G. S. Mahapatra

Robust feedforward and recurrent neural network based dynamic weighted combination models for software reliability prediction

Traditional parametric software reliability growth models (SRGMs) are based on some assumptions or distributions and none such single model can produce accurate prediction results in all circumstances. Non-parametric models like the artificial neural network (ANN) based models can predict software reliability based on only fault history data without any assumptions. In this paper, initially we propose a robust feedforward neural network (FFNN) based dynamic weighted combination model (PFFNNDWCM) for software reliability prediction. Four well-known traditional SRGMs are combined based on the dynamically evaluated weights determined by the learning algorithm of the proposed FFNN. Based on this proposed FFNN architecture, we also propose a robust recurrent neural network (RNN) based dynamic weighted combination model (PRNNDWCM) to predict the software reliability more justifiably. A real-coded genetic algorithm (GA) is proposed to train the ANNs. Predictability of the proposed models are compared with the existing ANN based software reliability models through three real software failure data sets. We also compare the performances of the proposed models with the models that can be developed by combining three or two of the four SRGMs. Comparative studies demonstrate that the PFFNNDWCM and PRNNDWCM present fairly accurate fitting and predictive capability than the other existing ANN based models. Numerical and graphical explanations show that PRNNDWCM is promising for software reliability prediction since its fitting and prediction error is much less relative to the PFFNNDWCM.

Entropy based region reducing genetic algorithm for reliability redundancy allocation in interval environment

Abstract This research paper presents a multi-objective reliability redundancy allocation problem for optimum system reliability and system cost with limitation on entropy of the system which is very essential for effective sustainability. Both crisp and interval-valued system parameters are considered for better realization of the model in more realistic sense. We propose that the system cost of the redundancy allocation problem depends on reliability of the components. A subpopulation and entropy based region reducing genetic algorithm (GA) with Laplace crossover and power mutation is proposed to determine the optimum number of redundant components at each stage of the system. The approach is demonstrated through the case study of a break lining manufacturing plant. A comprehensive study is conducted for comparing the performance of the proposed GA with the single-population based standard GA by evaluating the optimum system reliability and system cost with the optimum number of redundant components. Set of numerical examples are provided to illustrate the effectiveness of the redundancy allocation model based on the proposed optimization technique. We present a brief discussion on change of the system using graphical phenomenon due to the changes of parameters of the system. Comparative performance studies of the proposed GA with the standard GA demonstrate that the proposed GA is promising to solve the reliability redundancy optimization problem providing better optimum system reliability.

An Ant colony optimization approach for binary knapsack problem under fuzziness

In this paper, we represent a novel ant colony optimization algorithm to solve binary knapsack problem. In the proposed algorithm for n objects, n candidate groups are created, and each candidate group has exactly m values (for m ants) as 0 or 1. For each candidate value in each group a pheromone is initialized by the value between 0.1 and 0.9, and each ant selects a candidate value from each group. Therefore, the binary solution is generated by each ant by selecting a value from each group. In each generation, pheromone update and evaporation is done. During the execution of algorithm after certain number of generation the best solution is stored as a temporary population. After that, crossover and mutation is performed between the solution generated by ants. We consider profit and weight are fuzzy in nature and taken as trapezoidal fuzzy number. Fuzzy possibility and necessity approaches are used to obtain optimal decision by the proposed ant colony algorithm. Computational experiments with different set of data are given in support of the proposed approach.

Neuro-genetic approach on logistic model based software reliability prediction

We propose ANN based logistic growth curve model (LGCM) of software reliability.We propose neuro-genetic approach for ANN based LGCM by optimizing ANN using GA.Proposed model is compared with NHPP and ANN based software reliability models.ANN based LGCM has better fitting and predictive capability than other models.If GA is applied to train ANN based LGCM, it will give upmost prediction accuracy. In this paper, we propose a multi-layer feedforward artificial neural network (ANN) based logistic growth curve model (LGCM) for software reliability estimation and prediction. We develop the ANN by designing different activation functions for the hidden layer neurons of the network. We explain the ANN from the mathematical viewpoint of logistic growth curve modeling for software reliability. We also propose a neuro-genetic approach for the ANN based LGCM by optimizing the weights of the network using proposed genetic algorithm (GA). We first train the ANN using back-propagation algorithm (BPA) to predict software reliability. After that, we use the proposed GA to train the ANN by globally optimizing the weights of the network. The proposed ANN based LGCM is compared with the traditional Non-homogeneous Poisson process (NHPP) based software reliability growth models (SRGMs) and ANN based software reliability models. We present the comparison between the two training algorithms when they are applied to train the proposed ANN to predict software reliability. The applicability of the different approaches is explained through three real software failure data sets. Experimental results demonstrate that the proposed ANN based LGCM has better fitting and predictive capability than the other NHPP and ANN based software reliability models. It is also noted that when the proposed GA is employed as the learning algorithm to the ANN, the proposed ANN based LGCM gives more fitting and prediction accuracy i.e. the proposed neuro-genetic approach to the LGCM provides utmost predictive validity. Proposed model can be applied during software testing time to get better software reliability estimation and prediction than the other traditional NHPP and ANN based software reliability models.

