Design space exploration is an indispensable segment of High Level Synthesis (HLS) design of hardware accelerators. This paper presents a novel technique for Area-Execution time tradeoff using residual load decoding heuristics in genetic algorithms (GA) for integrated design space exploration (DSE) of scheduling and allocation. This approach is also able to resolve issues encountered during DSE of data paths for hardware accelerators, such as accuracy of the solution found, as well as the total exploration time during the process. The integrated solution found by the proposed approach satisfies the user specified constraints of hardware area and total execution time (not just latency), while at the same time offers a twofold unified solution of chaining based schedule and allocation. The cost function proposed in the genetic algorithm approach takes into account the functional units, multiplexers and demultiplexers needed during implementation. The proposed exploration system (ExpSys) was tested on a large number of benchmarks drawn from the literature for assessment of its efficiency. Results indicate an average improvement in Quality of Results (QoR) greater than 26% when compared to a recent well known GA based exploration method.