GRASP with hybrid heuristic-subproblem optimization for the multi-level capacitated minimum spanning tree problem

Martins, Alexandre Xavier; Souza, Maurício C. de; Souza, Marcone Jamilson Freitas; Toffolo, Túlio A. M.

doi:10.1007/s10732-008-9079-x

Cited by 10 publications

(22 citation statements)

References 21 publications

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“…Related research can be found in Sherali (1984), Pang and Fukushima (2005), Hu and Ralph (2007), De et al (2009) and will be not discussed in this book. In mathematical programming, it is described as an equilibrium problem with equilibrium constraints (EPEC).…”

Section: Problem Identificationmentioning

confidence: 99%

Multi-Level Decision Making

Zhang¹,

Lu²,

Gao³

2015

Intelligent Systems Reference Library

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The aim of this series is to publish a Reference Library, including novel advances and developments in all aspects of Intelligent Systems in an easily accessible and well structured form. The series includes reference works, handbooks, compendia, textbooks, well-structured monographs, dictionaries, and encyclopedias. It contains well integrated knowledge and current information in the field of Intelligent Systems. The series covers the theory, applications, and design methods of Intelligent Systems. Virtually all disciplines such as engineering, computer science, avionics, business, e-commerce, environment, healthcare, physics and life science are included.More information about this series at of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. v multi-level decision situations, as well as the use of decision support systems to obtain the desired solutions.• It reflects the latest academic research progress and state-of-the-art development through the results of our own and other authors' recent publications in this field. It does not attempt to provide exhaustive coverage of every fact or research result that exists.This monograph is principally based on our research developments over the past ten years, during which time we have produced more than 50 journal and conference publications in this field.The monograph has 14 chapters, organized into five parts. The first part, from Chaps. 1 to 3, covers concepts of decision-making, decision support systems and bi-level decision-making in general. The second part of the monograph, from Chaps. 4 to 6, presents bi-level multi-follower and tri-level multi-follower decisionmaking, including related models, solution methods, algorithms and case studies. The third part, from Chaps. 7 to 9, focuses on uncertainty issues in multi-level decision-making and discusses fuzzy bi-level and fuzzy multi-objective bi-level decision models and solution algorithms. In Part IV, Chap. 10 deals with a nonprogramming multi-level decision issue and proposes the framework and methods of rule-set-based bi-level decision-making. The last part, from Chaps. 11 to 14, shows the development of bi-level and tri-level decision support systems and related applications by using the methods presented in the previous chapters. These applications include the power market, supply chain management and railway organization.Our potential readers include organizational managers and practicing professionals, who can use the methods and software provided to solve their real decision problems; researchers in the areas of bi-level and multi-level decision-making and decision support systems; students at an advanced undergraduate or master's level in information systems, business administration, or the applicati...

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Section: Problem Identificationmentioning

confidence: 99%

Multi-Level Decision Making

Zhang¹,

Lu²,

Gao³

2015

Intelligent Systems Reference Library

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“…for producing good quality solutions in very restricted times is a growing trend in optimization [34,42]. A pervasive term in this area is subproblem optimization.…”

Section: Primal Bound Improvement : Mip Heuristicsmentioning

confidence: 99%

Integer programming techniques for the nurse rostering problem

et al. 2014

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This work presents Integer Programming (IP) techniques to tackle the problem of the International Nurse Rostering Competition. Starting from a compact and monolithic formulation in which the current generation of solvers performs poorly, improved cut generation strategies and primal heuristics are proposed and evaluated. A large number of computational experiments with these techniques produced the following results: the optimality of the vast majority of instances was proved, the best known solutions were improved by up to 15% and strong dual bounds were obtained. In the spirit of reproducible science, all code was implemented using the Computational Infrastructure for Operations Research (COIN-OR).

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“…The MLCMST problem has been recently treated in the literature by Gamvros et al [12, 13], and by Martins et al [19]. Gamvros et al [12] proposed two flow‐based mixed integer programming (MIP) formulations and several heuristic procedures for the problem, including exponential size neighborhoods and a hybrid genetic algorithm.…”

Section: Introductionmentioning

confidence: 99%

“…Gamvros et al [12] proposed two flow‐based mixed integer programming (MIP) formulations and several heuristic procedures for the problem, including exponential size neighborhoods and a hybrid genetic algorithm. Martins et al [19] proposed a Greedy Randomized Adaptive Search Procedure (GRASP) hybridized with an integer programming (IP) model. The heuristic defines subproblems that are solved by a commercial optimization package over that IP.…”

Section: Introductionmentioning

confidence: 99%

“…We then use the branch‐and‐cut within a GRASP similar to that in Ref. [19], optimizing subproblems during the construction and local search phases. As the new branch‐and‐cut is substantially more effective than the pure IP model, the resulting algorithm is able to find solutions better than those found by the former algorithm in a consistent way.…”

Section: Introductionmentioning

confidence: 99%

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Branch‐and‐cut and hybrid local search for the multi‐level capacitated minimum spanning tree problem

Uchôa¹,

Toffolo²,

Souza³

et al. 2011

Networks

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We propose algorithms to compute tight lower bounds and high quality upper bounds (UBs) for the multilevel capacitated minimum spanning tree problem. We first develop a branch-and-cut algorithm, introducing some new features: (i) the exact separation of cuts corresponding to some master equality polyhedra found in the formulation; (ii) the separation of Fenchel cuts, solving LPs considering all the possible solutions restricted to small portions of the graph. We then use that branchand-cut within a GRASP that performs moves by solving to optimality subproblems corresponding to partial solutions. The computational experiments were conducted on 450 benchmark instances from the literature. Numerical results show improved best known (UBs) for almost all instances that could not be solved to optimality.

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GRASP with hybrid heuristic-subproblem optimization for the multi-level capacitated minimum spanning tree problem

Cited by 10 publications

References 21 publications

Multi-Level Decision Making

Multi-Level Decision Making

Integer programming techniques for the nurse rostering problem

Branch‐and‐cut and hybrid local search for the multi‐level capacitated minimum spanning tree problem

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