In this paper we present a hybrid metaheuristic approach called PVS for the two-dimensional strip packing problem (2SPP). PVS (progress and verify strategy) relies on two procedures: a local search algorithm that delivers satisfying placements of the items on the horizontal axis, and an exact procedure that searches for the positions of the items on the vertical axis. This last one explores all the possibilities, starting with the most promising ones, and can be stopped at any moment. PVS follows a specific anytime strategy which continuously improves the current solution until it is provably optimal or a given time limit is reached. Experimental results show that the method is competitive on moderate-sized instances compared to the best known approaches.

In the domain of classical planning one distinguishes plans which are optimal in their number of actions, they are referred as sequential plans, from plans which are optimal in their number of levels, they are referred as parallel plans. Searching optimal sequential plans is generally considered harder than searching optimal parallel plans. Büttner and Rintanen have proposed a search procedure which computes plans whose numbers of levels are fixed and whose numbers of actions are minimal. This procedure is notably used to calculate optimal sequential plans, starting from an optimal parallel plan. In this paper we describe a similar approach, which we have developed from the planner FDP. The idea consists in maintaining two structures, the first one representing the parallel plan and the other representing the sequential plan, performing the choices simultaneously in both structures. The techniques which were developed in FDP to compute sequential plans or parallel plans enable failures detection in the two structures. Experimental results show that this approach is in some cases more efficient than FDP when searching optimal sequential plans.