An Experimental Study about Efficiency of the Approximation Algorithms for Minimum Latency Problem (original) (raw)
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An efficient exact algorithm for the Minimum Latency Problem
Progress in Informatics, 2013
The Minimum Latency Problem (MLP) is a class of combinational optimization problems that has many practical applications. In the general case, the MLP is proved to be NPhard. One of the approaches to solve the problem is using exact algorithms. However, the algorithms which were recently proposed are applied only to the problems with small size, i.e., 26 vertices. In this paper, we present a new exact algorithm to solve the MLPs with a larger size. Our algorithm is based on the branch and bound method and it has two new rules that improve the pruning technique. We have evaluated the algorithm on several data sets. The results show that the problems up to 40 vertices can be solved exactly.
The 2013 RIVF International Conference on Computing & Communication Technologies - Research, Innovation, and Vision for Future (RIVF), 2013
Minimum Latency Problem (MLP) is a class of NP-hard combinatorial optimization problems which has many practical applications. In this paper, we investigate the global structure of the MLP solution space to propose a suitable meta-heuristic algorithm for the problem, which combines Tabu search (TS) and Variable Neighborhood Search (VNS). In the proposed algorithm, TS is used to prevent the search from getting trapped into cycles, and guide VNS to escape local optima. In a cooperative way, VNS is employed to generate diverse neighborhoods for TS. We also introduce a novel neighborhoods' structure for VNS and present a constant time operation for calculating the latency cost of each neighboring solution. Extensive numerical experiments and comparisons with the state of the art meta-heuristic algorithms in the literature show that the proposed algorithm is highly competitive, providing the new best solutions for several instances.
Approximation algorithm for minimizing total latency in machine scheduling with deliveries
Discrete Optimization, 2008
We study the problem of minimizing total latency in machine scheduling with deliveries, which is defined as follows. There is a set of n jobs to be processed by a single machine at a plant, where job J i is associated with its processing time and a customer i located at location i to which the job is to be delivered. In addition, there is a single uncapacitated delivery vehicle available. All jobs (vehicle) are available for processing (delivery) at time 0. Our aim is to determine the sequence in which the jobs should be processed in the plant, the departure times of the vehicle from the plant, and the routing of the vehicle, so as to minimize the total latency (job delivery time). We present a 6e ∼ 16.309691-approximation algorithm for the problem.
Design and Analysis of Approximation Algorithms
Springer Optimization and Its Applications, 2012
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A Variation of Minimum Latency Problem
2010
In this paper we study the variation of the minimum latency problem(MLP) [2]. The MLP is to find a walk tour on the graph G(V, E) with a distance matrix d i,j. Where d i,j indicate the distance between v i and v j. Let (v i) is the latency length of v i , defined to be the distance traveled before first visiting v i. The minimum latency tour is to minimize n i=1 (v i). In some message broadcast and scheduling problem [8] the vertex also has latency time and weight. Those problem need to extend the objective function of the minimum latency tour as n i=1 (v i)w(v i). The definition is equivalent to the MLP with no edge distance but vertex latency time and vertex weight. We give an linear algorithm for the unweighted full k-ary tree or k-path graphs, and O(n log n) time for general tree graphs. The time complexity in trees is the same as Adolphson's result; however, the algorithm given here is not only simpler, easier to understand, but also more flexible and thus can be easily extended to other classes of graphs.
Computing Sharp Lower and Upper Bounds for the Minimum Latency Problem
2007
The Minimum Latency Problem, also known as Traveling Repairman Problem, the Deliveryman Problem and the Traveling Salesman Problem with Cumulative Costs is a variant of the Traveling Salesman Problem in which a repairman is required to visit customers located on each node of a graph in such a way that the overall waiting times of these customers is minimized. In the present work, an algorithm based on tight different linear programming lowerbounds and a specialized GRASP procedure are presented. The linear programming based lower-bounds are based on the Quadratic Assignment Problem with the aid of side constraints. Instances from 10 up to 60 nodes are solved very close to optimality in reasonable time.
