Tree Search and Simulation

This chapter presents a general methodology for embodying simulation as part of a tree search procedure, as a technique for solving practical problems in combinatorial optimization. Target problems are either difficult to express as mixed integer optimization models, or have models which provide rather loose bounds; in both cases, traditional, exact methods typically fail. The idea then is to have tree search instantiating part of the variables in a systematic way, and for each particular instantiation—i.e., a node in the search tree—resort to a simulation for assigning values to the remaining variables; then, use the outcome of the simulation for evaluating that node in the tree. This method has been used with considerable success in gameplaying, but has received very limited attention as a tool for optimization. Nevertheless, it has great potential, either as a way for improving known heuristics or as an alternative to metaheuristics. We depart from repeated, randomized simulation based on problem-specific heuristics for applications in scheduling, logistics, and packing, and show how the systematic search in a tree improves the results that can be obtained.