scholarly journals Makespan Minimizing on Multiple Travel Salesman Problem With a Learning Effect of Visiting Time

2020 ◽  
Vol 15 ◽  
Keyword(s):  
Confidence Interval ◽  
Large Scale ◽  
Learning By Doing ◽  
Small Scale ◽  
Exact Methods ◽  
Routing Problem ◽  
Multiple Traveling Salesman Problem ◽  
Metaheuristic Methods ◽  
Np Hard Problem ◽  
Visiting Time

The multiple traveling salesman problem (MTSP) involves the assignment and sequencing procedure simultaneously. The assignment of a set of nodes to each visitors and determining the sequence of visiting of nodes for each visitor. Since specific range of process is needed to be carried out in nodes in commercial environment, several factors associated with routing problem are required to be taken into account. This research considers visitors’ skill and category of customers which can affect visiting time of visitors in nodes. With regard to learning-by-doing, visiting time in nodes can be reduced. And different class of customers which are determined based on their potential purchasing of power specifies that required time for nodes can be vary. So, a novel optimization model is presented to formulate MTSP, which attempts to ascertain the optimum routes for salesmen by minimizing the makespan to ensure the balance of workload of visitors. Since this problem is an NP-hard problem, for overcoming the restriction of exact methods for solving practical large-scale instances within acceptable computational times. So, Artificial Immune System (AIS) and the Firefly (FA) metaheuristic algorithm are implemented in this paper and algorithms parameters are calibrated by applying Taguchi technique. The solution methodology is assessed by an array of numerical examples and the overall performances of these metaheuristic methods are evaluated by analyzing their results with the optimum solutions to suggested problems. The results of statistical analysis by considering 95% confidence interval for calculating average relative percentage of deviation (ARPD) reveal that the solutions of proposed AIS algorithm has less variation and Its’ confidence interval of closer than to zero with no overlapping with that of FA. Although both proposed metaheuristics are effective and efficient in solving small-scale problems, in medium and large scales problems, AIS had a better performance in a shorter average time. Finally, the applicability of the suggested pattern is implemented in a case study in a specific company, namely Kalleh.

scholarly journals Multidepot Heterogeneous Vehicle Routing Problem for a Variety of Hazardous Materials with Risk Analysis

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Bochen Wang ◽  
Qiyuan Qian ◽  
Zheyi Tan ◽  
Peng Zhang ◽  
Aizhi Wu ◽  
...  
Keyword(s):  
Risk Analysis ◽  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Large Scale ◽  
Programming Model ◽  
Hazardous Materials ◽  
Mixed Integer ◽  
Small Scale ◽  
Routing Problem ◽  
Heterogeneous Vehicle Routing Problem

This study investigates a multidepot heterogeneous vehicle routing problem for a variety of hazardous materials with risk analysis, which is a practical problem in the actual industrial field. The objective of the problem is to design a series of routes that minimize the total cost composed of transportation cost, risk cost, and overtime work cost. Comprehensive consideration of factors such as transportation costs, multiple depots, heterogeneous vehicles, risks, and multiple accident scenarios is involved in our study. The problem is defined as a mixed integer programming model. A bidirectional tuning heuristic algorithm and particle swarm optimization algorithm are developed to solve the problem of different scales of instances. Computational results are competitive such that our algorithm can obtain effective results in small-scale instances and show great efficiency in large-scale instances with 70 customers, 30 vehicles, and 3 types of hazardous materials.

scholarly journals A Multiobjective Optimization for Train Routing at the High-Speed Railway Station Based on Tabu Search Algorithm

2018 ◽  
Vol 2018 ◽  
pp. 1-22 ◽  
Author(s):  
Ziyan Feng ◽  
Chengxuan Cao ◽  
Yutong Liu ◽  
Yaling Zhou
Keyword(s):  
Tabu Search ◽  
High Speed ◽  
Large Scale ◽  
Computing Time ◽  
Mixed Integer ◽  
Small Scale ◽  
Railway Station ◽  
High Speed Railway ◽  
Routing Problem ◽  
Train Routing

