Shortest Path Problem

The problem of finding the shortest path from a path or graph has been quite widely discussed. There are also many algorithms that are the solution to this problem. The purpose of this study is to analyze the Greedy, A-Star, and Dijkstra algorithms in the process of finding the shortest path. The author wants to compare the effectiveness of the three algorithms in the process of finding the shortest path in a path or graph. From the results of the research conducted, the author can conclude that the Greedy, A-Star, and Dijkstra algorithms can be a solution in determining the shortest path in a path or graph with different results. The Greedy algorithm is fast in finding solutions but tends not to find the optimal solution. While the A-Star algorithm tends to be better than the Greedy algorithm, but the path or graph must have complex data. Meanwhile, Dijkstra's algorithm in this case is better than the other two algorithms because it always gets optimal results.

In India, many patients lost because they were unable to get to the hospital on time in the event of an accident. Therefore, we are developing an ambulance service application that will reduce the need to get to the hospital. The main task of this project is to reduce the time between the ambulance driver and the patient and this will save his life. When the user opens the user app on their Smartphone, they will enter a place to go, then search for a nearby ambulance. Two Smartphone, one for the user and the other for the ambulance driver. Traffic accidents in the city have made loss of life from accidents even more crucial. To implement this, we will introduce a system called the Automatic Ambulance Recovery System that uses algorithms to search for shorter distances. The main theme beyond this scheme is to provide a simple flow for the ambulance to get to hospitals on time and therefore minimize propitiation. The ambulance is regulated by the primary unit which provides the longest scanning route to the ambulance and this position of the ambulance and consequently reaches the hospital safely. The GPS server also decides the location of the accident location through the vehicle that encounters the accident, and then the server walks through the ambulance to the location. This project will be fully automated, so find the crash site and help get to the hospital on time. The proposed system is designed for this monitoring system for the transportation of patients in an emergency. The system will be useful to monitor the current position of the ambulance, it must be the closest position that the ambulance can reach at the accident site.

Efficient implementations of Dijkstra's shortest path algorithm are investigated. A new data structure, called the radix heap , is proposed for use in this algorithm. On a network with n vertices, m edges, and nonnegative integer arc costs bounded by C , a one-level form of radix heap gives a time bound for Dijkstra's algorithm of O ( m + n log C ). A two-level form of radix heap gives a bound of O ( m + n log C /log log C ). A combination of a radix heap and a previously known data structure called a Fibonacci heap gives a bound of O ( m + n a @@@@log C ). The best previously known bounds are O ( m + n log n ) using Fibonacci heaps alone and O ( m log log C ) using the priority queue structure of Van Emde Boas et al. [ 17].

In This work the efficient algorithm for optimal cargo transport of N types of containers with limited ship capacity, minimizing the transport costs, is being developed. It can be applied for transport planning on a voyage route with multiple loading ports and multiple ports of discharge. The problem is solved with network optimization approach that can be seen as the minimum cost multicommodity flow problem (MCMCF). The implemented algorithm is able to find appropriate load planning sequence and to ensure minimal loading, discharging and transshipment costs, but with fulfillment of cargo demands in a number of destination ports on the voyage route. Application of this efficient tool may significantly reduce transport costs and ensure maximal possible profit. It may improve the operation process in maritime transport technology.

In this article, modeling of shortest path routing problem with artificial neural network is considered. In order to make our
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This paper introduces a new type of constraints, related to schedule synchronization, in the problem formulation of aircraft fleet assignment and routing problems and it proposes an optimal solution approach. This approach is based on Dantzig–Wolfe decomposition/column generation. The resulting master problem consists of flight covering constraints, as in usual applications, and of schedule synchronization constraints. The corresponding subproblem is a shortest path problem with time windows and linear costs on the time variables and it is solved by an optimal dynamic programming algorithm. This column generation procedure is embedded into a branch and bound scheme to obtain integer solutions. A dedicated branching scheme was devised in this paper where the branching decisions are imposed on the time variables. Computational experiments were conducted using weekly fleet routing and scheduling problem data coming from an European airline. The test problems are solved to optimality. A detailed result analysis highlights the advantages of this approach: an extremely short subproblem solution time and, after several improvements, a very efficient master problem solution time.

In this paper we present a prototype of decision aid system for the logical layout design of unit-head machines with rotary table. User can add and modify characteristics of the part to be machined, the constraints related to the design of spindle heads and working positions, as well as precedence constraints related to operations. The goal of this software tool is minimize the total number of working positions and spindle heads, while reaching a given cycle time and satisfying the above constraints. The proposed method to solve the problem is based on its reduction to a constrained shortest path problem.

Laporan praktikum Riset Operasi: Shortes Path adalah salah satu permasalahan ‘mudah’ saat mempelajari materi tentang graph, yaitu dengan mencari cost dari jalur terpendek (jalur dengan cost terendah) dalam suatu graph. Ada beberapa algoritma yang dapat digunakan untuk memecahkan permasalahan ini, antara lain yang cukup terkenal adalah Bellman Ford dan Djikstra. Namun, masing-masing algoritma tersebut memiliki kelemahan dan kelebihan, semisal dari segi efisiensi antara Bellman Ford dan Djikstra yang lebih efisien adalah Djikstra, akan tetapi dalam beberapa kasus Bellman Ford lebih unggul yaitu jika salah satu cost dari edgenya ada yang bernilai negatif, hal ini disebabkan algoritma Djikstra hanya bisa dipakai jika semua cost dari edgenya tidak bernilai negatif. Kemudian maksimum flow, yaitu masalah bagaimana cara menentukan besarnya penugasan flow pada suatu jaringan kerja sehingga flow yang sampai ke tujuan maksimal. Penyelesaian masalah maksimum flow dapat lebih mudah dan efisien jika menggunakan algoritma. Dua algoritma yang sudah ada dan sering digunakan yaitu algoritma Lintasan Penambah dan algoritma Pelabelan Aka.

