SynthCharge: An Electric Vehicle Routing Instance Generator with Feasibility Screening to Enable Learning-Based Optimization and Benchmarking

The electric vehicle routing problem with time windows (EVRPTW) extends the classical VRPTW by introducing battery capacity constraints and charging station decisions. Existing benchmark datasets are often static and lack verifiable feasibility, which restricts reproducible evaluation of learning-based routing models. We introduce SynthCharge, a parametric generator that produces diverse, feasibility-screened EVRPTW instances across varying spatiotemporal configurations and scalable customer counts. While SynthCharge can currently generate large-scale instances of up to 500 customers, we focus our experiments on sizes ranging from 5 to 100 customers. Unlike static benchmark suites, SynthCharge integrates instance geometry with adaptive energy capacity scaling and range-aware charging station placement. To guarantee structural validity, the generator systematically filters out unsolvable instances through a fast feasibility screening process. Ultimately, SynthCharge provides the dynamic benchmarking infrastructure needed to systematically evaluate the robustness of emerging neural routing and data-driven approaches.

A Curriculum-Based Deep Reinforcement Learning Framework for the Electric Vehicle Routing Problem

The electric vehicle routing problem with time windows (EVRPTW) is a complex optimization problem in sustainable logistics, where routing decisions must minimize total travel distance, fleet size, and battery usage while satisfying strict customer time constraints. Although deep reinforcement learning (DRL) has shown great potential as an alternative to classical heuristics and exact solvers, existing DRL models often struggle to maintain training stability-failing to converge or generalize when constraints are dense. In this study, we propose a curriculum-based deep reinforcement learning (CB-DRL) framework designed to resolve this instability. The framework utilizes a structured three-phase curriculum that gradually increases problem complexity: the agent first learns distance and fleet optimization (Phase A), then battery management (Phase B), and finally the full EVRPTW (Phase C). To ensure stable learning across phases, the framework employs a modified proximal policy optimization algorithm with phase-specific hyperparameters, value and advantage clipping, and adaptive learning-rate scheduling. The policy network is built upon a heterogeneous graph attention encoder enhanced by global-local attention and feature-wise linear modulation. This specialized architecture explicitly captures the distinct properties of depots, customers, and charging stations. Trained exclusively on small instances with N=10 customers, the model demonstrates robust generalization to unseen instances ranging from N=5 to N=100, significantly outperforming standard baselines on medium-scale problems. Experimental results confirm that this curriculum-guided approach achieves high feasibility rates and competitive solution quality on out-of-distribution instances where standard DRL baselines fail, effectively bridging the gap between neural speed and operational reliability.

Fourier Learning Machines: Nonharmonic Fourier-Based Neural Networks for Scientific Machine Learning

We introduce the Fourier Learning Machine (FLM), a neural network (NN) architecture designed to represent a multidimensional nonharmonic Fourier series. The FLM uses a simple feedforward structure with cosine activation functions to learn the frequencies, amplitudes, and phase shifts of the series as trainable parameters. This design allows the model to create a problem-specific spectral basis adaptable to both periodic and nonperiodic functions. Unlike previous Fourier-inspired NN models, the FLM is the first architecture able to represent a complete, separable Fourier basis in multiple dimensions using a standard Multilayer Perceptron-like architecture. A one-to-one correspondence between the Fourier coefficients and amplitudes and phase-shifts is demonstrated, allowing for the translation between a full, separable basis form and the cosine phase--shifted one. Additionally, we evaluate the performance of FLMs on several scientific computing problems, including benchmark Partial Differential Equations (PDEs) and a family of Optimal Control Problems (OCPs). Computational experiments show that the performance of FLMs is comparable, and often superior, to that of established architectures like SIREN and vanilla feedforward NNs.