Evaluating Robustness of Metaheuristics in Stochastic Variants of the CVRPTW
Abstract
Modern logistics systems operate under uncertain and dynamically changing conditions, particularly in relation to customer demand and delivery time windows. This paper investigates a stochastic variant of the Capacitated Vehicle Routing Problem with Time Windows (CVRPTW), where both time-window boundaries and customer demands are perturbed across multiple scenarios. A complete MILP model integrating vehicle capacity constraints, soft time windows, and penalty-based feasibility relaxation is formulated. To solve large-scale stochastic instances, Tabu Search (TS) and Artificial Bee Colony (ABC) metaheuristics are developed and validated against an exact Gurobi solver and a greedy constructive baseline. The experimental evaluation, conducted over 1,200 stochastic scenarios derived from Solomon benchmarks, demonstrates that metaheuristics consistently outperform the greedy approach, with the ABC algorithm achieving a significant average cost reduction of 23.74%. Beyond average performance, the metaheuristics exhibit reduced variability and effectively mitigate extreme high-cost outcomes, ensuring higher operational reliability. Crucially, the observed reduction in variance and the mitigation of the most severe scenarios are highly significant for real-world applications, as they minimize operational risks and ensure predictable service levels in volatile environments. These results confirm that the proposed metaheuristics provide stable routing performance under uncertainty, primarily by prioritizing time-window compliance over simple distance minimization, which reduces penalties by up to 31.3%. The findings highlight a strategic trade-off where accepting slightly longer routes ensures significantly higher service predictability.
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