An Arable Field for Benchmarking of Metaheuristic Algorithms for Capacitated Coverage Path Planning Problems

Abstract

This study specifies an agricultural field (Latitude = 56°30′0.8″ N, Longitude = 9°35′27.88″ E) and provides the absolute optimal route for covering that field. The calculated absolute optimal solution for this field can be used as the basis for benchmarking of metaheuristic algorithms used for finding the most efficient route in the field. The problem of finding the most efficient route that covers a field can be formulated as a Traveling Salesman Problem (TSP), which is an NP-hard problem. This means that the optimal solution is infeasible to calculate, except for very small fields. Therefore, a range of metaheuristic methods has been developed that provide a near-optimal solution to a TSP in a “reasonable” time. The main challenge with metaheuristic methods is that the quality of the solutions can normally not be compared to the absolute optimal solution since this “ground truth” value is unknown. Even though the selected benchmarking field requires only eight tracks, the solution space consists of more than 1.3 billion solutions. In this study, the absolute optimal solution for the capacitated coverage path planning problem was determined by calculating the non-working distance of the entire solution space and determining the solution with the shortest non-working distance. This was done for four scenarios consisting of low/high bin capacity and short/long distance between field and storage depot. For each scenario, the absolute optimal solution and its associated cost value (minimum non-working distance) were compared to the solutions of two metaheuristic algorithms; Simulated Annealing Algorithm (SAA) and Ant Colony Optimization (ACO). The benchmarking showed that neither algorithm could find the optimal solution for all scenarios, but they found near-optimal solutions, with only up to 6 pct increasing non-working distance. SAA performed better than ACO, concerning quality, stability, and execution time.

Novel Route Planning Method to Improve the Operational Efficiency of Capacitated Operations. Case: Application of Organic Fertilizer

“…These new nodes should be added to the field graph and the cost matrix should be updated based on them. According to Figure 3, the original cost matrix includes the nodes (0, 1,6,7,12,13,16,17,20,21,24,25,26,27,28), and it shows the distances of these nodes from each other. For example, after adding the node 3, the distance from this node to the others can be determined by adding the length L1 to the values in the column corresponding to the node 1 in the original cost matrix [6].…”

“…Agricultural field area coverage planning enhances the efficiency of commercial autosteering or navigation-aid systems on agricultural machines [1][2][3]. Area coverage plans provide a path that visits all points of a targeted spatial environment under the criterion of minimization of unproductive time or traveled distance and avoiding machine maneuvering in the already worked area or cropping area [4,5].…”

“…For instance, in the case of a fertilizing operation, when the distributer is positioned in the middle of a track and a reloading action is required (e.g., the tanker become empty and it is urgent to revisit the depot for refilling), then there are various options open to the machine's operator to either continue in the same direction in that track to reach to the headland part and then go back to the depot or the operator can do a U-turn (180-degree turn) and go to an adjacent unworked track to return to the depot. In these studies [1,4,13,14], the capacitated field operations casted into the examples of vehicle routing problem (VRP). They showed that the agricultural fleet management problem could be expressed as the traversal of weighted graphs under some operational constraints.…”

Route Planning for Agricultural Machines with Multiple Depots: Manure Application Case Study

“…The cost matrix is square (n * n ) with an element C ij which represents the transition cost from vertex i to vertex j, where i j; otherwise, the cost is equal to 0. The shortest path search algorithm was applied for calculating the transition cost between every pair of nodes [28].…”

“…Simulated annealing (SA) as a stochastic algorithm is used in this study to investigate the near-optimal solution. This method has been implemented in several problems in various fields such as computer design, route planning, and image processing [6,28,29]. The mechanism of this algorithm is based on the simulation of a cooling process called annealing where a solid is gradually cooled.…”