Task　schedule　optimization　enables　to　attain　high　performance　in　both　homogeneous　and　heterogeneous　computing　environments.　The　primary　objective　of　task　scheduling　is　to　minimize　the　execution　time　of　an　application　graph.　However,　this　is　an　NP-complete　(non-deterministic　polynomial)　undertaking.　Additionally,　task　scheduling　is　a　challenging　problem　due　to　the　heterogeneity　in　the　modern　computing　systems　in　terms　of　both　computation　and　communication　costs.　An　application　can　be　considered　as　a　task　graph　represented　using　Directed　Acyclic　Graphs　(DAG).　Due　to　the　heterogeneous　system,　each　task　has　different　execution　time　on　different　processors.　The　primary　concern　in　this　problem　domain　is　to　reduce　the　schedule　length　with　minimum　complexity　of　the　scheduling　procedure.　This　work　presents　a　couple　of　hybrid　heuristics,　based　on　a　list　and　guided　random　search　to　address　this　concern.　The　proposed　heuristic,　i.e.,　Hybrid　Heuristic　and　Genetic-based　Task　Scheduling　Algorithm　for　Heterogeneous　Computing　(HHG)　uses　Genetic　Algorithm　and　a　list-based　approach.　This　work　also　presents　another　heuristic,　namely,　Hybrid　Task　Duplication,　and　Genetic-based　Task　Scheduling　Algorithm　for　Heterogeneous　Computing　(HTDG).　The　present　work　improves　the　quality　of　initial　GA　population　by　inducing　two　diverse　guided　chromosomes.　The　proposal　is　compared　with　four　state-of-the-art　methods,　including　two　evolutionary　algorithms　for　the　same　task,　i.e.,　New　Genetic　Algorithm　(NGA)　and　Enhanced　Genetic　Algorithm　for　Task　Scheduling　(EGA-TS),　and　two　list-based　algorithms,　i.e.,　Heterogeneous　Earliest　Finish　Time　(HEFT),　and　Predict　Earliest　Finish　Time　(PEFT).　Results　show　that　the　proposed　solution　performs　better　than　its　counterparts　based　on　occurrences　of　the　best　result,　average　makespan,　average　schedule　length　ratio,　average　speedup,　and　the　average　running　time.　HTDG　yields　89%　better　results　and　HHG　demonstrates　56%　better　results　in　comparisons　to　the　four　state-of-the-art　task　scheduling　algorithms.