Exploratory Data Analysis (EDA) is the interactive process of gaining insights from a dataset. Comparisons are popular insights that can be specified with comparison queries, i.e., specifications of the comparison of subsets of data. In this work, we consider the problem of automatically computing sequences of comparison queries that are coherent, significant and whose overall cost is bounded. Such an automation is usually done by either generating all insights and solving a multi-criteria optimization problem, or using reinforcement learning. In the first case, a large search space has to be explored using exponential algorithms or dedicated heuristics. In the second case, a dataset-specific, time and energy-consuming training, is necessary. We contribute with a novel approach, consisting of decomposing the optimization problem in two: the original problem, that is solved over a smaller search space, and a new problem of generating comparison queries, aiming at generating only queries improving existing solutions of the first problem. This allows to explore only a portion of the search space, without resorting to reinforcement learning. We show that this approach is effective, in that it finds good solutions to the original multi-criteria optimization problem, and efficient, allowing to generate sequences of comparisons in reasonable time.

International audience

This paper proposes an exact exponential algorithm for the problem of minimizing the total tardiness of jobs on a single machine. It exploits the structure of a basic branch-and-reduce framework based on the well known Lawler's decomposition property. The proposed algorithm, called branch-and-merge, is an improvement of the branch-and-reduce technique with the embedding of a node merging operation. Its time complexity is O*(2.247^n) keeping the space complexity polynomial. The branch-and-merge technique is likely to be generalized to other sequencing problems with similar decomposition properties.

International audience

International audience

We consider a two-machine flowshop-scheduling problem with an unknown common due date where the objective is minimization of both the number of tardy jobs and the unknown common due date. We show that the problem is NP-hard in the ordinary sense and present a pseudopolynomial dynamic program for its solution. Then, we propose an exact ϵ-constraint approach based on the optimal solution of a related single-machine problem. For this latter problem a compact ILP formulation is explored: a powerful variable-fixing technique is presented and several logic cuts are considered. Computational results indicate that, with the proposed approach, the pareto optima can be computed, in reasonable time, for instances with up to 500 jobs.