Optimization in Real Time

In this paper, we present a search algorithm called real-time search for solving combinatorial optimization problems under real-time constraints. The problems we study are NP-hard and have good heuristic algorithms for generating feasible solutions. The algorithm we develop aims at finding the best possible solution in a given deadline. Since this objective is generally not achievable without first solving the problem, we use an alternative heuristic objective that looks for the solution with the best ascertained approximation degree. Our algorithm schedules a sequence of guided depth-first searches, each searching for a more accurate solution (based on the approximation degree set), or solutions deeper in the search tree (based on the threshold set), or a combination of both. Five versions of the RTS algorithm for setting approximation degrees and/or thresholds are formulated, evaluated, and analyzed. We develop an exponential model for characterizing the relationship between the approximation degrees achieved and the time taken. Our results show that our RTS algorithm finds solutions better than a guided depth-first search, and solutions found are very close to the best possible solution that can be found in the time allowed. We evaluate our results using the symmetric traveling-salesman, the knapsack, and the production-planning problems.