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Heuristic search based on Petri nets is a partial reachability graph expansion technique. The paper proposes a modified best-first algorithm and applies it to a flexible manufacturing system with assembly. A heuristic function based on the Petri net structure and dynamics is presented. It performs well especially for nets called generalized symmetric and asymmetric nets. The heuristic function consists of two parts. The first part estimates the total remaining operation time for all jobs considering system dynamics. The second part approximates the maximal total remaining operation time of each job. We begin with the first part to search the reachability tree of a timed Petri net toward an optimal or near-optimal path until a depth-bound is reached. After the depth-bound, the second part is applied. We also propose a one-level backtracking procedure to avoid deadlocks and a pruning procedure to reduce the number of explored states. Experimental results of 1500 randomly generated test cases show that this work outperforms prior work.