An S-shaped software reliability model with imperfect debugging and improved testing learning process

In this paper, we propose a non-homogeneous Poisson process (NHPP) based S-shaped software reliability growth model (SRGM) in presence of imperfect debugging with a new exponentially increasing fault content function and S-shaped fault detection rate. We develop the fault content function considering learning capability of testing team during software development process. Fault content increases rapidly at the beginning of testing process while it grows gradually at the end of testing process due to increasing efficiency of testing team with testing time. We use maximum likelihood estimation (MLE) method to estimate model parameters. Applicability of the proposed model has been presented by comparing with established models in terms of goodness of fit and predictive validity using two software failure data sets. Experimental results show that the proposed model gives better fit to real failure data sets and predicts future failure behaviour of software development accurately than established models.

A genetic ant colony optimization based algorithm for solid multiple travelling salesmen problem in fuzzy rough environment

In this paper, a genetic-ant colony optimization algorithm has been presented to solve a solid multiple Travelling Salesmen Problem (mTSP) in fuzzy rough environment. In solid mTSP, a set of nodes (locations/cities) are given, and each of the cities must be visited exactly once by the salesmen such that all of them start and finish at a depot using different conveyance facility. A solid mTSP is an extension of mTSP where the travellers use different conveyance facilities for travelling from one city to another. To solve an mTSP, a hybrid algorithm has been developed based on the concept of two algorithms, namely genetic algorithm (GA) and ant colony optimization (ACO) based algorithm. Each salesman selects his/her route using ACO and the routes of different salesmen (to construct a complete solution) are controlled by the GA. Here, a set of simple ACO characteristics have further been modified by incorporating a special feature namely ‘refinement’. In this paper, we have utilized cyclic crossover and two-point’s mutation in the proposed algorithm to solve the problem. The travelling cost is considered as imprecise in nature (fuzzy-rough) and is reduced to its approximate crisp using fuzzy-rough expectation. Computational results with different data sets are presented and some sensitivity analysis has also been made.

Network reliability evaluation for fuzzy components: An interval programming approach

The probabilistic reliability estimation of complex system is complicated due to uncertainty of failure data, modeling or human failure. In this paper, reliability of components of complex network system is considered as fuzzy in nature to reduce the uncertainty. Trapezoidal fuzzy number is used to represent component’s reliability of network system. Then the reliability of the network system is assembled with fuzzy reliability of components and evaluated by Zadeh’s extension principle. Fuzzy reliability of the network system becomes an interval by -cuts operation. Interval nonlinear programming is used to evaluate the optimum network’s system reliability with interval valued cost constraint. The above approach is explained in details through a numerical example of very useful power system network of electrical engineering.

A new concept for fuzzy variable based non-linear programming problem with application on system reliability via genetic algorithm approach

Fuzziness is the primary and foremost perception of science and technology. This paper, for the first time, introduces a new concept on solution technique for fuzzy variable based non-linear programming problem with both decision variables and restriction being fuzzy in nature. First the problem is transformed in to a multi-objective non-linear programming problem, and then solving it by multiobjective genetic algorithm (MOGA) approach. The proposed procedure is applied on complex system reliability model to evaluate the system reliability in fuzzy environment, using MOGA by implementing new feature as refining operation. Numerical example is presented to illustrate proposed fuzzy system reliability model.

Fuzzy variable based fuzzy non-linear programming approach for optimization of complex system reliability

All most all systems in the field of science and technology are well complicated by the advent of modernity. Complex system reliability is mainly dependant on the credibility of its components. It is very difficult to evaluate precise value of components reliability at the beginning stage of reliability evaluation, due to unavailable or inadequate information. In this respect, fuzzy reliability variable can play an important role in complex system reliability evaluation. In this paper, a fuzzy reliability variable based fuzzy non-linear programming problem is formulated to maximize the complex system reliability. Symmetrical trapezoidal fuzzy numbers are used as fuzzy variable for the components reliability. Since fuzzy variable for optimization is not well defined, we first reduced the problem to an equivalent multi-objective non-linear programming problem. The proposed approach is applied on landing system of Boeing 747D airplane to evaluate the system reliability in fuzzy environment. The proposed approach and the complex system reliability model are well substantiated by providing numerical examples.

Neural network for software reliability analysis of dynamically weighted NHPP growth models with imperfect debugging

This paper propose a learning algorithm of supervised back‐propagation neural networks for dynamic weighted combination of software reliability model. The proposed model is an assimilation of 3 well‐known non‐homogeneous poisson process (NHPP)–based software reliability growth models with imperfect debugging. The novel approach of proposed supervised back propagation–based neural network 2‐stage architecture has a great impact on the network by combining the imperfect debugging models based on the nature of fault introduction rate during testing and debugging. Function approximation metrics are used for comparing the proposed model with individual models. Three data sets are trained using supervised back‐propagation neural networks to compare the performance and validity evaluation of proposed and existing NHPP models and dynamic weighted combinational model. Reliability analysis among important NHPP models incorporating imperfect debugging is illustrated through numerical and graphical explanation of several metrics using supervised back‐propagation neural networks.