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Search in a complex design space (e.g. in VLSI design) is only feasible when it is factored into smaller ones. A common and useful factoring is the hierarchy of abstraction. Such problems are then attacked by linking together stochastic search programs. At each point in the design process it is necessary to choose whether to continue looking for a better design at the current level, or working further on some design at a higher or lower level. We present a rational, i.e. utility-based, method for this choice, together with some experiments in the domain of VLSI placement and routing.