scholarly journals Valid Inequalities for the Green Vehicle Routing Problem

2020 ◽  
Author(s):  
Matheus Diógenes Andrade ◽  
Fábio Luiz Usberti
Keyword(s):  
Vehicle Routing ◽  
Electric Vehicles ◽  
Vehicle Routing Problem ◽  
Valid Inequalities ◽  
Alternative Fuel ◽  
Hard Problem ◽  
Np Hard ◽  
Green Logistics ◽  
Routing Problem ◽  
Np Hard Problem

This work aims to investigate the Green Vehicle Routing Problem (G-VRP), which is an NP-Hard problem that generalizes the Vehicle Routing Problem (VRP) and integrates it with the green logistics. In the G-VRP, electric vehicles with limited autonomy can be recharged at Alternative Fuel Stations (AFSs) to keep visiting customers. This research proposes MILP formulations, valid inequalities, and preprocessing conditions.

scholarly journals Algoritma Warshall untuk Penyelesaian Masalah Vehicle Routing (Studi Kasus : Pendistribusian PT Semen Bosowa di Makassar)

2019 ◽  
Vol 1 (1) ◽  
pp. 15
Author(s):  
Syafruddin Side ◽  
Maya Sari Wahyuni ◽  
Hadrianty Ramli
Keyword(s):  
Combinatorial Optimization ◽  
Vehicle Routing ◽  
Shortest Path ◽  
Vehicle Routing Problem ◽  
Path Length ◽  
Hard Problem ◽  
Np Hard ◽  
Exact Methods ◽  
Routing Problem ◽  
Np Hard Problem

Abstrak. Warshall merupakan algoritma untuk menghitung jarak terpendek untuk semua pasangan titik pada sebuah lokasi yang dapat diubah menjadi sebuah graf berarah dan berbobot, yang berupa titik-titik (V) dan sisi-sisi (E) serta paling memiliki minimal satu sisi pada setiap titik. Vehicle Routing Problem (VRP) termasuk dalam kelas NP-hard problem dalam combinatorial optimization, sehingga sulit diselesaikan dengan metode eksak yang berlaku secara umum. Penelitian ini diawal dengan konsep matematis Penerapan Algoritma Warshall, yaitu pengambilan data Pendistribusian dari Perusahaan, pencarian bobot lintasan, mengubah kedalam matriks dengan ukuran  dalam hal ini matriks yang digunakan berukuran , menerapkan Algoritma Warshall dalam matriks yang diperoleh. Persamaan yang digunakan adalah pertama Representasi graf ke matriks berbobot berjarak D = [dij] yaitu jarak dari vertex i ke j; Kedua Dekomposisi dengan urutan dij(k). D(k) menjadi matriks nxn [dij(k)] batasi k sampai n sehingga k = 0, 1, …, n; Ketiga Pengamatan struktur shortest path dilakukan dengan dua cara yaitu jika k bukan merupakan vertex pada path (path terpendek memiliki panjang dij(k-1)) dan k merupakan vertex pada path (path terpendek memiliki panjang dij(k-1)+dij(k-1)), hal tersebut memuat sebuah subpath dari i ke k dan sebuah subpath dari k ke j. Keempat Iterasi yang dimulai dari 0 sampai dengan n. Berdasarkan hasil penelitian diperoleh bahwa dengan Metode Algoritma Warshall dapat menyelesaikan permasalahan penentuan rute terpendek dalam pendistribusian PT Semen Bosowa dengan menghitung jarak seluruh jalur lintasan yang ada dalam pendistribusian semen Bosowa di Makassar.Kata Kunci : Algoritma Warshall, Masalah Vehicle Routing, Graf Berarah, Graf Berbobot, Jalur Terpendek.Abstract  Warshall is an algorithm to calculate the shortest distance for every pair of points in a location that can be converted into a directed and weighted graph, in the form of vertex (V) and edges (E), and most have at least one side at any vertex. Vehicle Routing Problem (VRP) is included in the class of NP-hard problem in combinatorial optimization, making it difficult to solve with exact methods applicable in general. This study beginning with mathematical concepts Implementation of Algorithms Warshall, which is taking the data distribution from the Company, the search for weight trajectory, changing into a matrix with n × n squares in this case matrix used measuring 11 x 11, apply the algorithm Warshall in the matrix obtained, the second is the implementation of Algorithms Warshall using Microsoft Visual Basic programming language. The equation used is the first representation of the graph to a weighted matrix D = [dij] ie the distance from the vertex i to j; The second order decomposition with dij (k). D (k) be the nxn matrix [dij (k)] so that the limit k to n for k = 0, 1, ..., n; Third observation structures shortest path done in two ways: if k is not a vertex on the path (the shortest path length dij (k-1)) and k is the vertex on the path (the shortest path length dij (k-1) + dij (k -1)), it contains a subpath from i to k and a subpath from k to j. The fourth iteration numbered 0 through n. The result showed that the method Warshall algorithm can solve the problems of determining the shortest route in the distribution of PT Semen Bosowa by calculating the distance of the entire passage is in the distribution of cement Bosowa in Makassar.Keywords: Algorithm Warshall, Vehicle Routing Problem, trending Graf, Graf Weighted, Shortest Path.

