Research on Generation Methods of Test Cases for Pair-wise Covering Combinatorial Test Cases

Combinatorial testing has lots of test cases, but software testers hope to get the best test coverage with the smallest test case suite. For the scale of produced test cases is so large that researchers have considered the implementation of the critical test cases. This article researches the classic combinatorial test methods and proposes methods to generate pair-wise testing cases with a priority. Firstly, we design formulas to compute the weights of priorities. Secondly, we adopt a greed algorithm to solve the combinatorial testing problems. Furthermore, we integrate the greed strategy into a genetic algorithm to improve the efficiency. It improves the testing efficiency while securing the detection rate of defects under limited resources.

Pairwise testing is a combinatorial testing technique that tests all possible pairs of input values. Although, finding a smallest set of test cases for pairwise testing is NP-complete, pairwise testing is regarded as a reasonable cost-benefit compromise among combinatorial testing methods. In this paper we formulate the problem of finding a pairwise test set as a search problem and apply a genetic algorithm to solve it. We also describe an open-source tool called PWiseGen for generating pairwise test sets. PWiseGen produces competitive results compared with existing pairwise testing tools. Besides, it provides a framework and a research platform for generating pairwise test sets using genetic algorithms; it is configurable, extensible, and reusable.

Despite recent progress in automated test generation research, significant challenges remain for applying these techniques on large-scale software systems. These systems under test often require structurally complex test inputs within a large input domain. It is challenging to automatically generate a reasonable number of tests that are both legal and behaviorally-diverse to exercise these systems. Constraint-based test generation is an effective approach for generating structurally complex inputs for systematic testing. While this approach can typically generate large numbers of tests, it has limited scalability – tests generated are usually only up to a small bound on input size. Combinatorial test generation, e.g., pair-wise testing, is a more scalable approach but is challenging to apply on commercial software systems that require complex input structures that cannot be formed by using arbitrary combinations. This paper introduces comKorat, which unifies constraint-based generation of structurally complex tests with combinatorial testing. Specifically, comKorat integrates Korat and ACTS test generators to generate test suites for large scale software systems with structurally complex test inputs. We have successfully applied comKorat on four software applications developed at eBay and Yahoo!. The experimental results show that comKorat outperforms existing solutions in execution time and test coverage. Furthermore, comKorat found a total of 59 previously unknown bugs in the four applications.

Verification tool for Vienna Development Method (BWDM) is a test case generation tool for the VDM++ specification. The existing BWDM could cause a combinatorial explosion of the generated test cases. To reduce the number of test cases, there is Pairwise Independent Combinatorial Testing Tool (PICT): a pairwise testing tool. We apply pairwise testing into BWDM. Here, BWDM cannot call PICT library directly. Hence, we have developed PICT-wrapper. It is an interface to connect PICT and BWDM. The extended BWDM eliminate the possibility of the combinatorial explosion.

Combinatorial testing (CT) is a well-known technique for improving the quality of test plans while reducing testing costs. Traditionally, CT is used by testers at testing phase to design a test plan based on a manual definition of the test space. In this work, we extend the traditional use of CT to other parts of the development life cycle. We use CT at early design phase to improve design quality. We also use CT after test cases have been created and executed, in order to find gaps between design and test. For the latter use case we deploy a novel technique for a semi-automated definition of the test space, which significantly reduces the effort associated with manual test space definition. We report on our practical experience in applying CT for these use cases to three large and heavily deployed industrial products. We demonstrate the value gained from extending the use of CT by (1) discovering latent design flaws with high potential impact, and (2) correlating CT-uncovered gaps between design and test with field reported problems.

Combinatorial test case generation faces a problem on how to reduce the test cases by uncover the unnecessary test cases. So, there is a need for expert applications or strategies that generate the most optimum test cases keeping in mind the most important combinations. Complementing existing work on combinatorial test case generation strategies, also known as t-way testing strategies (i.e., where t represents interaction degree), this paper presents the design and the implementation of a new combinatorial test list generation strategy based on Harmony Search (HS) algorithm, called General T-way Harmony Search-based Strategy (GTHS). HS has been chosen to be the main engine of test generation because it could balance between intensification and diversification. Benchmarking experimental results show that GTHS produces competitive results as compared to other existing well-known optimization-based strategies and provides the support for high combination degrees (i.e., t ≤ 12).