Dalam penelitian ini data ruas jalan direpresentasikan dalam graf berarah dimana jarak dari setiap node digunakan sebagai bobot untuk pencarian rute dengan Algoritma Floyd-Warshall. Data jarak dari setiap ruas jalan didapatkan dari Google map dengan memperhitungkan longitude dan latitude pada setiap node. Google map merupakan layanan pemetaan online gratis yang disediakan google dengan tampilan secara digital dan dapat diakses menggunakan browser oleh semua orang. Algoritma Floyd-Warshall akan melakukan pencarian rute terpendek kemudian Google Map akan menampikan data hasil perhitungan tersebut berupa rute beserta kode trayek yang dapat digunakan sebagai referensi oleh penumpang. Analisis hasil yang diperhatikan pada penelitian ini adalah hasil jarak dan rute yang dilalui oleh angkutan kota yang dibandingkan dari pilihan " public transportation " pada google maps.

In most vehicle routing and crew scheduling applications solved by column generation, the subproblem corresponds to a shortest path problem with resource constraints (SPPRC) or one of its variants. This chapter proposes a classification and a generic formulation for the SPPRCs, briefly discusses complex modeling issues involving resources, and presents the most commonly used SPPRC solution methods. First and foremost,

In this article we propose a new single‐source shortest‐path algorithm that achieves the same O(n · m) time bound as the Bellman‐Ford‐Moore algorithm but outperforms it and other state‐of‐the‐art algorithms in many cases in practice. Our claims are supported by experimental evidence.

When restricted to cost arrays possessing the sum Monge property, many combinatorial optimization problems with sum objective functions become significantly easier to solve. The more general algebraic assignment and transportation problems are similarly easier to solve given cost arrays possessing the corresponding algebraic Monge property. We show that Monge-array results for two sum-of-edge-costs shortest-path problems can likewise be extended to a general algebraic setting, provided the problems’ ordered commutative semigroup satisfies one additional restriction. In addition to this general result, we also show how our algorithms can be modified to solve certain bottleneck shortest-path problems, even though the ordered commutative semigroup naturally associated with bottleneck problems does not satisfy our additional restriction. We show how our bottleneck shortest-path techniques can be used to obtain fast algorithms for a variant of Hirschberg and Larmore’s optimal paragraph formation problem, and a special case of the bottleneck traveling-salesman problem.

In this paper, we deal with the solution of the multicriteria shortest path problem. In particular, we present a class of labeling methods to generate the entire set of Pareto-optimal path-length vectors from an origin node s to all other nodes in a multicriteria network. The proposed methods are supported theoretically by the principle of optimality and they are defined

Tree (SPT) problem. The presented algorithm is an improvement over a previously published work of the authors. The effort is put in to improve the running/execution time of the SPT problem. Introduced improvement is simple and easy to incorporate in to the ...

A new column generation based exact optimization approach for the vehicle routing and scheduling problem with semi soft time windows (VRPSSTW) is presented. Elementary shortest path problem with resource constraints and late arrival penalties is solved as a subproblem, which rises from the Dantzig–Wolfe decomposition method. Exact solutions of VRPSSTW and hard time windows variant are compared on Solomon’s benchmark instances as well as on an instance based on Tokyo road network. It was found that the VRPSSTW solution results in fewer routes thus overall costs are reduced and late arrival penalties contribute only a small fraction to total cost.

This paper proposes a weighted double-heuristic search algorithm to find the shortest path between two points. It can be used in numerous fields such as graph theory, game theory, and network. This algorithm, called T*, uses a weighted and heuristic function as f(x) = α × t(x) + β × h1(x) + γ × h2(x). It selects the path which minimises f(x) where x is a current node on the path, t(x) is cost of the path from start to x, h1(x) is a heuristic to estimate the cost from x to the straight line passing through start and target, and h2(x) is a heuristic to estimate cost of the cheapest path from x to target. Furthermore, α, β, and γ indicate effective weights of each sub-function on f(x). T* algorithm is compared to the Greedy and A* algorithms in terms of hit rate and the number of processed nodes. Comparison results show that the proposed algorithm has a high efficiency compared to other algorithms.

The present paper deals with the problem of locating hubs for freight mobility in urban and suburban areas. In particular, we present a heuristic method that combines aspects coming from both classical simple plant location problems and shortest path ones on multimodal graphs. In the first phase of the proposed heuristics, we identify those nodes that could be attractive poles

We consider two approaches that model timetable information in public transportation systems as shortestpath problems in weighted graphs. In the time-expanded approach every event at a station, e.g., the departure of a train, is modeled as a node in the graph, while in the time-dependent approach the graph contains only one node per station. Both approaches have been recently