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Search-based software engineering is an emerging paradigm that uses automated search algorithms to help designers iteratively find solutions to complicated design problems. For example, when designing a climate monitoring satellite, designers may want to use the minimal amount of computing hardware to reduce weight and cost while supporting the image processing algorithms running onboard. A key problem in these situations is that the hardware and software designs are locked in a tightly coupled cost-constrained producer/consumer relationship that makes it hard to find a good hardware/software design configuration. Search-based software engineering can be used to apply algorithmic techniques to automate the search for hardware/software designs that maximize the image processing accuracy while respecting cost constraints. This paper provides the following contributions to research on search-based software engineering: 1) We show how a cost-constrained producer/consumer problem can be modeled as a set of two multidimensional multiple-choice knapsack problems (MMKPs), 2) we present a polynomial-time search-based software engineering technique, called the Allocation-baSed Configuration Exploration Technique (ASCENT), for finding near optimal hardware/software codesign solutions, and 3) we present empirical results showing that ASCENT's solutions average over 95 percent of the optimal solution's value.