The current study on duality mapping proposed by Suda (2013) is a viable strategy to turn progression (forward search) into regression (backward search), and the experiment results suggest that the dual versions of standard IPCs benchmark domains are quite difficult to solve for heuristic-based search. We adopt width-based search (IW and SIW) in this thesis to test the performance on dual problems. The experiment results show that dual problems can be solved efficiently when the goal state is restricted to single fluent, but it becomes challenging when the goal state contains conjunctive fluents. Then, we turn serialized iterated width, SIW, best-first width search with the evaluation function f 5, BFWS(f5), and the polynomial variants of BFWS(f5), k-BFWS(f5) from progression into regression by modifying the state space. Results show that the backward versions are uncompetitive with the forward versions but still outperform in some IPCs benchmark domains in all SIW, BFWS(f5) and k-BFWS(f5). Furthermore, we build a bidirectional search, k-BFWBS by integrating forward and backward k-BFWS(f5) with six different combinations. Although these six combinations cannot solve more problems than only adopting forward k -BFWS(f 5) among tested IPCs benchmark domains, they are distinctive. However, if we run forward k -BFWS(f5) first and then run backward k-BFWS(f5), it outperforms only running forward k-BFWS(f5), which proves that backward search is useful. All results in this thesis indicate that although backward search is uncompetitive and multiple issues still exist, it is still worthy of having a deep exploration of backward search since it not only finds more plans in some domains but also proposes a different perspective to analyse classical planning tasks. Meanwhile, we point out the weaknesses of backward search and give relevant solutions, and a new method complete domain is presented to perfect backward search.