<p>The rapidly deployable service-oriented web applications lead to various complex services called web services. Web services are platform-independent and are utilizable in distributed networks, including edge computing networks. The web service composition (WSC) fulfills edge users' quality of service (QoS) aspects by delivering an optimal combination of available web services. Given the numerous services offer similar functions with different aspects of QoS, it is considered a non-deterministic polynomial-time hard (NP-hard) problem to identify the most appropriate network services with the best QoS. Currently, the WSC is regarded as a hot spot research field since, with the progressive growth of web services in the real world, it becomes increasingly difficult to use the existing methods. As a result, an enhanced chaotic-based hybrid artificial rabbit optimization and dandelion optimizer named ECARDO is presented in the current paper to solve the QoS-aware web service composition problem. In the ECARDO, the artificial rabbit optimization (ARO) and dandelion optimizer (DO) are discretized innovatively using swap, crossover, and random insert operators. The optimization process is accelerated by removing redundant parameters from the resulting discrete algorithms. Next, the algorithms are hybridized in a complementary way. Also, a neighborhood searching mechanism is introduced. Then, a chaotic hybrid map is provided to select operators over iterations. Eventually, the ECARDO is applied to ten real-world and artificial web service datasets. The results are compared with AOA, ARO, DO, JS, MVO, RSA, SCA, and SMA algorithms statistically and visually under specific user preferences. The experimental results indicated ECARDO's supremacy over competitors.</p>