The Electric Vehicle Routing Problem with Capacitated Charging Stations

Electric vehicle routing problems (E-VRPs) deal with routing a fleet of electric vehicles (EVs) to serve a set of customers while minimizing an operational criterion, for example, cost or time. The feasibility of the routes is constrained by the autonomy of the EVs, which may be recharged along the route. Much of the E-VRP research neglects the capacity of charging stations (CSs) and thus implicitly assumes that an unlimited number of EVs can be simultaneously charged at a CS. In this paper, we model and solve E-VRPs considering these capacity restrictions. In particular, we study an E-VRP with nonlinear charging functions, multiple charging technologies, en route charging, and variable charging quantities while explicitly accounting for the number of chargers available at privately managed CSs. We refer to this problem as the E-VRP with nonlinear charging functions and capacitated stations (E-VRP-NL-C). We introduce a continuous-time model formulation for the problem. We then introduce an algorithmic framework that iterates between two main components: (1) the route generator, which uses an iterated local search algorithm to build a pool of high-quality routes, and (2) the solution assembler, which applies a branch-and-cut algorithm to combine a subset of routes from the pool into a solution satisfying the capacity constraints. We compare four assembly strategies on a set of instances. We show that our algorithm effectively deals with the E-VRP-NL-C. Furthermore, considering the uncapacitated version of the E-VRP-NL-C, our solution method identifies new best-known solutions for 80 of 120 instances.

An iterated local search for the travelling salesman problem

O Problema do Caixeiro Viajante é um problema clássico da Ciência da Computação, com muitas extensões e variações sendo estudadas ao longo de décadas de pesquisas, principalmente para aplicações relacionadas à logística. Aqui, apresentamos um algoritmo Iterated Local Search (ILS) para encontrar soluções para instâncias do problema proposto pela Competição Brasileira de Descoberta de Conhecimento em Bancos de Dados (KDD-BR). O algoritmo ILS é um algoritmo simples que não depende de nenhuma biblioteca de terceiros. Além disso, foi um dos métodos mais eficazes na competição.

Modified Migrating Birds Optimization Algorithm: Multi-Depot Capacitated Vehicle Routing Problem

The multi-depot capacitated vehicle routing problem (MDCVRP) is a variation of the vehicle routing problem (VRP) modeled from distribution problems in the industrial world. This problem is a complex optimization problem in the field of operations research in applied mathematics. The MDCVRP is very interesting to discuss and find the best solution method. In this study, the authors apply the modified migrating birds' optimization (MMBO) algorithm, which is a hybrid of the migrating birds' optimization (MMBO) and iterated local search (ILS) algorithms. The purpose of this study is to analyze the results of applying the algorithm in solving MDCVRP. We used 20 MDCVRP data in simulation, grouped into four sizes (25, 50, 75, and 100 points). Based on the results of this research, it is known that the MMBO algorithm can produce the following solutions. First, on the data of 25 points, the experiment reaches the optimal value with small convergent iterations. Second, the best results on the data of 50 points have reached optimal value, but some other results have not been optimal. And, third, for data of 75 and 100 points, there is no optimal solution obtained by the MMBO algorithm. These results conclude that the MMBO algorithm effectively solves the MDCVRP problem with small data, but the bigger data, the more ineffective.Keywords: MDCVRP; VRP; optimization; operation research; applied Mathematics; MMBO. AbstrakMulti-depot capacitated vehicle routing problem (MDCVRP) adalah salah satu variasi dari vehicle routing problem (VRP) yang dimodelkan dari permasalahan distribusi di dunia industri. Permasalahan ini merupakan permasalahan optimasi kompleks dalam bidang riset operasi ilmu matematika terapan. MDCVRP sangat menarik untuk dibahas dan dicari metode penyelesaian terbaik. Dalam penelitian ini, penulis menerapkan algoritma modified migrating birds optimization (MMBO) yang merupakan hybrid algoritma migrating birds optimization (MBO) dan iterated local search (ILS). Tujuan penelitian ini adalah menganalisis hasil penerapan algoritma dalam menyelesaikan MDCVRP. Untuk simulasi, penulis menggunakan 20 data MDCVRP yang dikelompokkan menjadi empat ukuran (25, 50, 75, dan 100 titik). Berdasarkan hasil penelitian yang telah dilakukan, diketahui bahwa algoritma MMBO mampu menghasilkan solusi sebagai berikut. Pertama, Pada data 25 titik, percobaan mencapai nilai optimal dengan iterasi konvergen yang kecil. Kedua, Hasil terbaik pada data 50 titik telah mencapai nilai optimal namun sebagain hasil lainnya belum optimal. Dan ketiga, untuk data 75 dan 100 titik, tidak terdapat solusi optimal yang dihasilkan algoritma MMBO. Dari hasil tersebut dapat disimpulkan bahwa algoritma MMBO efektif untuk menyelesaikan MDCVRP data kecil, namun semakin besar datanya menjadi kurang efektif.Kata kunci: MDCVRP; VRP; optimasi; riset operasi; matematika terapan; MMBO.

