Browsing by Subject "Traveling salesman problem"
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Item Open Access Cache locality exploiting methods and models for sparse matrix-vector multiplication(Bilkent University, 2009) Akbudak, KadirThe sparse matrix-vector multiplication (SpMxV) is an important kernel operation widely used in linear solvers. The same sparse matrix is multiplied by a dense vector repeatedly in these solvers to solve a system of linear equations. High performance gains can be obtained if we can take the advantage of today’s deep cache hierarchy in SpMxV operations. Matrices with irregular sparsity patterns make it difficult to utilize data locality effectively in SpMxV computations. Different techniques are proposed in the literature to utilize cache hierarchy effectively via exploiting data locality during SpMxV. In this work, we investigate two distinct frameworks for cacheaware/oblivious SpMxV: single matrix-vector multiply and multiple submatrix-vector multiplies. For the single matrix-vector multiply framework, we propose a cache-size aware top-down row/column-reordering approach based on 1D sparse matrix partitioning by utilizing the recently proposed appropriate hypergraph models of sparse matrices, and a cache oblivious bottom-up approach based on hierarchical clustering of rows/columns with similar sparsity patterns. We also propose a column compression scheme as a preprocessing step which makes these two approaches cache-line-size aware. The multiple submatrix-vector multiplies framework depends on the partitioning the matrix into multiple nonzero-disjoint submatrices. For an effective matrixto-submatrix partitioning required in this framework, we propose a cache-size aware top-down approach based on 2D sparse matrix partitioning by utilizing the recently proposed fine-grain hypergraph model. For this framework, we also propose a traveling salesman formulation for an effective ordering of individual submatrix-vector multiply operations. We evaluate the validity of our models and methods on a wide range of sparse matrices. Experimental results show that proposed methods and models outperforms state-of-the-art schemes.Item Open Access Exact algorithms for a task assignment problem(World Scientific Publishing Company, 2009) Kaya, Kamer; Uçar, B.We consider the following task assignment problem. Communicating tasks are to be assigned to heterogeneous processors interconnected with a heterogeneous network. The objective is to minimize the total sum of the execution and communication costs. The problem is NP-hard. We present an exact algorithm based on the well-known A* search. We report simulation results over a wide range of parameters where the largest solved instance contains about three hundred tasks to be assigned to eight processors. © World Scientific Publishing Company.Item Embargo Exact solution approaches for the minimum total cost traveling salesman problem with multiple drones(Elsevier, 2023-01-04) Özbaygın Tiniç, G.; Karasan, Oya Ekin; Kara, Bahar Yetiş; Campbell, J.F.; Özel. A.Deployment of drones in delivery operations has been attracting growing interest from the commercial sector due to its prospective advantages for a range of distribution systems. Motivated by the widespread adoption of drones in last-mile delivery, we introduce the minimum cost traveling salesman problem with multiple drones, where a truck and multiple drones work in synchronization to deliver parcels to customers. In this problem, we aim to find an optimal delivery plan for the truck and drones operating in tandem with the objective of minimizing the total operational cost including the vehicles’ operating and waiting costs. Unlike most studies in the literature where the objective is to minimize completion time, which means one needs to know only the arrival time of the latest arriving vehicle (truck or drone) at each synchronization point, we need to keep track of all the individual waiting times of the truck and the drones to properly account for waiting costs, which makes it more challenging to handle the synchronization. We provide a flow based and two cut based mixed integer linear programming formulations strengthened with valid inequalities. For non-compact models, we devise a variety of branch-and-cut schemes to solve our problem to optimality. To compare our formulations/algorithms and to demonstrate their competitiveness, we conduct computational experiments on a range of instances. The results indicate the superiority of utilizing branch-and-cut methodology over a flow based formulation. We also use our model to conduct sensitivity analyses with several problem parameters and to explore the benefits of launch and retrieval at the same node, the tradeoff between the number of drones and the operational cost, and the special case with a minimize completion objective with one drone. We also document very low waiting times for drones in optimal solutions and show solutions from minimizing cost have much lower cost than those from minimizing makespan.Item Open Access Multi-population parallel genetic algorithm using a new genetic representation for the euclidean traveling salesman problem(İstanbul Technical University, 2005) Kapanoğlu, M.; Koç, İ. O.; Kara, İ.; Aktürk, Mehmet SelimThis paper introduces a multi-population genetic algorithm (M-PPGA) using a new genetic representation, the kth-nearest neighbor representation, for Euclidean Traveling Salesman Problems. The proposed M-PPGA runs M greedy genetic algorithms on M separate populations, each with two new operators, intersection repairing