Program

We introduce a new cooperative game theory model that we call production-distribution game to address a major open problem for operations research in forestry, raised by Rönnqvist et al. in 2015, namely, that of modelling and proposing efficient sharing principles for practical collaboration in transportation in this sector. The originality of our model lies in the fact that the value/strength of a player does not only depend on the individual cost or benefit of the goods she owns but also on her market shares (customers demand). We show that our new model is an interesting special case of a market game introduced by Shapley and Shubik in 1969. As such it exhibits the property of having a non-empty core. We prove that we can compute both the nucleolus and the Shapley value efficiently, in a nontrivial, interesting special case. We provide two algorithms to compute the nucleolus: a simple separation algorithm and a fast primal-dual one. We also show that our results can be used to tackle more general versions of the problem and we believe that our contribution paves the way towards solving the challenging open problems herein.

We routinely model engineering tasks as optimization problems. These come in various forms. Some we know how to solve; some we know we cannot. Of particular interest are those problems it appears we can solve, yet we do not know for sure: our theory fails us. Can we use such models in critical applications where mistakes have consequences? In continuous optimization, the known frontier of tractability is mostly defined by convexity. Yet, in recent years we have discovered many nonconvex problems it appears we can solve. I will describe some of their frequent traits, specifically through geometry and symmetry. This will lead us to consider optimization on Riemannian manifolds: I’ll share pointers and some of the essential ideas in that area.

The last decade has witnessed the impressive development of machine learning (ML) techniques. These techniques have been successfully applied to traditional statistical learning tasks as image recognition and led to breakthroughs like the famous AlphaGo system. Motivated by those successes, many scientific disciplines have started to investigate the potential of the use of large amount of data crunched by ML techniques in their context. Combinatorial optimization (CO) has been no exception to this trend and the ML use in CO has been analyzed from many different angles with various levels of success. In this talk, we will review the state of the art of such scientific path, interpreting the level of maturity reached by the integration of ML techniques in CO and discussing the challenges. We will finish by presenting one particular area in which we consider this integration having a remarkable potential, i.e., repeatedly solving CO problems with little data variations.

LocalSolver is a global optimization solver that combines exact and heuristic methods to find near-optimal solutions in minutes. This talk introduces LocalSolver’s modeling formalism and its main differences from traditional Mixed-Integer Linear Programming (MILP) or Constraint Programming (CP) formalisms. Key features such as set-based modeling give users more expressivity and benefit the solver with more information about the problem structure. We overview how the solver exploits the user model in a generic neighborhood search and computes lower bounds using automatic mixed-integer nonlinear reformulations. To illustrate LocalSolver’s difference in terms of performance, we present benchmarks on widely addressed routing and scheduling problems.