This paper focuses on the train routing problem at a high-speed railway station to improve the railway station capacity and operational efficiency. We first describe a node-based railway network by defining the turnout node and the arrival-departure line node for the mathematical formulation. Both considering potential collisions of trains and convenience for passengers’ transfer in the station, the train routing problem at a high-speed railway station is formulated as a multiobjective mixed integer nonlinear programming model, which aims to minimize trains’ departure time deviations and total occupation time of all tracks and keep the most balanced utilization of arrival-departure lines. Since massive decision variables for the large-scale real-life train routing problem exist, a fast heuristic algorithm is proposed based on the tabu search to solve it. Two sets of numerical experiments are implemented to demonstrate the rationality and effectiveness of proposed method: the small-scale case confirms the accuracy of the algorithm; the resulting heuristic proved able to obtain excellent solution quality within 254 seconds of computing time on a standard personal computer for the large-scale station involving up to 17 arrival-departure lines and 46 trains.

scholarly journals Alpha-T: Learning to Traverse over Graphs with An AlphaZero-inspired Self-Play Framework

2021 ◽  
Author(s):  
Qi Wang
Keyword(s):  
Large Scale ◽  
Optimization Problems ◽  
Optimal Path ◽  
Solution Space ◽  
Approximate Solutions ◽  
Small Scale ◽  
Traditional Methods ◽  
Routing Problem ◽  
Monte Carlo Tree Search ◽  
Combinatorial Optimization Problems

Abstract The combinatorial optimization problems on the graph are the core and classic problems in artificial intelligence and operations research. For example, the Vehicle Routing Problem (VRP) and Traveling Salesman Problem (TSP) are not only very interesting NP-hard problems but also have important significance for the actual transportation system. Traditional methods such as heuristics methods, precise algorithms, and solution solvers can already find approximate solutions on small-scale graphs. However, they are helpless for large-scale graphs and other problems with similar structures. Moreover, traditional methods often require artificially designed heuristic functions to assist decision-making. In recent years, more and more work has focused on the application of deep learning and reinforcement learning (RL) to learn heuristics, which allows us to learn the internal structure of the graph end-to-end and find the optimal path under the guidance of heuristic rules, but most of these still need manual assistance, and the RL method used has the problems of low sampling efficiency and small searchable space. In this paper, we propose a novel framework (called Alpha-T) based on AlphaZero, which does not require expert experience or label data but is trained through self-play. We divide the learning into two stages: in the first stage we employ graph attention network (GAT) and GRU to learn node representations and memory history trajectories, and in the second stage we employ Monte Carlo tree search (MCTS) and deep RL to search the solution space and train the model.

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.

Cobweb heuristic for multi-objective vehicle routing problem

2015 ◽  
Vol 4 (3) ◽  
pp. 430
Author(s):  
Joseph Okitonyumbe Y. F ◽  
Berthold Ulungu E.-L ◽  
Joel Kapiamba Nt.
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Large Dimension ◽  
Exact Methods ◽  
Routing Problem ◽  
Multi Objective ◽  
Metaheuristic Methods

<p>Solving a classical vehicle routing problem (VRP) by exact methods presents many difficulties for large dimension problem. Consequently, in multi-objective framework, heuristic or metaheuristic methods are required. Due to particular VRP structure, it seems that a dedicated heuristicis more suitable than a metaheuristic. The aim of this article is to collapse different heuristics solving classical VRP and adapt them for to solve the multi-objective vehicle routing problem (MOVRP). The so-called Cobweb Algorithm simulates spider’s behavior when weaving cobweb. This paper presents the algorithm, a didactic example, concluding remarks and way for further researches.</p>

An Improved Immune Clone Algorithm Logistics Delivery Strategy

2019 ◽  
Vol 23 (2) ◽  
pp. 309-312 ◽  
Author(s):  
Yan Song Tan ◽  
Keyword(s):  
High Frequency ◽  
Large Scale ◽  
Optimization Problems ◽  
Clonal Selection ◽  
Path Optimization ◽  
Routing Problem ◽  
Distribution Point ◽  
Np Hard Problem ◽  
Logistics Delivery ◽  
Frequency Variations

Logistics routing problem is a typical NP hard problem, which is very difficult to solve accurately. On the basis of establishing logistics path optimization model, an immune clone algorithm is proposed. To improve the accuracy of search algorithms, the clonal selection and high frequency variations in the immune algorithm method are introduced. Then the antibody encoding virtual distribution point algorithm is designed to improve search efficiency. The benchmark problem of logistics delivery path optimization is simulated and analyzed. Experimental results show that the proposed immune cloning algorithm expands the range of population search and it have obvious advantages in solving large-scale complex physical distribution optimization problems. Also, the proposed algorithm can solve the optimal distribution of logistics effectively.

scholarly journals Minimization of Delay and Travel Time of Yard Trucks in Container Terminals Using an Improved GA with Guidance Search

