A Modified Artificial Bee Colony Algorithm with a Load-Dependent Fuel Model for the Bi-Objective Green Capacitated Vehicle Routing Problem
Keywords:
artificial bee colony, capacitated vehicle routing problem, fuel consumption, green vehicle routing, bi-objective optimizationAbstract
The capacitated vehicle routing problem (CVRP) conventionally minimizes total travel distance, yet a distance-minimal route need not minimize fuel. As fuel rate rises with payload, so demand distribution across arcs matters even at fixed total distance. To address this gap, this study formulates a bi-objective green CVRP minimizing total distance and fuel under an arc-wise fuel rate that increases linearly with vehicle load, solved by an improved artificial bee colony algorithm (IABC). The IABC combines a scattered construction-based population, a dual-group employed-bee neighbourhood, and a forward-insertion scout, with an iteration-dependent capacity penalty in a normalized weighted-sum fitness, one tunable weight traces the distance–fuel trade-off. Across twelve Augerat instances (twelve runs each), the IABC matches the best-known distance on four, reduces mean fuel by 3.50% versus the Clarke–Wright savings baseline, and yields only capacity-feasible routes. On P-n16-k8, a two-stage lexicographic mixed-integer program certifies the distance-then-fuel optimum (450 km, 116.73 L), attained exactly by the IABC. Non-parametric tests rank the IABC above standard ABC, a genetic algorithm, and the savings heuristic on both objectives. Ablation attributes the gain to the load-aware objective, and the saving persists under ±20% fuel-coefficient perturbations, supporting robust green route planning.References
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