Today, based on fast development especially in Network-on-Chip (NoC)-based many-core systems, the task scheduling problem plays a critical role in high-performance computing. It is an NP-hard problem. The complexity increases further when the scheduling problem is applied to heterogeneous platforms. Exploring the whole search space in order to find the optimal solution is not time efficient, thus metaheuristics are mostly used to find a near-optimal solution in a reasonable amount of time. We propose a compound method to select the best near-optimal task schedule in the heterogeneous platform in order to minimize the execution time. For this, we combine a new parallel meta-heuristic method with a greedy scheme. We introduce a novel metaheuristic method for near-optimal scheduling that can provide performance guarantees for multiple applications implemented on a shared platform. Applications are modeled as directed acyclic task graphs (DAG) for execution on a heterogeneous NoC-based many-core platform with given communication costs. We introduce an order-based encoding especially for pipelined operation that improves (decreases) execution time by more than 46%. Moreover, we present a novel multi-population method inspired by both genetic and imperialist competitive algorithms specialized for the scheduling problem, improving the convergence policy and selection pressure. The potential of the approach is demonstrated by experiments using a Sobel filter, SUSAN filter, RASTA-PLP, and JPEG encoder as real-world case studies.