Lecture Notes in Computer Science, 1998
One of the foremost techniques in the design and analysis of approximation algorithms is to round the optimal solution to a linear programming relaxation in order to compute a near-optimal solution to the problem at hand. We shall survey recent work in this vein for two particular problems: the uncapacitated facility location problem and the problem of scheduling precedence-constrained jobs on one machine so as to minimize a weighted average of their completion times. completion time of job j, then we wish to minimize the average weighted complen n tion time w j C j /n, or equivalently, w j C j. In the notation of Graham, j=1 j=1 Lawler, Lenstra, & Rinnooy Kan [11], the problem is denoted 1|prec| w j C j ; it was shown to be N P-hard by Lawler [21]. The first non-trivial approximation algorithm for 1|prec| w j C j is due to Ravi, Agrawal, & Klein [33], who gave an O(lg n lg W)-approximation algorithm, where W = j w j. A slightly improved performance guarantee of O(lg n lg lg W) follows from work of Even, Naor, Rao, & Schieber [9]. We shall present a series of results that give constant approximation algorithms for this problem, where the resulting algorithms are both simple to state, and simple to analyze. We shall also consider the uncapacitated facility location problem. In this problem, there is a set of locations F at which we may build a facility (such as a warehouse), where the cost of building at location i is f i , for each i ∈ F. There is a set D of client locations (such as stores) that require to be serviced by a facility, and if a client at location j is assigned to a facility at location i, a cost of c ij is incurred. All of the data are assumed to be non-negative. The objective is to determine a set of locations at which to open facilities so as to minimize the total facility and assignment costs. Building on results for the set covering problem (due to Johnson [19], Lovász [25], and Chvátal [7]), Hochbaum [15] showed that a simple greedy heuristic is an O(log n)-approximation algorithm, where n denotes the total number of locations in the input. Lin & Vitter [24] gave an elegant filtering and rounding technique that yields an alternate O(log n)-approximation algorithm for this problem. We shall focus on the metric case of this problem, in which distances between locations are given in some metric (and hence satisfy the triangle inequality), and the assignment costs c ij are proportional to the distance between i and j, for each i ∈ F , j ∈ D. We shall present a series of results that give constant approximation algorithms for this problem, where, once again, the resulting algorithms are both simple to state, and (relatively) simple to analyze.
Improving a state‐of‐the‐art heuristic for the minimum latency problem with data mining
International Transactions in Operational Research
Recentemente, metaheurísticas híbridas têm se tornado uma tendência em pesquisa operacional. Um exemplo bem sucedido combina Greedy Randomized Adaptive Search Procedures (GRASP) e técnicas de mineração de dados, onde padrões frequentes encontrados em soluções de alta qualidade podem levar a uma exploração eficiente do espaço de busca, juntamente com uma redução significativa de tempo computacional. Neste trabalho, uma heurística estado-da-arte baseada em GRASP para o Problema da Mínima Latência (PML) é aperfeiçoada por meio de técnicas de mineração de dados em duas variantes do PML. Experimentos computacionais mostraram que as abordagens com mineração de dados igualaram ou melhoraram a qualidade de solução para um número expressivo de instâncias, juntamente com uma redução substancial de tempo de execução. Além disso, 88 novos valores de custos de soluções de ambos problemas são introduzidos na literatura. Para avaliar os resultados reportados, testes de significância estatística, impacto de uso de padrões minerados, comparações de mesmo tempo e gráficos time-to-target são apresentados.
A branch-and-price algorithm for the Minimum Latency Problem
Computers & Operations Research
This paper deals with the Minimum Latency Problem (MLP), a variant of the well-known Traveling Salesman Problem in which the objective is to minimize the sum of waiting times of customers. This problem arises in many applications where customer satisfaction is more important than the total time spent by the server. This paper presents a novel branch-and-price algorithm for MLP that strongly relies on new features for the ng-path relaxation, namely: (1) a new labeling algorithm with an enhanced dominance rule named multiple partial label dominance; (2) a generalized definition of ng-sets in terms of arcs, instead of nodes; and (3) a strategy for decreasing ng-set size when those sets are being dynamically chosen. Also, other elements of efficient exact algorithms for vehicle routing problems are incorporated into our method, such as reduced cost fixing, dual stabilization, route enumeration and strong branching. Computational experiments over TSPLIB instances are reported, showing that several instances not solved by the current state-of-the-art method can now be solved.
2019
Recentemente, metaheurísticas híbridas têm se tornado uma tendência em pesquisa operacional. Um exemplo bem sucedido combina Greedy Randomized Adaptive Search Procedures (GRASP) e técnicas de mineração de dados, onde padrões frequentes encontrados em soluções de alta qualidade podem levar a uma exploração eficiente do espaço de busca, juntamente com uma redução significativa de tempo computacional. Neste trabalho, uma heurística estado-da-arte baseada em GRASP para o Problema da Mínima Latência (PML) é aperfeiçoada por meio de técnicas de mineração de dados em duas variantes do PML. Experimentos computacionais mostraram que as abordagens com mineração de dados igualaram ou melhoraram a qualidade de solução para um número expressivo de instâncias, juntamente com uma redução substancial de tempo de execução. Além disso, 88 novos valores de custos de soluções de ambos problemas são introduzidos na literatura. Para avaliar os resultados reportados, testes de significância estatística, impacto de uso de padrões minerados, comparações de mesmo tempo e gráficos time-to-target são apresentados.