Boosting Binary Optimization via Binary Classification: A Case Study of Job Shop Scheduling

Abstract: Many optimization techniques evaluate solutions consecutively, where the next candidate for evaluation is determined by the results of previous evaluations. For example, these include iterative methods, "black box" optimization algorithms, simulated annealing, evolutionary algorithms and tabu search, to name a few. When solving an optimization problem, these algorithms evaluate a large number of solutions, which raises the following question: Is it possible to learn something about the optimum using these solutions? In this paper, we define this "learning" question in terms of a logistic regression model and explore its predictive accuracy computationally. The proposed model uses a collection of solutions to predict the components of the optimal solutions. To illustrate the utility of such predictions, we embed the logistic regression model into the tabu search algorithm for job shop scheduling problem. The resulting framework is simple to implement, yet provides a significant boost to the performance of the standard tabu search.