Designing screen layout in multimedia applications through integer programming and metaheuristic

Binding audiovisual content into multimedia applications requires the specification of each media item, including its size and position, to define a screen layout. The multimedia application author must plan the application’s screen layout (ASL), considering a variety of screen sizes where the application shall be executed. An ASL that maximizes the area occupied by media items on the screen is essential, given that screen space is a valuable asset for media broadcasters. In this paper, we introduce the Application Screen Layout Optimization Problem, and present its NP-hardness. Besides, two integer programming formulations and an Iterated Local Search (ILS) metaheuristic are proposed to solve it. The efficiency of the proposed methods is evaluated, showing that the metaheuristic achieves better results and is at least 12 times faster, on average, than the mathematical formulations. Also, the proposed approaches were compared to a layout design algorithm, showing their effectiveness.

THE TRAVELING SALESMAN PROBLEM WITH MULTI-VISIT DRONE

This paper deals with the Traveling Salesman Problem with Multi-Visit Drone (TSP-MVD) in which a truck works in collaboration with a drone that can serve up to q > 1 customers consecutively during each sortie. We propose a Mixed Integer Linear Programming (MILP) formulation and a metaheuristic based on Iterated Local Search to solve the problem. Benchmark instances collected from the literature of the special case with q = 1 are used to test the performance of our algorithms. The obtained results show that our MILP model can solve a number of instances to optimality. This is the first time optimal solutions for these instances are reported. Our ILS performs better other algorithms in terms of both solution quality and running time on several class of instances. The numerical results obtained by testing the methods on new randomly generated instances show again the effectiveness of the methods as well as the positive impact of using the multi-visit drone.

Modeling and scheduling hybrid open shops for makespan minimization

Purpose This study aims to address the hybrid open shop problem (HOSP) with respect to the minimization of the overall finishing time or makespan. In the HOSP, we have to process n jobs in stages without preemption. Each job must be processed once in every stage, there is a set of mk identical machines in stage k and the production flow is immaterial. Design/methodology/approach Computational experiments carried out on a set of randomly generated instances showed that the minimal idleness heuristic (MIH) priority rule outperforms the longest processing time (LPT) rule proposed in the literature and the other proposed constructive methods on most instances. Findings The proposed mathematical model outperformed the existing model in the literature with respect to computing time, for small-sized instances, and solution quality within a time limit, for medium- and large-sized instances. The authors’ hybrid iterated local search (ILS) improved the solutions of the MIH rule, drastically outperforming the models on large-sized instances with respect to solution quality. Originality/value The authors formalize the HOSP, as well as argue its NP-hardness, and propose a mixed integer linear programming model to solve it. The authors propose several priority rules – constructive heuristics based on priority measures – for finding feasible solutions for the problem, consisting of adaptations of classical priority rules for scheduling problems. The authors also propose a hybrid ILS for improving the priority rules solutions.