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. Buttner 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.

In the domain of planning, searching for optimal plans gives rise to many works. Most of the existing planners search for optimal parallel plans, that is plans which are optimal in the number of steps. FDP is an exception: it searches for optimal sequential plans, that is plans which are optimal in the number of actions. FDP implements a depth-first iterative-deepening search, using a CSP-like structure, decomposition rules, and filtering techniques similar to consistency-enforcing techniques. We propose a new planner based on FDP, which generates optimal parallel plans. This planner has been compared on a set of selected problems with the well-known optimal parallel planner SATPLAN, and with the planner FDP, so as to analyse the effects of the optimization criteria in the performances.