Bi-Objective Electric Vehicle Charging Scheduling Under Stochastic Charging Durations

This paper addresses the electric vehicle charging scheduling problem under stochastic charging durations, where uncertainty arises from variations in actual charging times that are typically assumed deterministic in existing literature. We formulate a bi-objective optimization problem minimizing the expected values of peak load and total tardiness. We explicitly enforce non-overlapping charging sessions within the objective function evaluation via a repair mechanism where this latter induces cascading stochastic dependencies. This makes both realized charging start and end times random variables, substantially increasing problem complexity compared to existing approaches. We derive the cumulative distribution functions of realized charging start and end times and obtain an analytical expression for expected total tardiness involving a high-dimensional integral, while showing that expected peak load is intractable to compute exactly. We therefore approximate both objectives using Monte Carlo simulation. To solve the problem, we adapt and compare three multi-objective evolutionary algorithms: NSGAII, MOPSO, and MOGWO. Comprehensive computational experiments on 20 real-world instances derived from the ACNData dataset, involving up to 200 vehicles, show that NSGAII achieves superior hypervolume performance on 15 out of 20 instances, with statistically significant differences confirmed by Friedman and Mann–Whitney U tests. The proposed Framework provides an effective decision-support approach for managing electric vehicle charging operations under uncertainty.