Complete Algorithm for Solving the Scripting Problem on Multi-Task Enabled Arcs
Authors: Silva Fausto Pinheiro da , Wilhelm Volmir Eugenio , Santos Cleverson Gonçalves dos , Thomaz Diego Venâncio , Sandmann André , Acordi Júnior Mauro 
Published: August 2024

Objective: This paper presents algorithms designed to support a linear model capable of optimizing the routes taken by meter readers to measure the instruments installed in a hydroelectric power plant.

Theoretical Framework: The study conducted by Tirkolaee was used as a reference point to address the challenge of determining the most efficient routes, serving as one of the foundations of this work. In addition to solving the PCARP, the article also focused on minimizing the number of vehicles required for the task. However, it does not include a predefined frequency approach as in Chu, nor does it address multiple tasks as in Cleverson and Fausto. Cleverson's work, in turn, is a generalization of Chu's, considering that the edges can have different demands, representing distinct tasks such as reading instruments like Thermometer, Pendulum, Seismograph, and Piezometer. This study distinguishes itself from the others by analyzing the subcycles that may arise during the resolution of the exact model and determining the feasibility of solving the model with constraints that eliminate the subcycles in the first iteration or adding them as necessary. Due to computational advancements, this work presents various methods to achieve the best solution for the PCARP.

Method: Develop a model that considers the following characteristics: selection of the combinations of days of the week to perform the tasks assigned to the meter readers; selection of the meter readers who will traverse route y, which includes gallery x and the instruments to be read; the meter reader must pass through the route at least once to perform the task but may need to traverse the edge without performing any specific action to maintain the route's flow; not all meter readers may be qualified to perform all tasks due to a lack of knowledge in handling the equipment required to read certain instruments; the meter reader must start their journey at the depot, represented by vertex "0," and return to this point at the end of the day; the total time to leave the depot, perform the instrument readings, and return must not exceed the meter reader's daily working hours.

Results and Conclusion: The results indicate that the Complete Algorithm demonstrated significant efficiency. In tests with various instances, it obtained a solution without subcycles in the first iteration 68% of the time. Additionally, in 63% of the cases, the time taken to reach this solution was shorter, without increasing the distance traveled, the number of vehicles required, or the number of days the vehicles were used. In cases where the meter reader's work time was "t/2," the Complete Algorithm achieved the best results: in 90% of the cases, it obtained solutions without subcycles, compared to 63% using the algorithm described in [11]. In 50% of the cases tested, a solution with zero GAP was achieved. This difference observed when the meter reader's work time was "t/2" is especially relevant in real-world situations, where the time needed to traverse the graph and perform the tasks, as suggested in the article, can be significantly longer than the meter reader's workday. Therefore, determining all subcycles is the best approach to achieving a feasible solution without subcycles.

Implications of the Research: A model that can be applied to determine the optimal route for meter readers as well as in other real-world situations, such as analyzing the routes for equipment inspections within an industry and for waste collection.

Originality/Value: The Complete Algorithm, in addition to the linear model, brings originality in its construction and compilation, as it provides a method to find a feasible solution without subcycles in the first iteration. With the Complete Algorithm, it is possible to achieve a feasible solution that determines the shortest distance and the minimum number of meter readers, ensuring resource savings and effective monitoring of auscultation instruments.