Lagrange Multipliers for Local Search on Planning Graphs

GPG is a planner based on planning graphs that combines local search and backtracking techniques for solving both plan-generation and plan-adaptation tasks. The space of the local search is formed by particular subgraphs of a planning graph representing partial plans. The operators for moving from one search state to the next one are graph modification operations corresponding to adding (deleting) actions to (from) a partial plan. GPG can use different types of heuristics based on a parametrized cost function, where the parameters weight different types of constraint violation that are present in the current subgraph. A drawback of this method is that the performance is sensitive to the static values assigned to these parameters.In this paper we propose a refined version of the local search heuristics of GPG using a cost function with dynamic parameters. In particular, the cost of the constraint violations are dynamically evaluated using Lagrange multipliers. As the experimental results show, the use of these multipliers gives two important improvements to our local search. First, the revised cost function is more informative and can discriminate more accurately the elements in the neighborhood. As a consequence, the new cost function can give better performances. Secondly, the performance of the search does not depend anymore on the values of the parameters that in the previous version need to be tuned by hand before the search.