Goal-Induced Pareto Fronts for a Bi-Criterion Truck–Multiple-Drone Routing Problem

Truck–multiple-drone routing problems involve conflicting operational criteria and are therefore naturally suited to multiobjective analysis. In practical settings, however, decision makers may also specify aspiration levels for the considered criteria, which call for a target-oriented perspective. This paper studies a bi-criterion truck–multiple-drone routing problem through a goal-induced deviation framework in which the original objectives are transformed to normalized positive deviations with respect to prescribed targets. First, a general mathematical framework is introduced, and several structural properties are established, including dominance preservation, invariance under positive weighting, equivalence with the original Pareto structure when all the targets are violated, and the loss of discrimination when the targets are attainable. To address this latter effect, an enhanced goal-programming scalarization is proposed and shown to preserve consistency with the Pareto efficiency. The framework is then specialized to a truck–multiple-drone routing problem with truck time and makespan as criteria and evaluated on representative benchmark instances together with a broader attainable-target benchmark battery, using a common agent-based metaheuristic search framework adapted from literature. This search framework is employed both to estimate a reference Pareto frontier and to solve the GP and EGP scalarizations under the same computational scheme. The computational results illustrate two target regimes: When the targets are unattainable, both formulations are mainly driven by the minimization of positive deviations; when they are attainable, classical goal programming may return satisfactory but dominated solutions, whereas the enhanced formulation preserves discrimination and selects Pareto-efficient alternatives.