Composite applications leveraging several functionalities offered by Web services are today the underpinnings of enterprise computing. There are two kinds of requirements of web service composition: QoS requirements and transactional requirements. The QoS requirements are recorded in service-level agreements (SLAs) contract. The transactional requirements are expressed by designers as a set of accepted termination states (ATS). In this paper, we propose a novel selection and composition approach called ATS and SLA-aware Web services composition (WSC). Our approach aims at finding composite service compliant with ATS and better satisfying the SLA contract. As the ATS and SLA-aware WSC is NP-hard problem, an efficient algorithm is required. This work adopts genetic algorithm to deal with combinatorial problem