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Lagrangian Relaxation for the Multiple Constrained Robust Shortest Path Problem

Yiyong Pan
2019 Mathematical Problems in Engineering  
Nonlinear optimization model is developed to model constrained robust shortest path problem. The dual nature of the proposed problem is deduced based on the Lagrangian duality theory.  ...  An efficient algorithm based on Lagrangian dual relaxation is designed to solve constrained robust shortest path problem. An extension problem that considers multiple constraints is discussed.  ...  GXL2015031, to which the author is very grateful.  ... 
doi:10.1155/2019/3987278 fatcat:iz4yjehrn5e2jhxdhr7fi6tl5i

Min-Max quickest path problems

Stefan Ruzika, Markus Thiemann
2012 Networks  
In a dynamic network, the quickest path problem asks for a path such that a given amount of flow can be sent from source to sink via this path in minimal time.  ...  In practical settings, for example in evacuation or transportation planning, the problem parameters might not be known exactly a-priori.  ...  Further research should also concentrate on robust versions of other (dynamic) network flow problems, including maximum (dynamic) flows, quickest flows, and minimum cost flows.  ... 
doi:10.1002/net.21473 fatcat:ceep2f4rrjfunjsnlaqjr7c5qe

Discrete Multiobjective Optimization [chapter]

Kathrin Klamroth
2009 Lecture Notes in Computer Science  
salesman problem, and other network problems like multiple objective minimum spanning tree, shortest path, and minimum cost flow problems.  ...  Since the set of feasible solutions of a MOCO problem is discrete and usually finite, it can at least theoretically be enumerated to identify all Pareto optimal solutions.  ...  Neighborhood Search and Connectedness Structural properties of the efficient set of MOCO problems play a crucial role for the development of efficient solution methods.  ... 
doi:10.1007/978-3-642-01020-0_4 fatcat:faj3iuqbkzc4tced3q3gu4azfe

A Compromise Decision Support Multi Objective Travelling Salesman Problem

2019 International journal of recent technology and engineering  
The dynamic programming approach for optimal path with state space tree is used to get the shortest route for the objectives.  ...  The multi objective travelling salesman problem simultaneously optimizes several objectives. It is also called as shortest cyclic route model with multiple objectives provides the shortest route.  ...  vector. ‖ The solution of this optimization problem is an efficient solution for the original multi objective problem.  ... 
doi:10.35940/ijrte.d4501.118419 fatcat:mwbkccm2mfcxzjiunlsqjiuxci

Martins' algorithm revisited for multi-objective shortest path problems with a MaxMin cost function

Xavier Gandibleux, Frédéric Beugnies, Sabine Randriamasy
2006 4OR  
This paper presents a straight extension of the label setting algorithm proposed by Martins in 1985 for a shortest path problem with multiple objectives.  ...  The main modications to Martins' algorithm for multi-objective shortest path problems touch upon the dominance test and the procedure for identifying efficient paths.  ...  Acknowledgements The authors would like to thank José Figueira, guest researcher at the University of Valenciennes for a month in 2001, for many fruitful discussions concerning shortest path problems with  ... 
doi:10.1007/s10288-005-0074-x fatcat:ladbegik35gefbohktpwvkelgm

An interactive bi-objective shortest path approach: searching for unsupported nondominated solutions

J.M. Coutinho-Rodrigues, J.C.N. Clı́maco, J.R. Current
1999 Computers & Operations Research  
Even for the biobjective shortest path problem, generating and presenting the whole set of nondominated solutions (paths) to a decision maker, in general, is not effective because the number of these paths  ...  This paper introduces an interactive procedure to assist the decision maker in identifying the "best compromise" solution for the bi-objective shortest path problem.  ...  nondominated solutions for the bi-objective shortest path problem.  ... 
doi:10.1016/s0305-0548(98)00094-x fatcat:3b4thxabcfbyrbexrvved5tdzu

Toll Pricing and Heterogeneous Users: Approximation Algorithms for Finding Bicriterion Time-Dependent Efficient Paths in Large-Scale Traffic Networks

Hani Mahmassani, Xuesong Zhou, Chung-Cheng Lu
2005 Transportation Research Record  
This method has been widely applied to solve the MOSP, because it can utilize efficient solution algorithms for the resulting single-objective shortest path problem.  ...  In addition, many applications in transportation planning and operations require efficient solution algorithms for optimum path problems with multiple objectives, such as travel time, reliability, and  ...  points in the criterion space) for the bi-objective time-dependent shortest path problem.  ... 
doi:10.3141/1923-04 fatcat:ktguow3mt5ganpv6gdmesw624e

Evolutionary Algorithms For The Multiobjective Shortest Path Problem

José Maria A. Pangilinan, Gerrit K. Janssens
2007 Zenodo  
This paper presents an overview of the multiobjective shortest path problem (MSPP) and a review of essential and recent issues regarding the methods to its solution.  ...  The paper further explores a multiobjective evolutionary algorithm as applied to the MSPP and describes its behavior in terms of diversity of solutions, computational complexity, and optimality of solutions  ...  They show how their results can be used to obtain efficient approximate solutions to the multiple constrained path problem and to the non-additive shortest path problem.  ... 
doi:10.5281/zenodo.1079535 fatcat:plsqsotxmfbznf7tuel7zcfwnq