Although combinatorial testing has been widely studied and used, there are still some situations and requirements that combinatorial testing does not apply to well, such as a system under test whose test cases need to be performed contiguously. For thorough testing, the testing requirements are not only to cover all the interactions among factors but also to cover all the value sequences of every factor. Generally, systems under test always involve constraints and dependencies in or among test cases. The constraints among test cases have not been effectively specified. First, we introduce extended covering arrays that can achieve both t-way combinatorial coverage and t-wise sequence coverage, and propose a clocked computation tree logic-based formal specification method for specifying constraints. Then, Particle Swarm Optimization (PSO) based Extended covering array Generator (PEG) is elaborated. To evaluate the constructed test suites, a method for verifying the constraints’ validity is presented, and kernel functions for measuring the coverage are also introduced. Finally, the performance of the proposed PEG is evaluated using several sets of benchmark experiments for some common constraints, and the feasibility and usefulness of PEG is validated.

Testing is considered as indispensable part in the development process life cycle of any software. Testing is performed to improve the performance, quality and reliability of the software. Designing of relevant test cases plays a major role in deciding the quality of testing. Hence test case designing activity is crucial for the success of testing. Combinatorial strategies are one of those most extensively used methods for generating test cases. These strategies detect failures which are caused by interactions of parameters in the Software under Test(SUT) and by using some sampling mechanisms a covering array test suite is generated. With increase in the number of parameter coverage, the t-way test size sets also increase exponentially which would result in explosion problem. This paper presents a technique to generate minimal test suites in Combinatorial testing(CT). Optimization technique used is Greedy computation strategy for mutation and selection of test cases, used in selecting the locally worst test case for elimination. That is the test case that does not cover maximum number of uncovered interactions from a pool of candidate test cases. Additionally, Branch and bound technique is used for cross over. It is used to branch for the possibilities of number of test cases as cross over inputs. If a particular test case is not possible the bounding happens, else branched for further selection of test cases as input. Experimental results show that Recast Ipog-D generates better/comparable results as compared to the existing algorithm. Additionally, Recast IPOG-D has also contributed to enhance many known Variable Strength Covering array(VSCA) that exist in literature.

A test scenario generation method based on combinatorial testing (CT) and Bayesian Network for autonomous vehicles is proposed in this paper. Firstly, some parameters are selected to describe the test scenarios which are classified according to road types and driving tasks. Then, the constraint sets for the scenarios with forbidden tuples are established to avoid the generated cases do not conform to the reality, in which the construct constraint set (CCS) algorithm is utilized to compute implied constraints. Furthermore, the Bayesian networks is used as the probabilistic models of the scenarios, where the traffic participants are represented as object nodes and the relative relationships between the participants are converted into the network structures. Finally, an improved automatic efficient test case generator (AETG) is developed to generate test cases. By considering both probability and frequency, the select function is designed for determining the values of scenario parameters. And the generation mode can be changed by modifying the weight and target parameters. The effectiveness of the proposed method is evaluated by generating six typical test scenarios. Compared with other algorithms, the numbers of test cases in the sets generated by this method are less and the probability deviations are smaller.

Software testing is required to verify and validate systems. Combinatorial testing in one of the significant testing techniques. Design and select test cases for combinatorial testing considered as combinatorial problem. Even though there are some existing optimization algorithm based combinatorial testing strategies, that minimize the number of test cases, but most of these strategies based on one-test-at-a-time (OTAT) approach and none of them has adopted the one-parameter-at-a-time (OPAT) approach. Therefore, this paper will propose a new OPAT strategy based on Harmony Search Algorithm (HS) called OPAT-HS. OPAT-HS was originally designed only to support Covering Array (CA) and Mixed Covering Array (MCA) for uniform interaction strength. The result obtained in the experiments appears that OPAT-HS is always best at configurations with MCA notations.

In last three decades, lot of research work has been done by statisticians and academicians (D. Richard Kuhn, Raghu N. Kacker, Vu Lei, Ljubomir Lazic, Sloane, Neil J. A., Madhav Phadke, D. M. Cohen, James Bach and others) in the field of Combinatorial testing (CT) and its use in software testing. However, its tremendous potential in terms of test optimization and fault detection is yet to be exploited to its fullest. This paper showcases some of the real-world examples from iGATE Corporation, where CT has been used successfully to achieve breakthrough results in software testing. The paper, through three case studies taken from different domains describes the challenges faced by testing teams in terms of test scenario complexities, schedule and budget constraints; and how CT helped resolve those challenges successfully. Our experience shows 60 to 70 percent benefits in terms of optimization of test efforts while enhancing test case coverage. In the end, the paper highlights some learnings from our experiences in implementing CT approach which may be of help to fellow practitioners.

