In this paper we formulate a bi-criteria search strategy of a heuristic learning algorithm forsolving multiple resource-constrained project scheduling problems. The heuristic solves problems intwo phases. In the pre-processing phase, the algorithm estimates distance between a state and the goalstate and measures complexity of problem instances. In the search phase, the algorithm uses estimatesof the pre-processing phase to further estimate distances to the goal state. The search continues in astepwise generation of a series of intermediate states through search path evaluation process withbacktracking. Developments of intermediate states are exclusively based on a bi-criteria new stateselection technique where we consider resource utilization and duration estimate to the goal state. Wealso propose a variable weighting technique based on initial problem complexity measures.Introducing this technique allows the algorithm to efficiently solve complex project schedulingproblems. A numerical example illustra In this paper we formulate a bi-criteria search strategy of a heuristic learning algorithm forsolving multiple resource-constrained project scheduling problems. The heuristic solves problems intwo phases. In the pre-processing phase, the algorithm estimates distance between a state and the goalstate and measures complexity of problem instances. In the search phase, the algorithm uses estimates of the pre-processing phase to further estimate distances to the goal state. The search continues in astepwise generation of a series of intermediate states through search path evaluation process withbacktracking. Developments of intermediate states are exclusively based on a bi-criteria new stateselection technique where we consider resource utilization and duration estimate to the goal state. Wealso propose a variable weighting technique based on initial problem complexity measures. Introducing this technique allows the algorithm tofficient solve complex project schedulingproblems. A numerica l example illustra