Ordered Genetic Algorithm for Entrance Dependent Vehicle Routing Problem in Farms

TL;DR

This work defines the Entrance Dependent VRP (EDVRP), a VRP variant where node size and dual entrances affect distances, with farm routing as the application context. It provides a formal EDVRP model and introduces the Ordered Genetic Algorithm (OGA), which encodes solutions with entrance-aware ordering and employs novel operators such as entrance inversion, intra-group sorting, and a greedy path strategy. Experimental results show that OGA outperforms random baselines and a non-ordered GA across total idle distance $s_P$, makespan $t_P$, and fuel $c_P$, with ablation studies confirming the impact of the new operators. The work delivers a practical baseline for EDVRP in farming scenarios and suggests extensions to other EDVRP settings and neural-network-based enhancements for future work.

Abstract

Vehicle Routing Problems (VRP) are widely studied issues that play important roles in many production scenarios. We have noticed that in some practical scenarios of VRP, the size of cities and their entrances can significantly influence the optimization process. To address this, we have constructed the Entrance Dependent VRP (EDVRP) to describe such problems. We provide a mathematical formulation for the EDVRP in farms and propose an Ordered Genetic Algorithm (OGA) to solve it. The effectiveness of OGA is demonstrated through our experiments, which involve a multitude of randomly generated cases. The results indicate that OGA offers certain advantages compared to a random strategy baseline and a genetic algorithm without ordering. Furthermore, the novel operators introduced in this paper have been validated through ablation experiments, proving their effectiveness in enhancing the performance of the algorithm.

Figures (6)

• Figure 1: A typical farm. The green polygons represent three fields, while the pentagrams denote the garage(depot). Thick solid lines represent roads within the farm, thin solid lines depict passable roads within fields, and dashed lines indicate working lines awaiting operation. The numbers on the edges of the working lines are their identifiers.
• Figure 2: In the scenario, the working lines represented by the red dashed lines have been assigned to one machine, which enters the field from above the leftmost working line. It can be observed that when $\cos \theta < 1/3$, the distance traveled for the left sequence is longer than that for the non-sequential operation on the right.
• Figure 3: The machine needs to complete tasks on three working lines from left to right. The left solution selects path 1 from the depot to the leftmost working line based on the greedy operator, while the right solution chooses the longer path 2. It is visually evident that the greedy path on the left is longer than the one on the right.
• Figure 4: Flowchart and visualization of operators.
• Figure 5: Farm used in case study. The star represents the depot. The dashed lines are the working lines. The white and black points are the entrances 0 and 1, respectively.