and cheapest insert. The M-PPGA finds optimal or near optimal solutions by using a novel communication operator among individually converged populations. The algorithm generates high quality building blocks within each population; then, combines these blocks to build the optimal or near optimal solutions by means of the communication operator. The proposed M-PPGA outperforms the GAs that we know of as competitive with respect to running times and solution quality, over the considered test problems including the Turkey81.Item Open Access New formulations for the hop-constrained minimum spanning tree problem via Sherali and Driscoll's tightened Miller-Tucker-Zemlin constraints(Elsevier, 2010) Akgün, İbrahimGiven an undirected network with positive edge costs and a natural number p, the hop-constrained minimum spanning tree problem (HMST) is the problem of finding a spanning tree with minimum total cost such that each path starting from a specified root node has no more than p hops (edges). In this paper, the new models based on the Miller-Tucker-Zemlin (MTZ) subtour elimination constraints are developed and computational results together with comparisons against MTZ-based, flow-based, and hop-indexed formulations are reported. The first model is obtained by adapting the MTZ-based Asymmetric Traveling Salesman Problem formulation of Sherali and Driscoll [18] and the other two models are obtained by combining topology-enforcing and MTZ-related constraints offered by Akgün and Tansel (submitted for publication) [20] for HMST with the first model appropriately. Computational studies show that the best LP bounds of the MTZ-based models in the literature are improved by the proposed models. The best solution times of the MTZ-based models are not improved for optimally solved instances. However, the results for the harder, large-size instances imply that the proposed models are likely to produce better solution times. The proposed models do not dominate the flow-based and hop-indexed formulations with respect to LP bounds. However, good feasible solutions can be obtained in a reasonable amount of time for problems for which even the LP relaxations of the flow-based and hop-indexed formulations can be solved in about 2 days. © 2010 Elsevier Ltd. All rights reserved.Item Open Access Optimization of last-mile deliveries with synchronous truck and drones(Bilkent University, 2020-07) Özel, AysuDeployment of drones in delivery operations has been attracting a growing interest from commercial sector due to its prospective advantages for the distribution systems. Motivated by the widespread adoption of drones in last-mile delivery, we introduce the minimum cost traveling salesman problem with multiple drones, where a truck and multiple drones work in synchronization to deliver parcels to customers. In this problem, we aim to find an optimal delivery plan for the truck and drones operating in tandem with the objective of minimizing the total operational cost including the vehicles’ operating and waiting costs. We provide flow based and cut based mixed integer linear programming formulations along with valid inequalities. Since the connectivity constraints in the cut based formulation and the proposed valid inequalities are exponential in the size of the problem, we devise different branch-and-cut schemes to solve our problem. We also provide an alternative solution methodology using another cut based formulation with undirected route variables. To compare our formulations/algorithms and to demonstrate their competitiveness, we conduct computational experiments on a set of instances. The results indicate the superiority of utilizing branch-and-cut methodology over flow based formulation and good computational performance of the proposed algorithms in comparison to existing exact solution approaches in the literature. We also conduct sensitivity analyses on problem parameters and discuss their effects on the optimal solutions.Item Open Access Traveling repairmen problem: A biogeography-based optimization(Springer Cham, 2022-07-14) Öder Uzun, G.; Dengiz, B.; Kara, İ.; Karasan, Oya Ekin; Xu, Jiuping; Altıparmak, Fulya; Hassan, Mohamed Hag Ali; Márquez, Fausto Pedro García; Hajiyev, AsafTraveling Repairman Problem (TRP), which is also known by names cumulative traveling salesman problem, the deliveryman prob lem and the minimum latency problem, is a special variant of Traveling Salesman Problem (TSP). In contrast to the minimization of completion time objective of TSP, the desired objective of TRP is to minimize the cumulative latency (waiting time or delay time) of all customers. In this paper, a generalized version of TRP with multi depots and time windows, namely Multi Depot Traveling Repairman Problem with Time Windows (MDTRPTW) is considered. A group of homogeneous repairmen initi ate and finish their visit tours at multiple depots. Each customer must be visited exactly by one repairman within their provided earliest end latest times. Being a challenging Nondeterministic Polynomial-hard (NP hard) optimization problem, exact solution approaches are not expected to scale to realistic dimensions of MDTRPTW. Thus, we propose a biogeography-based optimization algorithm (BBOA) as a metaheuristic approach to solve large size MDTRPTW problems. The proposed meta heuristic is analyzed in terms of solution quality, coefficient of variation as well as computation time by solving some test problems adapted from the related literature. The efficacy of the proposed solution methodology is demonstrated by solving instances with 288 customers within seconds.