This paper proposes a genetic inspired algorithm for negotiating the tradeoffs between the workload Quality of Service requests and the service center computing resources energy consumption with the goal of allocating the service center computing resources in an energy efficient manner. The bilateral negotiation algorithm has two main parties: the workload task's Quality of Service request, as a client, and the service center servers available computing resources, as a provider. Both the provider and the client are represented by agents and their offers/requests are modeled as chromosomes. A chromosome gene represents the value of the computing resources subject of negotiation. The genetic inspired negotiation process has an initial phase and a bargaining phase. In the initial phase, an initial chromosome population is generated for both the provider and the client and the values of their associated goal chromosomes are set. In the bargaining phase, the client and provider chromosomal populations are evolved using a cognitive process similar to the genetic evolution. An agreement is reached when the distance between one of the received offer/request chromosomes and a corresponding goal chromosome is below a predefined threshold.