  The ability to generate multiple plans is central to using planning in
real-life applications. Top-quality planners generate sets of such top-cost
plans, allowing flexibility in determining equivalent ones. In terms of the
order between actions in a plan, the literature only considers two extremes --
either all orders are important, making each plan unique, or all orders are
unimportant, treating two plans differing only in the order of actions as
equivalent. To allow flexibility in selecting important orders, we propose
specifying a subset of actions the orders between which are important,
interpolating between the top-quality and unordered top-quality planning
problems. We explore the ways of adapting partial order reduction search
pruning techniques to address this new computational problem and present
experimental evaluations demonstrating the benefits of exploiting such
techniques in this setting.
