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Rajesh Gandham

Publications and source records attributed to Rajesh Gandham.

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Accelerating Vehicle Routing via AI-Initialized Genetic Algorithms

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. In many applications, one has to repeatedly solve VRP instances drawn from the same distribution, 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 across various 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 we demonstrate on real e-commerce delivery data of a previously unseen city. By combining reinforcement learning and genetic algorithms, our hybrid framework takes a step forward to closer interdisciplinary collaboration between AI and optimization communities towards real-time optimization in diverse domains.

cs.LG

A GPU Accelerated Aggregation Algebraic Multigrid Method

We present an efficient, robust and fully GPU-accelerated aggregation-based algebraic multigrid preconditioning technique for the solution of large sparse linear systems. These linear systems arise from the discretization of elliptic PDEs. The method involves two stages, setup and solve. In the setup stage, hierarchical coarse grids are constructed through aggregation of the fine grid nodes. These aggregations are obtained using a set of maximal independent nodes from the fine grid nodes. We use a ``fine-grain'' parallel algorithm for finding a maximal independent set from a graph of strong negative connections. The aggregations are combined with a piece-wise constant (unsmooth) interpolation from the coarse grid solution to the fine grid solution, ensuring low setup and interpolation cost. The grid independent convergence is achieved by using recursive Krylov iterations (K-cycles) in the solve stage. An efficient combination of K-cycles and standard multigrid V-cycles is used as the preconditioner for Krylov iterative solvers such as generalized minimal residual and conjugate gradient. We compare the solver performance with other solvers based on smooth aggregation and classical algebraic multigrid methods.

math.NA