Solving a capacitated waste collection problem using an open-source tool

Increasing complexity in municipal solid waste streams worldwide is pressing Solid Waste Management Systems (SWMS), which need solutions to manage the waste properly. Waste collection and transport is the first task, traditionally carried out by countries/municipalities responsible for waste management. In this approach, drivers are responsible for decision-making regarding collection routes, leading to inefficient resource expenses. In this sense, strategies to optimize waste collection routes are receiving increasing interest from authorities, companies and the scientific community. Works in this strand usually focus on waste collection route optimization in big cities, but small towns could also benefit from technological development to improve their SWMS. Waste collection is related to combinatorial optimization that can be modeled as the capacitated vehicle routing problem. In this paper, a Capacitated Waste Collection Problem will be considered to evaluate the performance of metaheuristic approaches in waste collection optimization in the city of Bragança, Portugal. The algorithms used are available on Google OR-tools, an open-source tool with modules for solving routing problems. The Guided Local Search obtained the best results in optimizing waste collection planning. Furthermore, a comparison with real waste collection data showed that the results obtained with the application of OR-Tools are promising to save resources in waste collection.This work has been supported by FCT - Fundação para a Ciência e Tecnologia within the R &D Units Project Scope: UIDB/05757/2020, UIDB/00690/2020, UIDB/50020/2020, and UIDB/00319/2020. Adriano Silva was supported by FCT-MIT Portugal PhD grant SFRH/BD/151346/2021, and Filipe Alves was supported by FCT PhD grant SFRH/BD/143745/2019

A revisited branch-and-cut algorithm for large-scale orienteering problems

The orienteering problem is a route optimization problem which consists of finding a simple cycle that maximizes the total collected profit subject to a maximum distance limitation. In the last few decades, the occurrence of this problem in real-life applications has boosted the development of many heuristic algorithms to solve it. However, during the same period, not much research has been devoted to the field of exact algorithms for the orienteering problem. The aim of this work is to develop an exact method which is able to obtain the optimum in a wider set of instances than with previous methods, or to improve the lower and upper bounds in its disability. We propose a revisited version of the branch-and-cut algorithm for the orienteering problem which includes new contributions in the separation algorithms of inequalities stemming from the cycle problem, in the separation loop, in the variables pricing, and in the calculation of the lower and upper bounds of the problem. Our proposal is compared to three state-of-the-art algorithms on 258 benchmark instances with up to 7397 nodes. The computational experiments show the relevance of the designed components where 18 new optima, 76 new best-known solutions and 85 new upper-bound values were obtained

Logic learning and optimized drawing: two hard combinatorial problems

Nowadays, information extraction from large datasets is a recurring operation in countless fields of applications. The purpose leading this thesis is to ideally follow the data flow along its journey, describing some hard combinatorial problems that arise from two key processes, one consecutive to the other: information extraction and representation. The approaches here considered will focus mainly on metaheuristic algorithms, to address the need for fast and effective optimization methods. The problems studied include data extraction instances, as Supervised Learning in Logic Domains and the Max Cut-Clique Problem, as well as two different Graph Drawing Problems. Moreover, stemming from these main topics, other additional themes will be discussed, namely two different approaches to handle Information Variability in Combinatorial Optimization Problems (COPs), and Topology Optimization of lightweight concrete structures

Distance-constrained vehicle routing problem: exact and approximate solution (mathematical programming)

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.The asymmetric distance-constrained vehicle routing problem (ADVRP) looks at finding vehicle tours to connect all customers with a depot, such that the total distance is minimised; each customer is visited once by one vehicle; every tour starts and ends at a depot; and the travelled distance by each vehicle is less than or equal to the given maximum value. We present three basic results in this thesis. In the first one, we present a general flow-based formulation to ADVRP. It is suitable for symmetric and asymmetric instances. It has been compared with the adapted Bus School Routing formulation and appears to solve the ADVRP faster. Comparisons are performed on random test instances with up to 200 customers. We reach a conclusion that our general formulation outperforms the adapted one. Moreover, it finds the optimal solution for small test instances quickly. For large instances, there is a high probability that an optimal solution can be found or at least improve upon the value of the best feasible solution found so far, compared to the other formulation which stops because of the time condition. This formulation is more general than Kara formulation since it does not require the distance matrix to satisfy the triangle inequality. The second result improves and modifies an old branch-and-bound method suggested by Laporte et al. in 1987. It is based on reformulating a distance-constrained vehicle routing problem into a travelling salesman problem and uses the assignment problem as a lower bounding procedure. In addition, its algorithm uses the best-first strategy and new branching rules. Since this method was fast but memory consuming, it would stop before optimality is proven. Therefore, we introduce randomness in choosing the node of the search tree in case we have more than one choice (usually we choose the smallest objective function). If an optimal solution is not found, then restart is required due to memory issues, so we restart our procedure. In that way, we get a multistart branch and bound method. Computational experiments show that we are able to exactly solve large test instances with up to 1000 customers. As far as we know, those instances are much larger than instances considered for other VRP models and exact solution approaches from recent literature. So, despite its simplicity, this proposed algorithm is capable of solving the largest instances ever solved in literature. Moreover, this approach is general and may be used in solving other types of vehicle routing problems. In the third result, we use VNS as a heuristic to find the best feasible solution for groups of instances. We wanted to determine how far the difference is between the best feasible solution obtained by VNS and the value of optimal solution in order to use the output of VNS as an initial feasible solution (upper bound procedure) to improve our multistart method. Unfortunately, based on the search strategy (best first search), using a heuristic to find an initial feasible solution is not useful. The reason for this is because the branch and bound is able to find the first feasible solution quickly. In other words, in our method using a good initial feasible solution as an upper bound will not increase the speed of the search. However, this would be different for the depth first search. However, we found a big gap between VNS feasible solution and an optimal solution, so VNS can not be used alone unless for large test instances when other exact methods are not able to find any feasible solution because of memory or stopping conditions

The bus sightseeing problem

The basic characteristic of vehicle routing problems with profits (VRPP) is that locations to be visited are not predetermined. On the contrary, they are selected in pursuit of maximizing the profit collected from them. Significant research focus has been directed toward profitable routing variants due to the practical importance of their applications and their interesting structure, which jointly optimizes node selection and routing decisions. Profitable routing applications arise in the tourism industry aiming to maximize the profit score of attractions visited within a limited time period. In this paper, a new VRPP is introduced, referred to as the bus sightseeing problem (BSP). The BSP calls for determining bus tours for transporting different groups of tourists with different preferences on touristic attractions. Two interconnected decision levels have to be jointly tackled: assignment of tourists to buses and routing of buses to the various attractions. A mixed-integer programming formulation for the BSP is provided and solved by a Benders decomposition algorithm. For large-scale instances, an iterated local search based metaheuristic algorithm is developed with some tailored neighborhood operators. The proposed methods are tested on a large family of test instances, and the obtained computational results demonstrate the effectiveness of the proposed solution approaches