  In this paper, we consider a temporal logic planning problem in which the
objective is to find an infinite trajectory that satisfies an optimal selection
from a set of soft specifications expressed in linear temporal logic (LTL)
while nevertheless satisfying a hard specification expressed in LTL. Our
previous work considered a similar problem in which linear dynamic logic for
finite traces (LDLf), rather than LTL, was used to express the soft
constraints. In that work, LDLf was used to impose constraints on finite
prefixes of the infinite trajectory. By using LTL, one is able not only to
impose constraints on the finite prefixes of the trajectory, but also to set
`soft' goals across the entirety of the infinite trajectory. Our algorithm
first constructs a product automaton, on which the planning problem is reduced
to computing a lasso with minimum cost. Among all such lassos, it is desirable
to compute a shortest one. Though we prove that computing such a shortest lasso
is computationally hard, we also introduce an efficient greedy approach to
synthesize short lassos nonetheless. We present two case studies describing an
implementation of this approach, and report results of our experiment comparing
our greedy algorithm with an optimal baseline.