scholarly journals Implementation of discrete particle swarm optimization algorithm in the capacitated vehicle routing problem

2020 ◽  
Vol 4 (2) ◽  
pp. 117-128
Author(s):  
Aisyahna Nurul Mauliddina ◽  
Faris Ahmad Saifuddin ◽  
Adesatya Lentera Nagari ◽  
Anak Agung Ngurah Perwira Redi ◽  
Adji Candra Kurniawan ◽  
...  
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Optimal Solution ◽  
Computational Time ◽  
Hard Problem ◽  
Np Hard ◽  
Routing Problem ◽  
Capacitated Vehicle Routing Problem ◽  
Np Hard Problem ◽  
Capacitated Vehicle

Capacitated Vehicle Routing Problem (CVRP) is known as an NP-hard problem. It is because CVRP problems are very hard for finding optimal solutions, especially in large instances. In general, the NP-hard problem is difficult to solve in the exact method, so the metaheuristic approach is implemented in the CVRP problem to find a near-optimal solution in reasonable computational time. This research uses the DPSO algorithm for solving CVRP with ten instances of benchmark datasets. DPSO implementation uses tuning parameters with the One Factor at Time (OFAT) method to select the best DPSO parameters. The outcome objective function will be compared with several PSO models proposed in previous studies. Statistical test using One Way Reputed Measure ANOVA is needed to compare algorithm performance. First, ANOVA uses for comparing’s results. Then, ANOVA is also used to test DPSO’s performance compared with DPSO-SA, SR-1, and SR-2 algorithm. The computational result shows that the basic DPSO algorithm not competitive enough with other methods for solving CVRP.

BFO Optimization Algorithms for Vehicle Routing Problem with Time Windows

2014 ◽  
Vol 543-547 ◽  
pp. 1884-1887
Author(s):  
Li Jing Tan ◽  
Fu Yong Lin ◽  
Hong Wang
Keyword(s):  
Convergence Rate ◽  
Swarm Intelligence ◽  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Time Windows ◽  
Hard Problem ◽  
Rapid Convergence ◽  
Bacterial Foraging Optimization ◽  
Routing Problem ◽  
Np Hard Problem

Vehicle Routing Problem with Time Windows (VRPTW) is a constrained NP-hard problem that designs the least cost routes from one depot to a set of geographically scattered points. Most of traditional techniques are difficult to solve this kind of problem. In this paper, we explored the validity of another swarm-intelligence-based model-Bacterial Foraging Optimization (BFO) for VRPTW solving. Original BFO, BFO with linear decreasing chemotaxis step (BFO-LDC) and BFO with non-linear decreasing chemotaxis step (BFO-NDC) are used to obtain the best solutions of a given VRPTW problem, respectively. The experimental results demonstrated that the proposed BFO algorithms have the potential to solve Vehicle Routing Problem with Time Windows (VRPTW) with rapid convergence rate and the good result accuracy.

