Vehicle routing problems (VRP) are an extension of the Traveling Salesperson Problem and are a fundamental NP-hard challenge in combinatorial optimization. Solving VRP in real-time at large scale has become critical in numerous applications, from growing markets like last-mile delivery to emerging use-cases like interactive logistics planning. Such applications involve solving similar VRP instances repeatedly, yet current state-of-the-art solvers treat each instance on its own without leveraging previous examples. We introduce an optimization framework where a reinforcement learning agent is trained on prior instances and quickly generates initial solutions, which are then further optimized by a genetic algorithm. This framework, Evolutionary Algorithm with Reinforcement Learning Initialization (EARLI), consistently outperforms current state-of-the-art solvers under limited time budgets. For example, EARLI handles vehicle routing with 500 locations within one second, 10x faster than current solvers for the same solution quality, enabling real-time and interactive routing at scale. EARLI can generalize to new data, as demonstrated on real e-commerce delivery data of a previously unseen city.
Ido Greenberg, P. Sielski, Hugo Linsenmaier et al.· Communications AI & Computin...· 1 citation
Dimension reduction for dynamical systems is standard practice, and the standard route is spectral: model the transfer (Koopman) operator by its leading modes. We show that on systems assembled from several weakly interacting components --- a structure common in physical and biological settings --- this may either require an exponential number of modes, or drop an entire component: the component is absent from the model rather than modeled coarsely, and no function of it can be predicted at any accuracy. We call this linear masking. The cause is that a rank-based model pays one coordinate per mode. We propose to score instead the $\sigma$-algebra the coordinates generate, so that products and powers come free and a component's cost is governed only by its generators rather than by all its interactions. The criterion is a $\chi^2$-divergence between the embedded present and future, and it carries a budget guarantee: twice the intrinsic dimension of the dynamics is enough coordinates for an embedding whose algebra carries the operator's entire spectrum, with its full infinite rank. In variational form the criterion admits off-the-shelf estimators, and restricting its critic to the bilinear class returns the VAMP score on the span, so rank-based methods are one end of the same family. We demonstrate the proposed objective on a composite of published benchmark systems. We exhibit examples where the rank-based methods completely miss the masked components at all ranks $k<100$, while ten algebra coordinates recover all of them. In addition, the resulting algebra representation supports predicting the masked components from few labels, while direct regression from the high-dimensional observation or from the VAMP features fail.
Mark Kozdoba, Shie Mannor· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
