CBGA-ES+: A Cluster-Based Genetic Algorithm with Non-Dominated Elitist Selection for Supporting Multi-Objective Test Optimization

Many real-world test optimization problems (e.g., test case prioritization) are multi-objective intrinsically and can be tackled using various multi-objective search algorithms (e.g., Non-dominated Sorting Genetic Algorithm (NSGA-II)). However, existing multi-objective search algorithms have certain randomness when selecting parent solutions for producing offspring solutions. In a worse case, suboptimal parent solutions may result in offspring solutions with bad quality, and thus affect the overall quality of the solutions in the next generation. To address such a challenge, we propose CBGA-ES⁺, a novel cluster-based genetic algorithm with non-dominated elitist selection to reduce the randomness when selecting the parent solutions to support multi-objective test optimization. We empirically compared CBGA-ES⁺ with random search and greedy (as baselines), four commonly used multi-objective search algorithms (i.e., Multi-objective Cellular genetic algorithm (MOCell), NSGA-II, Pareto Archived Evolution Strategy (PAES), and Strength Pareto Evolutionary Algorithm (SPEA2)), and the predecessor of CBGA-ES⁺ (named CBGA-ES) using five multi-objective test optimization problems with eight subjects (two industrial, one real world, and five open source). The results showed that CBGA-ES⁺ managed to significantly outperform the selected search algorithms for a majority of the experiments. Moreover, for the solutions in the same search space, CBGA-ES⁺ managed to perform better than CBGA-ES, MOCell, NSGA-II, PAES, and SPEA2 for 2.2, 13.6, 14.5, 17.4, and 9.9 percent, respectively. Regarding the running time of the algorithm, CBGA-ES⁺ was faster than CBGA-ES for all the experiments.

1 Introduction

Many real-world test optimization problems are multi-objective intrinsically, which requires considering multiple conflicting objectives when finding optimal solutions. For instance, based on our long-term collaboration with Cisco Systems [1], [2], we identified a test case prioritization problem [3] with four conflicting objectives (e.g., fault detection capability) to prioritize a given number of test cases into an optimal order. Another example is the testing resource allocation problem [4], [5] (i.e., allocating test resources optimally to different software modules), to minimize testing cost (e.g., testing time) and maximize the reliability of the modules.