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High-level synthesis is comprised of interdependent tasks such as scheduling, allocation, and module selection. For today's very large-scale integration (VLSI) designs, the cost of solving the combined scheduling, allocation, and module selection problem by exhaustive search is prohibitive. However, to meet design objectives, an extensive design space exploration is often critical to obtaining superior designs. We present a framework for efficient design space exploration during high-level synthesis of datapaths for data-dominated applications. The framework uses a genetic algorithm (GA) to concurrently perform scheduling and allocation with the aim of finding schedules and module combinations that lead to superior designs while considering user-specified latency and area constraints. The GA uses a multichromosome representation to encode datapath schedules and module allocations and efficient heuristics to minimize functional and storage area costs, while minimizing circuit latencies. The framework provides the flexibility to perform resource-constrained scheduling, time-constrained scheduling, or a combination of the two, using a simple and fast list-scheduling technique. A graded penalty function is used as an objective function in evaluating the quality of designs to enable the GA to quickly reach areas of the search space where designs meeting user specified criteria are most likely to be found. Since GAs are population-based search heuristics, a unique feature of our framework is its ability to offer a large number of alternative datapath designs, all of which meet design specifications but differ in module, register, and interconnect configurations. Many experiments on well-known benchmarks show the effectiveness of our approach.