An improved NSGA-III algorithm with adaptive mutation operator for Big Data optimization problems

doi:10.1016/j.future.2018.06.008

Future Generation Computer Systems

Volume 88, November 2018, Pages 571-585

https://doi.org/10.1016/j.future.2018.06.008 Get rights and content

Highlights

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An adaptive mutation operator is introduced to enhance the performance of NSGA-III.
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The proposed adaptive mutation operator strategy is evaluated on three crossover operators of NSGA-III.
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Three improved NSGA-III algorithms are developed.
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The proposed NSGA-III algorithms are implemented to solve an array of Big Data optimization problems.

Abstract

One of the major challenges of solving Big Data optimization problems via traditional multi-objective evolutionary algorithms (MOEAs) is their high computational costs. This issue has been efficiently tackled by non-dominated sorting genetic algorithm, the third version, (NSGA-III). On the other hand, a concern about the NSGA-III algorithm is that it uses a fixed rate for mutation operator. To cope with this issue, this study introduces an adaptive mutation operator to enhance the performance of the standard NSGA-III algorithm. The proposed adaptive mutation operator strategy is evaluated using three crossover operators of NSGA-III including simulated binary crossover (SBX), uniform crossover (UC) and single point crossover (SI). Subsequently, three improved NSGA-III algorithms (NSGA-III SBXAM, NSGA-III SIAM, and NSGA-III UCAM) are developed. These enhanced algorithms are then implemented to solve a number of Big Data optimization problems. Experimental results indicate that NSGA-III with UC and adaptive mutation operator outperforms the other NSGA-III algorithms.

Introduction

As the world steadily becomes more connected, more and more data is being created leading to the generation of huge volumes of structured and unstructured data, commonly referred to as “Big Data” [[1], [2]]. The outburst of Big Data concept has raised the concerns about developing efficient optimization methods that can provide immense power and capabilities to address associated problems. The traditional optimization techniques generate only one function value at each run and lack of parallelism. In addition, they often demand a long time to get a satisfactory solution. The inherent drawbacks of the traditional optimization techniques push scientists toward modern intelligent optimization techniques such as swarm intelligence [[3], [4], [5], [6]], evolutionary algorithms (EAs) [[7], [8]].

The performance of the commonly-used EAs eventually diminish to a large extent while addressing Big Data optimization problems that include numerous decision variables. On the other hand, for Big Data optimization problems, a fast real-time processing is an essential requirement. The convergent speed of EAs is heavily influenced by two main operators that are mutation and crossover operators [[9], [10]]. Up to now, several studies have been carried out to design more efficient mutation and crossover operators with the aim of improving the performance of EAs.

Genetic algorithm, the third version, (NSGA-III) is a fairly new multi-objective evolutionary algorithm (MOEA) [[11], [12]]. While studies have been implemented to improve the performance of NSGA-III algorithm, none of them have presented more in-depth analysis of its mutation and crossover operators. The basic NSGA-III algorithm uses a fixed rate for mutation operator to solve various optimization problems. Though NSGA-III is one of the most powerful and representative MOEAs, it may generate unsatisfactory results on certain complicated problems because of the fixed rate for mutation opertor. In the present study, we investigate the performance of NSGA-III on complicated high-dimensional multi-objective problems (MOP) [13] with many decision variables. An adaptive mutation operator is introduced for the NSGA-III algorithm to improve its performance. On this basis, three variants of NSGA-III are proposed and implemented to solve a number of Big Data optimization problems. The remained of the paper is organized as follows: Section 2 reviews mostrepresentative works in the area of Big Data optimization problems. In Section 3,the basic NSGA-III is presented. Adaptive mutation operator is detailed in Section 4. The Big Data optimizationproblem are described in Section 5. Section 6 presents the simulation results on IEEE CEC 2015 Big Data competition problems. Finally, Section 7 provides a summary of the present work.

Section snippets

Related work

Over the past decade, several multi-objective optimization(MOO) techniques have been developed. In this context, MOEAs are perhaps the most widely-used techniques for tackling the MOO problems. Some well-known MOEAs are: non-dominated sorting GA [14], multi-objective particle swarm optimization (MOPSO) [15], strength-Pareto EA (SPEA) [16], NSGA-IIs [17], Pareto archived ES (PAES) [18], multi-objective fruit fly optimization algorithm [19], reference-vector-guided evolutionary algorithm (RVEA) [

NSGA-III

NSGA-III is an extension to the standard NSGA-II algorithm. In order to understand how NSGA-II algorithm evolves at $t$ th generation, assume that the parent population at this generation is $P_{t}$ that has $N$ individuals, and the generated offspring population is $Q_{t}$ having $N$ individuals. First, the optimal $N$ individuals are chosen from the combined population $R_{t}$ $=$ $P_{t} \cup Q_{t}$ (having 2 $N$ individuals). The population $R_{t}$ is sorted according to different nondomination levels ( $F_{1}$ , $F_{2}$ , and so on). Then, one individual is

Mutation operator

In the standard NSGA-III, the SBX crossover operator and mutation operator with fixed crossover rate and mutation rate are used to generate new chromes/individuals [11]. In this paper, an adaptive strategy is used to adjust the mutation rate, and then an improved version of mutation rate is proposed. The proposed adaptive mutation operator is further combined with three crossover operators (SBX, SI, and UC) in order to generate new chromes/individuals. Accordingly, three variants of NSGA-III

Big Data optimization problems

Six variants of NSGA-IIIs are verified using a number of Big Data optimization problems originated from 2015 Big Data Competition [13]. These problems involve thousands of variables. In several of the previous studies, the number of fitness evaluations (NFES) is used as performance indicator. In this paper, the maximum generation is considered as an indicator because of the same population size. The analyzed Big Data optimization problems are stemmed from the electroencephalographic (EEG)

Performance analysis of the NSGA-III variants

The considered Big Data optimization problems are D4, D4N, D12, D12N, D19, and D19N. The “N” is noisy that indicates the noisy element at 0.1 is introduced into the original dataset. More detailed information about the introduced noise can be found in [[13], [68]]. The parameter settings adopted in the present work are provided in Table 1.

Zitzler [69] has introduced a widely-used indicator called Hypervolume (HV) which can provide the performance of both the exploitation and the exploration of

Conclusions

The present study introduces a novel adaptive mutation operator for the NSGA-III algorithm. Three enhanced NSGA-III algorithms (NSGA-III SBXAM, NSGA-III SIAM,and NSGA-III UCAM) are proposed based on this concept. The performance of these algorithm along with the standard NSGA-III with SBX, SI, and UC operators is evaluated on six Big Data optimization problems stemmed from the EEG data processing. As one would expect, the performance of the adaptive mutation strategy on NSGA-III is dependent on

Acknowledgments

This work was supported by the National Natural Science Foundation of China (No. 61503165, No. 41576011, No. 41706010, and No. U1706218) and Natural Science Foundation of Jiangsu Province(No. BK20150239).

Jiao-Hong Yi is a researcher at School of Information and Control Engineering, Qingdao University of Technology. Her main research interests are intelligent algorithm, communications, and geodetic engineering.

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An improved NSGA-III algorithm with adaptive mutation operator for Big Data optimization problems

Highlights

Abstract

Introduction

Section snippets

Related work

NSGA-III

Mutation operator

Big Data optimization problems

Performance analysis of the NSGA-III variants

Conclusions

Acknowledgments

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