## 1 Introduction
Thus, 3L-CVRP is a multidimensional coupled optimization problem influenced by multiple constraints, and requires a dynamic balance between physical feasibility in 3D space and economic efficiency in the time dimension [20]. Moreover, the complexity of the 3L-CVRP mathematical model grows as O(\(n^{3}\)) with the number of customers \(n\). Existing heuristic algorithms face a dilemma: enhancing global search capabilities (e.g., expanding population size) increases the number of 3D packing verifications, while focusing on local search efficiency (e.g., strengthening mutation operators) risks premature convergence. To address 3L-CVRP challenges, existing approaches can be broadly categorized into metaheuristics and hybrid algorithms. The artificial bee colony (ABC) algorithm [21], as a representative swarm intelligence method, has demonstrated promising performance in vehicle routing problems due to its strong global exploration capability. However, its convergence speed tends to degrade when handling multi-layer constraints. Another notable approach is the GA-TS hybrid algorithm, which combines genetic algorithms' evolutionary mechanisms with tabu search's local intensification [22]. While this integration improves solution quality, it introduces increased computational complexity that may -hinder real-time applications. These inherent limitations in current methodologies motivate our development of the RSO-IGA framework, which aims to synergize the explorative strengths of swarm intelligence with adaptive local search mechanisms while maintaining computational efficiency. Therefore, RSO-IGA is compared with these two algorithms in the following case analysis. The results show that RSO-IGA performs better in express delivery scenarios. Although the solution set of path length and loading rate can be obtained by using multi-objective optimization, and the internal relationship between path length and loading rate can be clearly seen, the efficiency of this method is low and the calculation time is long. In the actual logistics scenario, we need to obtain a specific optimal delivery scheme (path scheme and packing scheme) in an acceptable calculation time, especially in the circumstances in which the customers have individual requirements. Therefore, this paper adopts the method of multi-objective normalization to solve the problem. This method has a short calculation time and accurate optimal solution, which is suitable for the problem to be solved in this paper. To address these challenges, this study proposes a collaborative optimization framework based on the residual space optimization (RSO) strategy and an improved genetic algorithm (IGA). The innovations of this research are as follows: (1) Introducing a linear weighting method to construct a multi-objective transformation model that integrates packing and route topology features, balancing route economy and loading efficiency. (2) Designing a three-layer encoding system that includes route layer _R_chrom_, loading layer _L_chrom_, and orientation layer _P_chrom_, combining an improved Clarke-Wright algorithm to generate initial solutions and using the Gaode Maps API to obtain real road network distances instead of Manhattan distances. (3) Enhancing the RSO packing scheme through dynamic space partitioning rules and the LIFO constraint reverse verification to ensure the feasibility of 3D loading. Two experiments are conducted based on 22 extended test cases derived from the Cordeau standard dataset and the real logistics data of a Chinese university on a shopping festival. The results show that the proposed approach to 3L-CVRP has practical value in large-scale scenarios.