3 research outputs found
BQ-NCO: Bisimulation Quotienting for Efficient Neural Combinatorial Optimization
Despite the success of neural-based combinatorial optimization methods for
end-to-end heuristic learning, out-of-distribution generalization remains a
challenge. In this paper, we present a novel formulation of Combinatorial
Optimization Problems (COPs) as Markov Decision Processes (MDPs) that
effectively leverages common symmetries of COPs to improve out-of-distribution
robustness. Starting from a direct MDP formulation of a constructive method, we
introduce a generic way to reduce the state space, based on Bisimulation
Quotienting (BQ) in MDPs. Then, for COPs with a recursive nature, we specialize
the bisimulation and show how the reduced state exploits the symmetries of
these problems and facilitates MDP solving. Our approach is principled and we
prove that an optimal policy for the proposed BQ-MDP actually solves the
associated COPs. We illustrate our approach on five classical problems: the
Euclidean and Asymmetric Traveling Salesman, Capacitated Vehicle Routing,
Orienteering and Knapsack Problems. Furthermore, for each problem, we introduce
a simple attention-based policy network for the BQ-MDPs, which we train by
imitation of (near) optimal solutions of small instances from a single
distribution. We obtain new state-of-the-art results for the five COPs on both
synthetic and realistic benchmarks. Notably, in contrast to most existing
neural approaches, our learned policies show excellent generalization
performance to much larger instances than seen during training, without any
additional search procedure
Routing in Multimodal Transportation Networks with Non-Scheduled Lines
Over the last decades, new mobility offers have emerged to enlarge the coverage and the accessibility of public transportation systems. In many areas, public transit now incorporates on-demand transport lines, that can be activated at user need. In this paper, we propose to integrate lines without predefined schedules but with predefined stop sequences into a state-of-the-art trip planning algorithm for public transit, the Trip-Based Public Transit Routing algorithm [Witt, 2015]. We extend this algorithm to non-scheduled lines and explain how to model other modes of transportation, such as bike sharing, with this approach. The resulting algorithm is exact and optimizes two criteria: the earliest arrival time and the minimal number of transfers. Experiments on two large datasets show the interest of the proposed method over a baseline modelling
On the Generalization of Neural Combinatorial Optimization Heuristics
Neural Combinatorial Optimization approaches have recently leveraged the
expressiveness and flexibility of deep neural networks to learn efficient
heuristics for hard Combinatorial Optimization (CO) problems. However, most of
the current methods lack generalization: for a given CO problem, heuristics
which are trained on instances with certain characteristics underperform when
tested on instances with different characteristics. While some previous works
have focused on varying the training instances properties, we postulate that a
one-size-fit-all model is out of reach. Instead, we formalize solving a CO
problem over a given instance distribution as a separate learning task and
investigate meta-learning techniques to learn a model on a variety of tasks, in
order to optimize its capacity to adapt to new tasks. Through extensive
experiments, on two CO problems, using both synthetic and realistic instances,
we show that our proposed meta-learning approach significantly improves the
generalization of two state-of-the-art models.Comment: Published in ECML PKDD 202