An Approach for the Fast Calculation Method of Pareto Solutions of a Two-objective Network

Natsumi Takahashi, Tomoaki Akiba, Shuhei Nomura, Hisashi Yamamoto
2015 International Journal of Reliability, Quality and Safety Engineering (IJRQSE)  
In this study, we consider two-objective shortest path problem and propose efficient algorithms for obtaining the Pareto solutions.  ...  The multi-objective shortest path problem is a kind of optimization problem of multi-objective network. In the general cases, multi-objectives are rarely optimized by a solution.  ...  In this study, we consider two-objective shortest path problem and propose efficient algorithms for obtaining the Pareto solutions.  ... 
doi:10.1142/s0218539315500059 fatcat:jleycvxmbvhzdfykhljtqg42xq

The Bi-objective Shortest Path Network Interdiction Problem: Subgraph Algorithm and Saturation Property

Kaiming Xiao, Cheng Zhu, Weiming Zhang, Xiangyu Wei
2020 IEEE Access  
This paper presents a bi-objective shortest path network interdiction model with node interdiction, in which the interdictor seeks to interdict a set of nodes in the network that is Pareto-optimal with  ...  A novel subgraph sequence algorithm is developed to identify the efficient frontier through a sequence of single-objective problems.  ...  The weak efficient solutions of BOSPNI problem can be obtained by solving SPNI problem with single objective to maximize the shortest path length with specific resources according to Theorem 7, and the  ... 
doi:10.1109/access.2020.3012963 fatcat:vbyg77e7hnecxkg7km27rf4efa

Solving fuzzy multi-objective shortest path problem based on data envelopment analysis approach

M. Bagheri, Ali Ebrahimnejad, S. Razavyan, F. Hosseinzadeh Lotfi, N. Malekmohammadi
2021 Complex & Intelligent Systems  
These types of SPPs are known as the multi-objective shortest path problem (MOSPP) and can be solved with the existing various approaches.  ...  Hence, the FMOSPP is converted into a single objective Fuzzy Shortest Path Problem (FSPP) that can be solved using existing FSPP algorithms.  ...  Acknowledgements The authors would like to thank the anonymous reviewers and the associate editor for their insightful comments and suggestions.  ... 
doi:10.1007/s40747-020-00234-4 fatcat:zetg5ealfzhcnp5a3zroqeor3q

High-Performance Heuristics for Optimization in Stochastic Traffic Engineering Problems [chapter]

Evdokia Nikolova
2010 Lecture Notes in Computer Science  
Both the nonconvex objective and exponentially sized feasible set of available routes present a challenging optimization problem for which no efficient algorithms are known.  ...  The objective function is a positive linear combination of the mean and standard deviation of the route.  ...  The optimal solution of the nonconvex problem (2) minimizes the linear objective βµ T x + (1 − β)τ T x for some β ∈ [0, 1].  ... 
doi:10.1007/978-3-642-12535-5_41 fatcat:4tt3zxjc6fdajea7xuklwmnrfy

Optimal Simplification of Cartographic Lines Using Shortest-path Formulations

Gerard M. Campbell, Robert G. Cromley
1991 Journal of the Operational Research Society  
In this paper, the line simplification problem is formulated using shortest-path formulations for which efficient solution algorithms can be applied.  ...  This would eliminate the need for solving multiple shortest-path problems for every line, resulting in significant computational savings.  ... 
doi:10.1057/jors.1991.150 fatcat:d4tmzaa6yrd6tfghps7xokef7e

Bicriteria product design optimization: An efficient solution procedure using AND/OR trees

S. Raghavan, Michael O. Ball, Vinai S. Trichur
2002 Naval Research Logistics  
We develop an enumerative solution algorithm for the bicriteria problem that requires as a subroutine the solution of the parametric shortest path problem.  ...  As a result we develop an efficient solution algorithm for the product design optimization problem that does not require the use of complex and expensive linear/integer programming solvers.  ...  The problem of finding efficient solutions to problem P, i.e., that of solving P for different values of , can thus be viewed as that of finding shortest s-t paths through the corresponding series parallel  ... 
doi:10.1002/nav.10031 fatcat:v4wmpufvs5frlkie64trh5ah5m

Enhancing wavelength converter placement optimization with traffic-engineering-aware shortest-path routing

Y. C. Foo, Youngseok Lee, C. F. Teo, S. F. Chien, Andy L. Y. Low
2004 IEICE Electronics Express  
This paper proposes the combination of multiple shortestpaths routing and particle swarm optimization algorithm to solve the wavelength converters placement problem.  ...  Both equal-cost multipath routing and traffic-engineering-aware shortest-path routing are included in the experiments to examine their effectiveness in reducing the overall blocking probability.  ...  Conclusion We presented a highly efficient integrated optimization framework by combining multiple shortest-paths routing and BPSO to solve the NP-hard converter placement problem.  ... 
doi:10.1587/elex.1.416 fatcat:6ipiohdgirh4rebmicljasmi2a
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