Distance Approximation for Dynamic Waste Collection Planning

Abstract

Approximating the solution value of transportation problems has become more relevant in recent years, as these approximations can help to decrease the computational effort required for solving those routing problems. In this paper, we apply several regression methods to predict the total distance of the traveling salesman problem (TSP) and vehicle routing problem (VRP). We show that distance can be estimated fairly accurately using simple regression models and only a limited number of features. We use features found in scientific literature and introduce a new class of geographical features. The model is validated on a dynamic waste collection case in the city of Amsterdam, The Netherlands. We introduce a cost function that combines the travel distance and service level, and show that our model can reduce distances up to 17%, while maintaining the same service level, compared to a well-known heuristic approximation. Furthermore, we show the benefits of using approximations for combining offline learning with online or frequent optimization.

Estimating optimal objective values for the TSP, VRP, and other combinatorial problems using randomization

“…Note that N = 100 for these 10,000 instances, so the feature N is not included in the model after stepwise regression. From this table, we see that our mean CW 3 and std CW 3 model clearly outperforms the model in row 6 which is based on Akkerman et al (2020).…”

“…They built linear regression, random forest, and neural network models We compare six models on the 10,000 VRP instances in Table 5. The last model is based on the 11 features that are most important and easy to compute from Akkerman et al (2020), mentioned earlier. We obtain this model by stepwise regression using backward elimination.…”

“…In addition to comparing these models with the one in the bottom row of Table 3, we add another model considering the following list of features: number of customers N, capacity of the vehicle C, perimeter of the convex hull P, area of the convex hull A, height of the enclosing rectangle H, width of the enclosing rectangle W, average distance between customers d c , means of variances in customer latitude and longitude mean Var(x,y) , average distance between the depot and all customers d d , average demand demand, and variance in demand V (demand ). This list of features comes from Akkerman et al (2020). They built linear regression, random forest, and neural network models We compare six models on the 10,000 VRP instances in Table 5.…”

“…Then, they used linear regression, random forest regression, and neural networks to construct multiple models. The best models developed by Cavdar and Sokol (2015), Nicola et al (2019), and Akkerman et al (2020) obtained promising results, with r-squared values higher than 0.95 on their test instances. These more recent works considered instances where vertices have known x-y coordinates, and the distance between vertices is Euclidean.…”

“…Nicola et al (2019) used stepwise regression and built a model including instance size N, maximum distance across all pairs of vertices, and the sum of distances to the nearest neighbor for each vertex. Akkerman et al (2020) considered 21 different structural properties from the literature and 11 newly proposed structural properties before the feature selection step. Then, they used linear regression, random forest regression, and neural networks to construct multiple models.…”