. RPSOA has been used to solve data mining problems, especially in the automatic mining of numeric association rules [48].
Classification Spam detection could be seen as a special case of classification problems. Based on clonal principle in the natural immune system, the clonal particle swarm optimization (CPSO) algorithm was utilized in solving spam detection problems [49]. By cloning the best individual of successive generations, the CPSO algorithm could enlarge the area near the promising candidate solution and accelerate the evolution of solutions [49]. A PSO algorithm based semisupervised learning method was engaged to categorize Chinese text in [13]. A prototype generation method based on multiobjective PSO was developed to improve the performance of nearest neighbor classification techniques [50].
For other data mining problems, a PSO algorithm aided orthogonal forward regression was utilized in solving unified data modeling problem [51]; and a binary PSO algorithm proved effective to select the small subset of informative genes from gene expression data [52].
Ant colony optimization
ACO algorithm was originally designed for discrete optimization problems. It has also been applied in different kinds of data mining problems, such as classification rules extraction, decision trees induction.
An ACO algorithm was used to induce decision trees method in [53]. An algorithm for data mining called AntMiner (antcolonybased data miner) was proposed to extract classification rules from data [54]. A new sequential covering strategy for inducing classification rules with ant colony algorithms was introduced [55]. The vast majority of ACO algorithms for inducing classification rules by an ACObased procedure are proposed [56].
Artificial immune system
An artificial immune system uses principles in the operation of the human immune system and applies them to computationally intelligent systems. Artificial immune system (AIS) has been exploited to solve various data mining problems, especially classification or anomaly detection problems.
Classification A problemoriented approach by designing an AIS algorithm for data mining, especially for classification, was advocated in [57]. An artificial immune system based multiclass classifier, named artificial immune system with local feature selection (AISLFS), was introduced in [58]. The local feature selection mechanism was embedded to reduce the dimensionality of the problem.
Anomaly detection Artificial immune system has been utilized to solve realworld anomaly detection problems, which are related to information security. A hybrid system based on artificial immune system and the selforganizing map was introduced to solve network intrusion detection problems [59]. An artificial immune system based virus detection system (VDS) was introduced in [60]. An artificial immune system based method for spam filtering was introduced in [61].
Genetic algorithms
Genetic algorithms have been utilized to solve many kinds of data mining problems, such as classification, clustering, Web mining, and association rules mining.
Classification Genetic algorithms have been used to construct a compact fuzzy classification system consisting of a small number of linguistic classification rules [62]. Two objectives are optimized by this fuzzy classification system, one is to maximize the number of correctly classified training patterns and the other is to minimize the number of selected rules. A genetic algorithm has been utilized to solve multilabel classification [63]. The goal of the multilabel classification task is to learn a classifier that predicts multiple class labels to an unlabeled instance based on features of an instance. A realcoded genetic algorithm (RCGA) was proposed to improve the classification performance of a polynomial neural network (PNN) [64]. The mean classification accuracy (CA) is used as the fitness value of each solution for the training dataset.
Clustering Genetic algorithm has been used to optimize the clusters created during unsupervised clustering [65]. The solutions are consisted by hard partitions of the feature space, and the fitness function is a version of the hard cmeans optimization function. In [66], genetic algorithms were utilized to search for the optimal, in the least squares sense, hierarchical clustering of a dataset. A multiobjective genetic algorithm based approach was proposed for fuzzy clustering of categorical data [67]. The fuzzy compactness and fuzzy separation of the clusters are optimized at the same time. A multiobjective algorithm, named DYNMOGA (DYNamic MultiObjective Genetic Algorithms) was proposed to solve community discovery problems in dynamic networks [68]. The aims of this proposed algorithm are to maximize cluster accuracy with respect to incoming data of the current time step, and to minimize clustering drift from one time step to the successive one. Two objectives are optimized by DYNMOGA, the first is the maximization of cluster accuracy, i.e., to maximize the snapshot quality of the current time step, and the second is the minimization of clustering drift, i.e., to minimize the temporal cost, which measures the distance between two clusters from one time step to the successive one. A genetic algorithm with spectralbased methodologies, named GANY was proposed to deal with the large data analysis problem [69]. The goal of GANY is generating a method to analyze more data using less resource.
Web mining Genetic algorithms were used for datadriven Web question answering problems, which need to find exact answers to natural languages (NL) questions. Answers are extracted directly from the Nbest snippets, which have been identified by a standard Web search engine using NL questions [70].
