Backpropagation Neural Network optimization and software defect estimation modelling using a hybrid Salp Swarm optimizer-based Simulated Annealing Algorithm

Abstract

Software Defect Estimation (SDE) is a fundamental problem solving mechanism in the field of software engineering (SE). SDE is a task that identifies software models that are likely to have defects. In addition, SDE plays a vital overall role in improving software quality, reducing software development costs and accelerating software development processes. The Backpropagation Neural Network (BPNN) is a popular machine learning (ML) estimator widely utilized in SE estimation problems. Unfortunately, its performance depends on the initial weight and bias values. Metaheuristic optimization algorithms, as an alternative method, have proven to have strengths in parameter optimizations. Additionally, population-based metaheuristic algorithms suffer from low exploitation capabilities. In this paper, a new hybrid metaheuristic algorithm-based BPNN (SSA–SA) is proposed by hybridizing the Salp Swarm Algorithm (SSA) with the Simulated Annealing (SA) algorithm. The main goal of the hybridization is to adjust the balance between exploration and exploitation in SSA. The proposed algorithm is also assembled with the BPNN estimator to optimize its parameters to reduce the overall estimation error, which boosts the estimation accuracy. Thus, the proposed algorithm addresses the SDE problem. Experimental results prove the superiority of the proposed hybrid algorithm in optimizing BPNN parameters in comparisons against other estimators and algorithms in most SDE datasets and evaluation criteria.

Introduction

In machine learning (ML) research communities, many models have been proposed to address various software engineering estimation problems [1], [2]. The software defect estimation (SDE) problem [3] is one of these significant problems. The estimation process is considered a supervised learning technique and a pattern discovery based on historical data.

In the last decade, a significant amount of research has been done in the field of SDE using ML methods to address the limitations of traditional and parametric estimation methods and to align with existing development and management strategies [4], such as Artificial Neural Networks (ANNs) [5], [6], [7], [8], Bayesian Network (BN) [9], Multilayer Perception (MLP) [9], Fuzzy Clustering (FC) [10], Case-based Reasoning (CR) [11], Logistic Regression (LR) [10], Decision Trees [12], Naïve Bayes [13] and Support Vector Machines (SVMs) [14], [15], [16].

Artificial neural networks (ANNs) are a prominent type of ML technology. In addition, Backpropagation Neural Networks (BPNNs) are also one of the most popular types of ANNs [17], as they have a reliable training algorithm that enables them to address both common and complex problems [18], in addition to their accuracy and self-organizing capabilities for estimation problems [19], [20], [21]. Consequently, BPNN is more broadly used for estimation problems as compared to other ML techniques [22], [23]. Unfortunately, the traditional BPNN training algorithm has some limitations, such as easily falling into a local optimum trap [24], [25], the need for extensive parameter settings [26], and a slow convergence rate [24]. Therefore, it is essential to define a metaheuristic optimizer that can be integrated with BPNN to overcome these limitations, which will be a valuable contribution to the research community.

Recently, several studies have integrated metaheuristic algorithms with ANNs for the purpose of optimizing ANN parameters to boost estimation accuracy [1], [3], [27]. These studies utilized the Salp Swarm Algorithm to optimize the Backpropagation Neural Network to boost its estimation accuracy to model software reliability and software fault estimation problems. In addition, to estimate the team size of the software testing phase workers, Kassaymeh et al. [28] some studies combined the Salp Swarm Algorithm with an ANN predictor to enhance the accuracy of its estimation [28]. These integration attempts succeeded in developing new models that performed better than other traditional estimation methods [29], [30]. Furthermore, the integration improved the BPNN estimation accuracy, thus overcoming the performance drawbacks [31].

Recently, by mimicking the navigation and foraging behaviour of salps in the sea environment, a new stochastic, nature-inspired, metaheuristic optimizer, namely, the Salp Swarm Algorithm (SSA), was proposed [32] to address global optimization issues. SSA has been applied to a wide range of optimization problems and has proven its robustness as an effective optimizer. Some of its applications include feature selection [33], [34], [35], estimation and forecasting [36], [37], [38], [39], image thresholding [40], multiobjective problems [34] and constrained engineering optimization problems [41].

The robustness of the SSA is due to the presence of fewer parameters to be tuned [42] and its ability to handle a wide range of engineering optimization problems [3]. Despite the aforementioned, the SSA still suffers from some limitations, such as a low exploitation ability, which can lead to slow convergence behaviour [24], [43]. To address these limitations, SSA must be hybridized using a local search algorithm with strong exploitation capabilities. Recently, a local search algorithm called the Simulated Annealing Algorithm (SA) [44], which has proven its ability in many optimization problems and has been examined in numerous hybridization studies with many population-based metaheuristic algorithms, was hybridized with SSA for the purpose of balancing search exploration and exploitation.

In this paper, a new hybrid metaheuristic algorithm-based BPNN called SSA–SA is proposed by hybridizing the SSA optimizer with the SA algorithm. The main motivation behind selecting the SSA algorithm is due to several SSA characteristics, such as its ease of use [45], superior performance [46], [47], [48], [49], [50], ease of tailoring [45], [46], [51], convergence speed [51], effective optimization [25], [48], [52] and high robustness [25]. On the other hand, the SA algorithm has unique exploitation abilities [53], [54], boosting the SSA algorithm in local search exploitation [55] and also has the ability to enhance the balance between exploitation and exploration when hybridized with population-based metaheuristic algorithms [56], [57]. Therefore, this study utilizes a combination of the SSA and SA algorithms to combine the benefits of both algorithms and remove their drawbacks. The hybrid algorithm is also integrated with the BPNN estimator to optimize its parameters (weights and biases) to reduce the total estimation error, which in turn boosts the estimation’s accuracy [58]. In addition, the proposed algorithm is utilized to address the software defect estimation (SDE) problem. Experimental results proved the superiority of the proposed hybrid algorithm in optimizing BPNN parameters in comparisons against the traditional BPNN estimator, the standard SSA algorithm and other state-of-the-art algorithms in most SDE datasets and evaluation criteria.

This paper is organized as follows: The research background is reviewed in Section 2. The software defect estimation problem is explored in Section 3. The proposed algorithm is described in Section 4. The experimental results and performance evaluation are presented and discussed in Section 5. The conclusion and prospects for future work are provided in Section 6.