OR-Library: Distributing Test Problems by Electronic Mail

Beasley, John E.

doi:10.2307/2582903

Cited by 386 publications

(539 citation statements)

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“…Problem instances The considered rrKP instances are slight modifications of multi-dimensional knapsack instances taken from the ORLIB [6,8,5] created by Chu and Beasley. The original problem files are named mknapcb1.txt to mknapcb9.txt and contain 30 test instances each.…”

Section: Computationsmentioning

confidence: 99%

Recoverable robust knapsacks: the discrete scenario case

2011

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Admission control problems have been studied extensively in the past. In a typical setting, resources like bandwidth have to be distributed to the different customers according to their demands maximizing the profit of the company. Yet, in real-world applications those demands are deviating and in order to satisfy their service requirements often a robust approach is chosen wasting benefits for the company. Our model overcomes this problem by allowing a limited recovery of a previously fixed assignment as soon as the data are known by violating at most k service promises and serving up to ℓ new customers. Applying this approaches to the call admission problem on a single link of a telecommunication network leads to a recoverable robust version of the knapsack problem.In this paper, we show that for a fixed number of discrete scenarios this recoverable robust knapsack problem is weakly NP-complete and any such instance can be solved in pseudo-polynomial time by a dynamic program. If the number of discrete scenarios is part of the input, the problem is strongly NP-complete and in special cases not approximable in polynomial time, unless P = NP.Next to its complexity status we were interested in obtaining strong polyhedral descriptions for this problem. We thus generalized the well-known concept of covers to gain valid inequalities for the recoverable robust knapsack polytope. Besides the canonical extension of covers we introduce a second kind of extension exploiting the scenario-based problem structure and producing stronger valid inequalities. Furthermore, we present two extensive computational studies to (i) investigate the influence of parameters k and ℓ to the objective and (ii) evaluate the effectiveness of our new class of valid inequalities.

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Section: Computationsmentioning

confidence: 99%

Recoverable robust knapsacks: the discrete scenario case

2011

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“…Para este segundo experimento foi utilizada a instância Grafo274 retirada da base de dados Operational Research Library (Beasley, 1990 A principal característica do Grafo274 é ser um problema multimodal que contém vários ótimos globais, ou seja, existem diversas árvores geradoras mínimas (T*) que podem ser a solução ótima do problema, pois todas têm grau de possibilidade igual a 1. Essa característica influencia diretamente na eficiência dos métodos, pois o fato de existir diversos "picos" candidatos à solução pode induzir os indivíduos da população se aglomerarem em um pico específico fazendo com que o espaço de busca não seja explorado de forma eficiente.…”

Section: Experimento II -Grafo274unclassified

Sistema imunológico artificial para resolver o problema da árvore geradora mínima com parâmetros fuzzy

2007

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ResumoNeste trabalho é proposta uma meta-heurística baseada em técnicas da computação evolutiva que visa encontrar um conjunto de árvores geradoras mínimas, para problemas de grafos que possuem incertezas em relação às informações associadas aos parâmetros. Resolver problemas dessa natureza é um processo NP-Completo, pois envolve um número enorme de comparações. A fim de contornar essa complexidade, é proposto um sistema imunológico artificial capaz de explorar eficientemente o espaço de busca e de obter resultados satisfatórios, sem a necessidade de confrontar todas as soluções entre si. Palavras-chave: computação evolutiva; grafos fuzzy; programação matemática fuzzy. AbstractThis work proposes an heuristical approach based on evolutionary computation, whose goal is to find a set of minimum spanning trees in graphs that contain uncertainties in their parameters. This kind of problem is a NP-Hard one, because it involves an enormous number of comparisons. In order to avoid this complexity, this work proposes an artificial immune system that explores efficiently the search space of solutions to looking for satisfactory results, without the necessity of comparing all possible solutions.

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“…In addition to the problem instances that were generated for testing the performance of the new approach we used 4 distance matrices of "standard test problems" pmed1-pmed5 (see [22]) in order to see whether the proposed solution 5 method works for these (larger) problems as well. The results of these computations, for some selected λ-values, are given 6 in Table 11 whereas the first four columns show the problem instances, the fifth the preprocessing and total solution time 7 and the last two the number of nodes in the branching tree and the number of applied cuts.…”

Section: Results For Pmed1-pmed5mentioning

confidence: 99%

“…Furthermore, apart from being valid for the proposed formulation, the inequalities (19) can be used to replace binary 22 restrictions on x jk -variables. This statement is proved by the following proposition.…”

Section: Valid Inequalitiesmentioning

confidence: 99%

“…Moreover, In order to test the performance of the proposed solution method, problem instances with eight different λ-vectors have 11 been used. These λ-vectors are given in Table 2 (for T1-T8 see also [13,19] In addition, the distance matrices of the OR-Lib instances pmed1-pmed5 (see [22]), extended by T1-T10, have been tested 6 (see Section 5.6). ) and the average number of cuts which have been applied (# C.).…”

Section: Computer and Test Problemsmentioning

confidence: 99%

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