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.
Cascading portfolio scheduling is a static algorithm selection strategy which uses a sample of test instances to compute an optimal ordering (a cascading schedule) of a portfolio of available algorithms. The algorithms are then applied to each future instance according to this cascading schedule, until some algorithm in the schedule succeeds. Cascading algorithm scheduling has proven to be effective in several applications, including QBF solving and the generation of ImageNet classification models. It is known that the computation of an optimal cascading schedule in the offline phase is NP-hard. In this paper we study the parameterized complexity of this problem and establish its fixed-parameter tractability by utilizing structural properties of the success relation between algorithms and test instances.
The article describes the proposition and application of a local search metaheuristic for multi-objective optimization problems. It is based on two main principles of heuristic search, intensification through variable neighborhoods, and diversification through perturbations and successive iterations in favorable regions of the search space. The concept is successfully tested on permutation flow shop scheduling problems under multiple objectives and compared to other local search approaches. While the obtained results are encouraging in terms of their quality, another positive attribute of the approach is its simplicity as it does require the setting of only very few parameters.
Considering directed graphs on n vertices and m edges with real (possibly negative) weights, we present two new, efficient algorithms for computing all-pairs shortest paths (APSP). These algorithms make use of directed path consistency (DPC) along a vertex ordering d. The algorithms run in O(n 2 w d ) time, where w d is the graph width induced by this vertex ordering. For graphs of constant treewidth, this yields O(n 2 ) time, which is optimal. On chordal graphs, the algorithms run in O(nm) time. We show empirically that also in many general cases, both constructed and from realistic benchmarks, the algorithms often outperform Johnson's algorithm, which represents the current state of the art with a run time of O(nm + n 2 log n). These algorithms can be used for temporal and spatial reasoning, e.g. for the Simple Temporal Problem (STP), which underlines its relevance to the planning and scheduling community.
There hardly exists a general solver that is efficient for scheduling problems due to their diversity and complexity. In this study, we develop a two-stage framework, in which reinforcement learning (RL) and traditional operations research (OR) algorithms are combined together to efficiently deal with complex scheduling problems. The scheduling problem is solved in two stages, including a finite Markov decision process (MDP) and a mixed-integer programming process, respectively. This offers a novel and general paradigm that combines RL with OR approaches to solving scheduling problems, which leverages the respective strengths of RL and OR: The MDP narrows down the search space of the original problem through an RL method, while the mixed-integer programming process is settled by an OR algorithm. These two stages are performed iteratively and interactively until the termination criterion has been met. Under this idea, two implementation versions of the combination methods of RL and OR are put forward. The agile Earth observation satellite scheduling problem is selected as an example to demonstrate the effectiveness of the proposed scheduling framework and methods. The convergence and generalization capability of the methods are verified by the performance of training scenarios, while the efficiency and accuracy are tested in 50 untrained scenarios. The results show that the proposed algorithms could stably and efficiently obtain satisfactory scheduling schemes for agile Earth observation satellite scheduling problems. In addition, it can be found that RL-based optimization algorithms have stronger scalability than non-learning algorithms. This work reveals the advantage of combining reinforcement learning methods with heuristic methods or mathematical programming methods for solving complex combinatorial optimization problems.