Combinatorial testing is a prevailing approach to finding out faults in the extremely complex systems of train operation for railway. While combinatorial testing is applied to Chinese Train Control Systems (CTCS) for revealing faults, some potential faults tend to be arduous to trigger due to the interaction of multiple test cases. For the sake of accurate and efficient fault localization of CTCS under the circumstances of masking effects, a novel method of locating the faults of CTCS using the relationship matrix with frequent terms has been proposed in the paper. To begin with, failed test cases from CTCS were made full use of to calculate the frequentness of failure‐inducing elements for ordered tables. Then, the relationship matrix with frequent terms for CTCS was established to work out the suspiciousness of failure‐inducing combinations by the following relation of failure‐inducing elements in the above tables. Furthermore, an iterative approach to locating failure‐inducing combinations was adopted to obtain the full list of rankings of failure‐inducing combinations, among which top combinations, especially MFS (Minimal Failure‐causing Schema), were prone to discover the faults of CTCS. Finally, the effectiveness and accuracy of the proposed method for CTCS was confirmed on the simulation platform of CTCS for Beijing‐Shenyang High‐speed Rail. Empirical studies suggest that compared to the method of fault forest, the average suspiciousness in the proposed method is 12.17% higher than that and the number of additional test cases are reduced by 31.7% on average, which can produce more precise and efficient results of identifying the faults of CTCS in case of masking effects. The research achievements can provide some references for the safety evaluation and system optimization of CTCS for high‐speed rail. © 2022 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Usage of combinatorial testing is wide spreading as an effective technique to reveal unintended feature interaction inside a given system. To this aim, test cases are constructed by combining tuples of assignments of the different input parameters, based on some effective combinatorial strategy. The most commonly used strategy is two-way (pairwise) coverage, requiring all combinations of valid assignments for all possible pairs of input parameters to be covered by at least one test case. In this paper a new heuristic strategy developed for the construction of pairwise covering test suites is presented, featuring a new approach to support expressive constraining over the input domain. Moreover, it allows the inclusion or exclusion of ad-hoc combinations of parameter bindings to let the user customize the test suite outcome. Our approach is tightly integrated with formal logic, since it uses test predicates to formalize combinatorial testing as a logic problem, and applies an external model checker tool to solve it. The proposed approach is supported by a prototype tool implementation, and early results of experimental assessment are also presented.

Due to the complexity of the nuclear industrial distributed control system (DCS), input-domain testing techniques, including random testing and combinatorial testing, are usually utilized to test the control logics in nuclear industrial DCS. To improve the fault detection efficiency of random testing, the adaptive random testing technique selects a test case that significantly differs from all existing test cases. Similarly, to improve the fault detection efficiency of combinatorial testing, the greedy combinatorial testing technique adopts a greedy strategy to generate test cases that cover more uncovered tuple-combinations of parametric values. In this paper, we designed an experiment to compare the fault detection efficiency between adaptive random testing technique and greedy combinatorial testing technique for control logics of nuclear industrial DCS. Through the analysis of the fault detection ratios, the f-measure values, and the values of average percent of faults detected (APFD) on two experimental subjects, including the commonly used benchmarks in the field of Boolean-specification testing as well as a group of Boolean expressions extracted from the control logics in nuclear industrial DCS, the experimental results give us the following conclusions: (1) If the test suites' sizes are relatively small, the fault detection efficiencies of the two techniques are very close though there is a slight advantage in adaptive random testing; (2) With the gradual increase of test suites' sizes, the fault detection efficiency of greedy combinatorial testing is beyond adaptive random testing gradually. Such a result can help us select the appropriate testing techniques in the testing of the control logics in nuclear industry DCS.

In complex software systems, identification of parameter combinations that lead to failures is important for effective debugging and robust software quality assurance. Combinatorial testing (CT) can greatly reduce the number of test cases (TC) used for testing a complex system by generating TCs based on various parameter combinations, while still maintaining high fault-detection capabilities. In this paper, a rule-based approach is presented that will aid in identifying Failure Inducing Combinations (FIC) of parameters that caused a fault in CT generated TCs. The approach uses heuristics to identify rules to methodically split parameter combinations into more likely or less probable combinations causing failure, thus reducing the set of failure sources. This approach is tested on two different case studies i) Three factor authentication system and ii) Existing literature-based input. The results obtained show significant accuracy and time saving for program debugging, thereby indicating applicability of the approach to real-world problems. The approach was found to be successful in identifying the pair-wise combinations of parameters that are likely to cause failure.