The problem of configuring a variability model is widespread in many different domains. Renault has developed its technology internally to model vehicle diversity. This technology relies on the approach known as knowledge compilation to explore the configurations space. However, the growing variability and complexity of the vehicles’ range hardens the space representation problem and may impact performance requirements. This paper tackles these issues by exploiting symmetries that represent isomorphic parts in the configuration space. The extensive experiments we conducted on datasets from Renault show our approach’s robustness and effectiveness: the achieved gain is a reduction of 52.13% in space representation and 49.81% in processing time on average.

Many state-of-the-art methods for combinatorial games rely on Monte Carlo Tree Search (MCTS) method, coupled with machine learning techniques, and these techniques have also recently been applied to combinatorial optimization. In this paper, we propose an efficient approach to a Travelling Salesman Problem with time windows and capacity constraints from the automotive industry. This approach combines the principles of MCTS to balance exploration and exploitation of the search space and a backtracking method to explore promising branches, and to collect relevant information on visited subtrees. This is done simply by replacing the Monte-Carlo rollouts by budget-limited runs of a DFS method. Moreover, the evaluation of the promise of a node in the Monte-Carlo search tree is key, and is a major difference with the case of games. For that purpose, we propose to evaluate a node using the marginal increase of a lower bound of the objective function, weighted with an exponential decay on the depth, in previous simulations. Finally, since the number of Monte-Carlo rollouts and hence the confidence on the evaluation is higher towards the root of the search tree, we propose to adjust the balance exploration/exploitation to the length of the branch. Our experiments show that this method clearly outperforms the best known approaches for this problem.