Hybrid Planning by Combining SMT and Simulated Annealing

We present a new approach to the concrete planning (CP) shown to be a NP-hard problem [7]. This is the third stage of Web service composition (WSC) in the PlanICS framework [1]. The first two phases, namely an abstract planning and offer collecting, basing on an ontology, a user query, and a service registry provide data necessary for CP. A new hybrid algorithm (HSA), which combines Simulated Annealing (SA) [6] with Satisfiability Modulo Theories (SMT) [3], has been designed and implemented. The main idea of our hybrid solution relies upon generating an initial individual by an SMT-based procedure. Then, in the subsequent iterations of SA, the individual is improved. The experimental results show that HSA is superior to the other methods we have applied to the CP problem, including these based on Genetic Algorithm (GA) [4], SMT used separately [10], and SMT combined into the hybrid algorithms RH and SRH [9], as well as the IPH algorithm [8]. Our direct motivation to develop hybrid algorithms is based on the observation that every method applied separately to WSC yields fair results, but suffers from some disadvantages. While the SMT-based algorithm is able to find always the optimal solution, its main problem is a long execution time and large memory consumption. On the other hand the evolutionary methods are quick and demand less resources, but at the price of the quality and a lower probability of finding solutions. We are aiming at combining the algorithms in order to get a trade-off between speed and quality. Recently, we have developed three planning methods based on joining GA and SMT: RH (Random Hybrid), SRH (Semi-Random Hybrid), and IPH (Initial Population Hybrid). The first two algorithms run alternately several iterations of GA and the SMT-based procedure which is aimed at improving the best individuals of a GA population. The IPH algorithm makes use of an SMT-based procedure in order to generate (a part of) the initial population meeting the given constraints, and then the individuals are improved by GA. The experiments have shown that the latter method is superior in most cases, thus we have chosen this scheme to be used in further investigations.