Association rules mining Association rules mining problem is usually modeled as a multiobjective optimization problem. A literature reviews on multiobjective genetic algorithms and multiobjective genetic programming for rule knowledge discovery in data mining are given in [71]. An automated clustering method based on multiobjective genetic algorithms was proposed to solve fuzzy association rules mining problems [72]. The method is applied to decide on the number of fuzzy sets and for the autonomous mining of both fuzzy sets and fuzzy association rules. The goal of the method is to obtain a large number of itemset in less time by automatically cluster values of a quantitative attribute. A multiobjective genetic algorithm based approaches were utilized for mining optimized fuzzy association rules [73]. Two different forms of criterion are used: the one tries to determine the appropriate fuzzy sets of quantitative attributes in a prespecified rule, which is also called as certain rule, and the other deals with finding both uncertain rules and their appropriate fuzzy sets.
Genetic programming
The genetic programming (GP) has the similar operators to the genetic algorithm (GA), which includes crossover, mutation and selection. The difference between genetic programming and genetic algorithm is that the GP has a population of treeshaped individuals, while the GA has a population of stringshaped individuals [1]. GP has been utilized to solve many kinds of data analysis problems.
Regression Symbolic regression based on Pareto Front GP is utilized to generate empirical models for industrial applications [74]. From the results of a smallsized industrial data set, the optimal settings of three parameters: the number of cascades, the number of generations, and the population size are tuned based on Pareto front GP.
Classification Performance bias may occur due to the unbalanced data sets, which may lead classifiers have good accuracy on the majority class, but very poor accuracy on the minority class. A multiobjective genetic programming (MOGP) is proposed, with accurate and diversified classifiers, performed satisfactory on both minority and majority classes [75, 76]. New fitness functions in GP for binary classification with unbalanced data are introduced in [77].
More literature about the evolutionary algorithms for clustering or data mining problems could be found in [78–80].
Data analysis in populationbased algorithms
The data mining techniques could be applied to design or analyze swarm intelligence algorithms. Massive information exists during the search process. For swarm intelligence/evolutionary algorithms, there are several individuals existing at the same time, and each individual has a corresponding fitness value. New individuals are generated as the iteration increases. There is also a massive volume of information on the “origin” of an individual, such as that an individual was created by applying which strategy and parameters to which former individual(s). The datadriven evolutionary computation/swarm intelligence is a new approach to analyze and guide the search in evolutionary algorithms/swarm intelligence. These strategies could be divided into offline methods and online methods. An offline method is based on the analysis of previous storage search history, such as history based topological speciation for multimodal optimization [81] or maintaining and processing submodels (MAPS) based estimation of distribution algorithm on multimodal problems [82]. In comparison, for an online method, the parameters could be adaptively changed during the different search states.
The data modeling methods could be applied to inspire new swarm intelligence algorithms. In the brain storm optimization algorithm [5], every solution is spread in the search space. The distribution of solutions can be utilized to reveal the landscape of a problem. From the clustering analysis of solutions, the search results can be obtained. In the estimation of distribution algorithms [6], the space of potential solutions is explored by building and sampling explicit probabilistic models of promising candidate solutions.
Data clustering method could be utilized to improve the performance of swarm intelligence/evolutionary algorithms. A cluster and gradientbased artificial immune system is proposed to apply in optimization scenarios [83], and a clusteringbased adaptive crossover and mutation probabilities for genetic algorithms are proposed in [84]. The number of clusters was analyzed in BSO algorithm solving different kinds of problems [85]. Based on clusters analysis, the search status could be obtained.
Freight prediction and recommendation system
The price changes for a week
Date  Mon  Tue  Wed  Fri  Sun 
Price  60  0  40  0  50 
The price changes for the same schedule at ten times
Run  1  2  3  4  5  6  7  8  9  10 
Price  50  30  20  40  60  70  90  80  40  50 
There are several primary carrier companies in China, and the number of freight forwarders is more than thirty thousand. The freight price changes at each week. It is difficult to predict the future freight market price and give different forwarders a recommended price. Currently, with the assistance of big data analytics techniques, the large amount of historical shipping and trading data could be analyzed to help companies make predictions.
The freight shipment system has to handle a large volume of multidimensional data, dynamically changing data, and multiple objectives. There are thousands of freight forwarders on the current system. A visitor from factories or freight companies can search the price of forwarding courses. The search keywords contain source port, destination port, the schedule of ships, the name of shipping company, etc. The search could be one keyword or the combination of keywords. The visitors’ identification, login time, logout time are also recorded in the system.
Based on the analysis among the browsing data, search data and trading data, the hot course, potential quantity of goods for different courses, the future market price (based on regions, on ports, on historical data of a single company) could be predicted. The future market price for different courses could be predicted. From the predicted price, the potential quantity of goods, and the capacity of forwarders, the system could give a recommendation price to obtain the largest benefits for different forwarders.