An Ant Colony Algorithm with Memory Grouping List for Multi-Depot Vehicle Routing Problem

2014 ◽  
Vol 926-930 ◽  
pp. 3354-3358 ◽  
Author(s):  
Wei Zeng ◽  
Yong Le He ◽  
Xiao Jun Zheng
Keyword(s):  
Vehicle Routing ◽  
Computational Efficiency ◽  
Vehicle Routing Problem ◽  
Ant Colony Algorithm ◽  
Ant Colony ◽  
Hard Problem ◽  
Routing Problem ◽  
Optimal Value ◽  
Np Hard Problem ◽  
With Memory

Multi-depot vehicle routing problem (MDVRP for short) is complex and a typical NP-Hard problem in manufactories, especially in assembly plant. We herein present an ant colony algorithm with memory grouping list (ACMGL for short) to solve this problem. To handle affiliation between clients and depots, we present certain point grouping (CP Grouping) and uncertain point grouping (UP Grouping) and obtain variable grouping purposes, make a grouping memory list for each depot store the optimal value and path of uncertain grouping after UP grouping, and thus improve the efficiency of the operation. Experimental results verified our algorithm in the computational efficiency.

scholarly journals Hybrid Genetic Algorithms and Simulated Annealing for Multi-trip Vehicle Routing Problem with Time Windows

2018 ◽  
Vol 8 (6) ◽  
pp. 4713 ◽  
Author(s):  
Amalia Kartika Ariyani ◽  
Wayan Firdaus Mahmudy ◽  
Yusuf Priyo Anggodo
Keyword(s):  
Genetic Algorithm ◽  
Simulated Annealing ◽  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Computational Experiment ◽  
Time Windows ◽  
Hard Problem ◽  
Routing Problem ◽  
Search Area ◽  
Np Hard Problem

Vehicle routing problem with time windows (VRPTW) is one of NP-hard problem. Multi-trip is approach to solve the VRPTW that looking trip scheduling for gets best result. Even though there are various algorithms for the problem, there is opportunity to improve the existing algorithms in order gaining a better result. In this research, genetic algoritm is hybridized with simulated annealing algoritm to solve the problem. Genetic algoritm is employed to explore global search area and simulated annealing is employed to exploit local search area. Four combination types of genetic algorithm and simulated annealing (GA-SA) are tested to get the best solution. The computational experiment shows that GA-SA1 and GA-SA4 can produced the most optimal fitness average values with each value was 1.0888 and 1.0887. However GA-SA4 can found the best fitness chromosome faster than GA-SA1.

scholarly journals A hybrid metaheuristic for solving asymmetric distance-constrained vehicle routing problem

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Ha-Bang Ban ◽  
Phuong Khanh Nguyen
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Natural Extension ◽  
Solution Space ◽  
Neighborhood Search ◽  
Np Hard ◽  
Routing Problem ◽  
Hybrid Metaheuristic ◽  
Asymmetric Distance ◽  
Constrained Vehicle Routing

AbstractThe Asymmetric Distance-Constrained Vehicle Routing Problem (ADVRP) is NP-hard as it is a natural extension of the NP-hard Vehicle Routing Problem. In ADVRP problem, each customer is visited exactly once by a vehicle; every tour starts and ends at a depot; and the traveled distance by each vehicle is not allowed to exceed a predetermined limit. We propose a hybrid metaheuristic algorithm combining the Randomized Variable Neighborhood Search (RVNS) and the Tabu Search (TS) to solve the problem. The combination of multiple neighborhoods and tabu mechanism is used for their capacity to escape local optima while exploring the solution space. Furthermore, the intensification and diversification phases are also included to deliver optimized and diversified solutions. Extensive numerical experiments and comparisons with all the state-of-the-art algorithms show that the proposed method is highly competitive in terms of solution quality and computation time, providing new best solutions for a number of instances.

The Research on VRP Based on Max-Min Ant Colony Algorithm

2011 ◽  
Vol 219-220 ◽  
pp. 1285-1288 ◽  
Author(s):  
Chang Min Chen ◽  
Wei Cheng Xie ◽  
Song Song Fan
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Ant Colony Algorithm ◽  
Search Time ◽  
Ant Colony ◽  
Local Optimum ◽  
Simulation Data ◽  
Routing Problem ◽  
Np Hard Problem ◽  
The Cost

Vehicle routing problem (VRP) is the key to reducing the cost of logistics, and also an NP-hard problem. Ant colony algorithm is a very effective method to solve the VRP, but it is easy to fall into local optimum and has a long search time. In order to overcome its shortcomings, max-min ant colony algorithm is adopted in this paper, and its simulation system is designed in GUI of MATLAB7.0. The results show that the vehicle routing problem can well achieves the optimization of VRP by accessing the simulation data of database.

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