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This paper describes an architecture to build self-optimizable and self-stabilizable cloud applications. The design of the proposed architecture, SymbioticSphere, is inspired by key biological principles such as decentralization, evolution, and symbiosis. In SymbioticSphere, each cloud application consists of application services and middleware platforms. Each service and platform is designed as a biological entity and implements biological behaviors such as energy exchange, migration, reproduction, and death. Each service/platform possesses behavior policies, as genes, each of which governs when to and how to invoke a particular behavior. SymbioticSphere allows services and platforms to autonomously adapt to dynamic network conditions by optimizing their behavior policies with a multiobjective genetic algorithm. Moreover, SymbioticSphere allows services and platforms to autonomously seek stable adaptation decisions as equilibria (or symbiosis) between them with a game theoretic algorithm. This symbiosis augments evolutionary optimization to expedite the adaptation of agents and platforms. It also contributes to stable performance that contains very limited amounts of fluctuations. Simulation results demonstrate that agents and platforms successfully attain self-optimization and self-stabilization properties in their adaptation process. Copyright © 2012 John Wiley & Sons, Ltd.