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Z. X. Wang ◽  
Felix T. S. Chan ◽  
S. H. Chung ◽  
Ben Niu
Keyword(s):  
Travel Time ◽  
Large Scale ◽  
Container Terminal ◽  
Container Terminals ◽  
Computational Time ◽  
Small Scale ◽  
Storage Allocation ◽  
Total Delay ◽  
Truck Scheduling ◽  
Np Hard Problem

Yard truck scheduling and storage allocation problems (YTS-SAP) are two important issues that influence the efficiency of a container terminal. These two problems aim to determine the routing of trucks and proper storage locations for discharging containers from incoming vessels. This paper integrates YTS and SAP as a whole and tries to minimize the weighted summation of total delay and total yard trucks travel time. A genetic algorithm (GA) is proposed to deal with the problem. In the proposed GA, guidance mutation approach and exhaustive heuristic for local searching are used in order to force the GA to converge faster and be steadier. To test the performance of the proposed GA, both small scale and large scale cases are studied. The results of these cases are compared with CPLEX for the small scale cases. Since this problem is an NP-hard problem, which CPLEX cannot solve, a simple GA is studied for comparison in large scale cases. The comparison demonstrates that the proposed GA can obtain near optimal solutions in much shorter computational time for small scale cases. In addition, the proposed GA can obtain better results than other methods in reasonable time for large scale cases.

scholarly journals Analyze the Effectiveness of the Algorithm for Agricultural Product Delivery Vehicle Routing Problem Based on Mathematical Model

2021 ◽  
Vol 12 (3) ◽  
pp. 26-38
Author(s):  
Kairong Yu ◽  
Yang Liu ◽  
Ashutosh Sharma
Keyword(s):  
Hybrid Algorithm ◽  
Large Scale ◽  
Service Providers ◽  
Cost Effective ◽  
Agricultural Products ◽  
Small Scale ◽  
Agricultural Product ◽  
Small Range ◽  
Routing Problem ◽  
Delivery Services

With the recent development in the economic system, the requirement for logistic services has also increased gradually. This increased the demand for efficient and cost-effective delivery services without compromising the quality and timeliness. This has become a challenge to the logistic service providers to maintain the high-quality standards along with reliable delivery services. A mathematical equation model is proposed in this work to solve the problem of random quantity of agricultural products collected/distributed by working vehicle collection/distribution path planning. This article proposes a hybrid algorithm which combines the taboo algorithm search and the taboo hybrid algorithm to solve the problem. In the proposed algorithm, a large-scale problem is several small-scale problems to reduce the time complexity of the algorithm. Since randomness is much more complicated than certain types of problems, accurate algorithms can only be applied to a small range of problem types. The heuristic calculations involved in the development of algorithms make it a convenient simplified tool for the collection and distribution of random agricultural products. An average validation accuracy of 94% has been obtained for the proposed algorithm after completing 200 iterations while obtaining 94.37%, 94.57%, and 94.56% precision, recall, and F-score values, respectively.

scholarly journals The electric vehicle routing problem with partial recharge and vehicle recycling

2021 ◽  
Author(s):  
Yuzhen Zhou ◽  
Jincai Huang ◽  
Jianmai Shi ◽  
Rui Wang ◽  
Kuihua Huang
Keyword(s):  
Electric Vehicle ◽  
Large Scale ◽  
Mixed Integer ◽  
Neighborhood Search ◽  
Small Scale ◽  
Routing Problem ◽  
Practical Applications ◽  
New Variant ◽  
Commercial Solver ◽  
Charging Stations

AbstractIn this paper, a new variant of the electric vehicle (EV) routing problem, which considers heterogeneous EVs, partial recharge, and vehicle recycling, is investigated based on logistic companies' practical operation. A mixed integer linear programming (MILP) model is proposed to formulate the problem. For small-scale scenarios, commercial solver, e.g., CPLEX, is leveraged. For large-scale instances faced by practical applications, a hybrid metaheuristic is designed through integrating a modified Greedy Algorithm with the Variable Neighborhood Search (VNS). The proposed algorithm was tested by real-world instances from JD, an e-commerce enterprise in China. Computational results indicate that partial recharge and vehicle recycling can save costs effectively. It also shows that the number of charging stations is an important factor for the application of EVs.

Small-Scale Science to Large-Scale Profession

2000 ◽  
Vol 45 (4) ◽  
pp. 396-398
Author(s):  
Roger Smith
Keyword(s):  
Large Scale ◽  
Small Scale
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