Many-objective Optimization

Abstract: Search-based approaches have been used in the literature to automate the process of creating unit test cases. However, related work has shown that generated tests with high code coverage could be ineffective, i.

Abstract Search-based test case generation approaches make use of static type information to determine which data types should be used for the creation of new test cases. Dynamically typed languages like JavaScript, however, do not have this type information.

A key idea in many-objective optimization is to approximate the optimal Pareto front using a set of representative non-dominated solutions. The produced solution set should be close to the optimal front (convergence) and well-diversified (diversity). Recent studies have shown that measuring both convergence and diversity depends on the shape (or curvature) of the Pareto front. In recent years, researchers have proposed evolutionary algorithms that model the shape of the non-dominated front to define environmental selection strategies that adapt to the underlying geometry. This paper proposes a novel method for non-dominated front modeling using the Newton-Raphson iterative method for roots finding. Second, we compute the distance (diversity) between each pair of non-dominated solutions using geodesics, which are generalizations of the distance on Riemann manifolds (curved topological spaces). Thereafter, we have introduced an evolutionary algorithm within the Adaptive Geometry Estimation based MOEA (AGE-MOEA) framework, which we called AGE-MOEA-II. Computational experiments with 17 problems from the WFG and SMOP benchmarks show that AGE-MOEA-II outperforms its predecessor AGE-MOEA as well as other state-of-the-art many-objective algorithms, i.e., NSGA-III, MOEA/D, VaEA, and LMEA.

Abstract State-of-the-art search-based approaches for test case generation work at test case level, where tests are represented as sequences of statements. These approaches make use of genetic operators (i.e., mutation and crossover) that create test variants by adding, altering, and removing statements from existing tests.

Software testing is an important and time-consuming task that is often done manually. In the last decades, researchers have come up with techniques to generate input data (e.g., fuzzing) and automate the process of generating test cases (e.g., search-based testing). However, these techniques are known to have their own limitations: search-based testing does not generate highly-structured data; grammar-based fuzzing does not generate test case structures. To address these limitations, we combine these two techniques. By applying grammar-based mutations to the input data gathered by the search-based testing algorithm, it allows us to co-evolve both aspects of test case generation. We evaluate our approach by performing an empirical study on 20 Java classes from the three most popular JSON parsers across multiple search budgets. Our results show that the proposed approach on average improves branch coverage for JSON related classes by 15% (with a maximum increase of 50%) without negatively impacting other classes.

Implementation of AGE-MOEA in Matlab

In the last decade, several evolutionary algorithms have been proposed in the literature for solving multi- and many-objective optimization problems. The performance of such algorithms depends on their capability to produce a well-diversified front (diversity) that is as closer to the Pareto optimal front as possible (proximity). Diversity and proximity strongly depend on the geometry of the Pareto front, i.e., whether it forms a Euclidean, spherical or hyperbolic hypersurface. However, existing multi- and many-objective evolutionary algorithms show poor versatility on different geometries. To address this issue, we propose a novel evolutionary algorithm that: (1) estimates the geometry of the generated front using a fast procedure with O(M × N) computational complexity (M is the number of objectives and N is the population size); (2) adapts the diversity and proximity metrics accordingly. Therefore, to form the population for the next generation, solutions are selected based on their contribution to the diversity and proximity of the non-dominated front with regards to the estimated geometry. Computational experiments show that the proposed algorithm outperforms state-of-the-art multi and many-objective evolutionary algorithms on benchmark test problems with different geometries and number of objectives (M=3,5, and 10).