Many engineering systems are required to operate under changing operating conditions. A special class of systems called adaptive systems have been proposed in the literature to achieve high performance under changing environments. Adaptive systems acquire this powerful feature by allowing their design configuration to change with operating conditions. In the optimization of the adaptive systems, designers are often required to select (i) adaptive and (ii) non-adaptive (or fixed) design variables of the design configuration. Generally, the selection of these variables, and the optimization of adaptive systems are performed sequentially, thus leaving a likelihood of a sub-optimal design. In this paper, we propose the Selection-Integrated Optimization (SIO) methodology that integrates the two key processes: (1) the selection of the adaptive and fixed design variables, and (2) the optimization of the adaptive system, thereby leading to an optimum design. A major challenge to integrating these two key processes is the selection of the number of fixed and adaptive design variables, which is discrete in nature. We propose the Variable-Segregating Mapping-Function (VSMF) that overcomes this roadblock by progressively approximating the discreteness in the design variable selection process. This simple yet effective approach allows the SIO methodology to integrate the selection and optimization processes, and help avoid one significant source of sub-optimality from typical optimization formulations. The SIO methodology finds its applications in a variety of other engineering fields as well, such as product family optimization. However, in this paper, we limit the scope of our discussion to adaptive system optimization. The effectiveness of the SIO methodology is demonstrated by optimally designing a new air-conditioning system called Active Building Envelope (ABE) System.