Nowadays, the satisfaction of the users' requirements of a composition process execution in a grid environment remains a difficult task to be accomplished. It is done by brokers or using simple mechanisms of matchmaking. There users must express their needs in the grid language and then the grid determines the way to execute. In this article we propose a genetic sequencing approach for the research of the best way to execute a composition of services in a grid environment satisfying the user's need. This paper presents the genetic sequencing approach and then presents how to adapt this approach for the determination of the best time to execute the service composition.