The data analytics and optimization are combined together in this case. This realworld application could be modeled as a dynamic, large scale optimization problem. A more detailed example of a commodity routing system in the Ningbo port is introduced in [86]. Based on the data analytics, the optimization model could help the forwarders to obtain the largest profits.
Key challenges and future directions
Key challenges
A rough association between big data analytics and populationbased algorithms
Big data analytics  Populationbased algorithms 

Volume  Large scale/high dimension 
Variety  
Velocity  Dynamic environment 
Veracity  Noise/uncertain/surrogates 
Value  Fitness/objective 
There are five accepted properties of big data, which are volume, variety, velocity, veracity, and value. These complexities are a collection of different research problems that existed for decades. Corresponding to the populationbased algorithms, the volume and the variety mean largescale and high dimensional data; the velocity means data is rapidly changing, like an optimization problem in dynamic environment; the veracity means data is inconsistent and/or incomplete, like an optimization problem with noise or approximation; and the value is the objective of the big data analytics, like the fitness or objective function in an optimization problem.
The key challenges of populationbased metaheuristics algorithms solving big data analytics problems could be divided into four elements: handling a large amount of data, handling high dimensional data, handling dynamical data, and multiobjective optimization. Most real world big data problems can be modeled as a large scale, dynamical, and multiobjective problems.
Future directions
The future direction is combining the strengths of populationbased algorithms and big data analytics to design new algorithms on the optimization or data analytics.
Populationbased algorithms for big data problems
The big data is created in many areas in our everyday life. The big data analytics problem not only occurs in Internet data mining, but also in complex engineering or design problems [39]. The big data problem could be analyzed from the perspective of computational intelligence and metaheuristic global optimization [87]. A realworld application could be modeled as a multiobjective, dynamic, large scale optimization problem. It is recognized that the populationbased algorithms are good ways to handle this kind of problems. Based on the utilization of swarm intelligence algorithms, the realworld system will be more efficient and effective [45, 86].
Big data analytics for populationbased algorithms
A population of individuals in Populationbased algorithms is utilized to evolve the optimized functions or goals by cooperative and competitive interaction among individuals. Massive information exists during the search process, such as the distribution of individuals and the fitness of each solution. To improve the search efficiency or to recognize the search state, the data generated in the optimization process should be analyzed.
Conclusions
In swarm intelligence and evolutionary algorithms, a population of individuals is utilized to evolve the optimized functions or goals by cooperative and competitive interaction among individuals. Massive information exists during the search process, such as the distribution of individuals and the fitness of each solution. To improve the search efficiency or to recognize the search state, the data generated in the optimization process should be analyzed.
With the amount of data growing constantly and exponentially, the data processing tasks have been beyond the computing ability of traditional computational models. To handle these massive data, i.e., deal with the big data analytics problem, more effective and efficient methods should be designed. There is no complex mathematical model in swarm intelligence/evolutionary algorithms. The algorithm is updated based on few iterative rules and the evaluation of solution samples. The massive data analytics may be benefited from these properties because massive data are difficult or impossible represented by mathematical models.
This paper has reviewed the connection between data science and swarm intelligence/evolutionary algorithms. The potential combination of data science and swarm intelligence/evolutionary algorithm in optimization and data analytics was also analyzed. Data science involves prediction or inference on a large amount of data. Swarm intelligence studies the collective behaviors in a group of individuals. With the combination of data science, swarm intelligence and evolutionary algorithms, more rapid and effective methods can be designed to solve optimization and data analytics problem.
Abbreviations
ACO, ant colony optimization; AIS, artificial immune system; BSO, brain storm optimization; EA, evolutionary algorithm; EC, evolutionary computation; EDA, estimation of distribution algorithms; FWA, fireworks algorithms; GA, genetic algorithm; GP, genetic programming; PSO, particle swarm optimization; SI, swarm intelligence
Declarations
Acknowledgements
This work is partially supported by Natural Science Foundation of China under grant no. 71402103, 60975080, 61273367, 61571238, 61302158 and 61473236, the Natural Science Foundation of Jiangsu Province (BK20141005), the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (14KJB520025), Foundation for Distinguished Young Talents in Higher Education of Guangdong, China, under grant 2012WYM_0116 and the MOE Youth Foundation Project of Humanities and Social Sciences at Universities in China under grant 13YJC630123, and Ningbo Science & Technology Bureau (Science and Technology Project No.2012B10055).
Authors’ contributions
SC and BL planned and drafted the content of the paper. Both authors, together with TOT and YS, wrote the paper. Other authors participated in critical revision of the manuscript and approved the final submission.
Competing interests
The authors declare that they have no competing interests.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License(http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
Authors’ Affiliations
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