Hybridizing 0/1 Knapsack and Priority-Aware TSP for Vehicle Routing: an Applied Variant of the TSP with Profits

Aron da Silva Bezerra; Francisco Márcio Barboza

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arXiv · 2610.36526

Hybridizing 0/1 Knapsack and Priority-Aware TSP for Vehicle Routing: an Applied Variant of the TSP with Profits

Aron da Silva Bezerra·Francisco Márcio Barboza

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Abstract

Distribution logistics with capacity constraints and service priorities can be modeled as a variant of the \emph{TSP with Profits} (TSPP), in which not all customers need to be visited and the selection of which customers to serve is part of the problem. This paper proposes an applied variant with two adaptations: (i) a 0/1 Knapsack objective function weighted by client priority squared ($v_i \cdot p_i^2$), and (ii) a priority bias in the Nearest Neighbor heuristic for the TSP, parameterized by $α$. The approach is evaluated on a scenario with 14 customers and a 1,100~kg capacity, complemented by a comparative experimental protocol against the classical greedy heuristic ($v_i/w_i$ ordering) and an integer programming solver. Results on the base scenario show 9 customers served, 96.4\% capacity utilization, and R\$~18,392.60 revenue, with all 5 excluded customers being low-priority. A sensitivity analysis of the priority exponent justifies the quadratic choice. The limitations of the hierarchical decomposition are explicitly discussed.

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Aron da Silva Bezerra, Francisco Márcio Barboza. 2026-10-27. Hybridizing 0/1 Knapsack and Priority-Aware TSP for Vehicle Routing: an Applied Variant of the TSP with Profits. https://arxiv.org/abs/2610.36526

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