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On the Complexity of Solution Extension of Optimization Problems [article]

Katrin Casel, Henning Fernau, Mehdi Khosravian Ghadikolaei, Jérôme Monnot, Florian Sikora
2018 arXiv   pre-print
In this regard, we study the parameterised complexity of extension problems with respect to parameters related to the partial solution, as well as the optimality of simple exact algorithms under the Exponential-Time  ...  The question if a given partial solution to a problem can be extended reasonably occurs in many algorithmic approaches for optimization problems.  ...  Acknowledgements Partially supported by the Deutsche Forschungsgemeinschaft (FE 560/6-1) and by the project "ESIGMA" (ANR-17-CE23-0010).  ... 
arXiv:1810.04553v1 fatcat:7owbd2k6ivc53li62vmax6eoti

A Hybrid ILP-CP Model for Mapping Directed Acyclic Task Graphs to Multicore Architectures

Andreas Emeretlis, George Theodoridis, Panayiotis Alefragis, Nikolaos Voros
2014 2014 IEEE International Parallel & Distributed Processing Symposium Workshops  
In this paper, a hybrid Integer Linear Programming -Constraint Programming method that uses the Benders decomposition is used to find proven optimal solutions.  ...  The proposed method is augmented with cuts generation schemes for accelerating the solution process.  ...  The developed methods are based on hybrid ILP-CP models along with advanced algorithms achieving the solution of complex optimization problems with outstanding speedups [14] , [15] .  ... 
doi:10.1109/ipdpsw.2014.24 dblp:conf/ipps/EmeretlisTAV14 fatcat:flxvbtgqmjeutbvoqq2cc5vjoq

Applicability of Genetic and Ant Algorithms in Highway Alignment and Rail Transit Station Location Optimization

Sutapa Samanta, Manoj K. Jha
2012 International Journal of Operations Research and Information Systems  
AA seems to require lesser computation than GA considering the mechanisms of both the algorithms based on which they reach to the optimal or near-optimal solutions.  ...  The suitability of such algorithms depends on the nature of the problem to be solved.  ... 
doi:10.4018/joris.2012010102 fatcat:ve3hwb5cv5cqhiv3l2nxvfgo3m

Complexity Results and Algorithms for Extension Enforcement in Abstract Argumentation

Johannes Wallner, Andreas Niskanen, Matti Järvisalo
2016 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
Complementing the complexity results, we propose algorithms for NP-hard extension enforcement based on constrained optimization.  ...  In this work, we focus on the so-called extension enforcement problem in abstract argumentation.  ...  the enforcement problems based on applying constraint optimization solvers.  ... 
doi:10.1609/aaai.v30i1.10101 fatcat:chwtrbjljvh5vafxjivc6r7dfe

Recurrence-Aware Instruction Set Selection for Extensible Embedded Processors

P. Bonzini, L. Pozzi
2008 IEEE Transactions on Very Large Scale Integration (vlsi) Systems  
Because of its complexity, only simplified versions of the problem have been solved exactly so far.  ...  We then propose a range of novel algorithms, both exact and approximate, to solve the covering problem in conjunction with the recurrence of candidate extensions.  ...  After 2-optimal, compilation time grows much faster, testifying to the complexity of the problem.  ... 
doi:10.1109/tvlsi.2008.2001863 fatcat:kyoj7ddzgvet7psnqkqmiiokcq

Page 2386 of Mathematical Reviews Vol. , Issue 81F [page]

1981 Mathematical Reviews  
Each iteration cycle requires the solution of a linear programming problem.  ...  An iterative procedure of solution is proposed in which both the design and the imaginary displacements are modified until the compatible optimal solution is reached.  ... 

Static scheduling research to minimize weighted and unweighted tardiness: A state-of-the-art survey

Tapan Sen, Joanne M Sulek, Parthasarati Dileepan
2003 International Journal of Production Economics  
Heuristic methods and optimizing techniques are surveyed for both types of problems in the single-machine environment. Complexity theory related to these problems is also discussed.  ...  This paper reviews research on the total tardiness (TT) and total weighted tardiness (TWT) problems.  ...  We then discuss the complexity theory related to the combinatorial optimization problems and also mention how complex the TT and TWT problems are in terms of this theory.  ... 
doi:10.1016/s0925-5273(02)00265-7 fatcat:6rpojr3f6neovlh7znzyx5ymzu

Positive Linear Programming Extensions: Parallel Complexity and Applications [chapter]

Pavlos S. Efraimidis, Paul G. Spirakis
2000 Lecture Notes in Computer Science  
In this paper, we propose a general class of linear programs that admit efficient parallel approximations and use it for efficient parallel approximations to hard combinatorial optimization problems.  ...  The problem determining the parallel complexity of a search problem assuming an efficient solution to the corresponding decision problem is called the problem of "parallel self-reducibility" ( [3] ,  ...  Introduction One of the foremost paradigms in the design and analysis of approximation algorithms to hard combinatorial optimization problems [9] is: 1.  ... 
doi:10.1007/3-540-44520-x_60 fatcat:tdjex3xi7rhrfmh2qhsjngjaem

A Convex Optimization Approach to Generalized Moment Problems [chapter]

Christopher I. Byrnes, Anders Lindquist
2003 Control and Modeling of Complex Systems  
In this paper we present a universal solution to the generalized moment problem, with a nonclassical complexity constraint.  ...  In particular, these approaches give a constructive parameterization of all solutions to the Nevanlinna-Pick interpolation problem, with possible higher-order interpolation at certain points in the complex  ...  The question of actually finding, or computing solutions to either problem can be solved in the context of nonlinear convex optimization.  ... 
doi:10.1007/978-1-4612-0023-9_1 fatcat:5ju72tuu2nd65km67bkzq2ufvq

Fuzzy Calculus Theory and Its Applications

Omar Abu Arqub, Carla Pinto, Rosana Rodríguez López, Vedat Suat Ertürk
2018 Complexity  
Qiu propose the solution concepts for the fuzzy optimization problems in the quotient space of fuzzy numbers. In "Random Fuzzy Differential Equations with Impulses" by H.  ...  In "The Karush-Kuhn-Tucker Optimality Conditions for the Fuzzy Optimization Problems in the Quotient Space of Fuzzy Numbers," N. Yu and D.  ... 
doi:10.1155/2018/5463920 fatcat:ey4om3gzb5efnoajwv3mhuhnia

Recent Advances in Multiobjective Optimization [chapter]

Christos Zaroliagis
2005 Lecture Notes in Computer Science  
On the other hand, even if a decision maker is armed with the entire Pareto set, s/he is still left with the problem of which is the "best" solution for the application at hand.  ...  Its object of study is to investigate solutions to combinatorial optimization problems that are evaluated under several objective functionstypically defined on multidimensional attribute (cost) vectors  ...  Due to the exponential size of the Pareto set, a fair portion of research had focussed on solving relaxed versions of the optimization problem, which corresponds to finding the best solution in the convex  ... 
doi:10.1007/11571155_5 fatcat:jysibvbqh5gd3lhx43egsb27du

Complexity Results and Algorithms for Extension Enforcement in Abstract Argumentation

Johannes P. Wallner, Andreas Niskanen, Matti Järvisalo
2017 The Journal of Artificial Intelligence Research  
Complementing the complexity results, we propose algorithms for NP-hard extension enforcement based on constraint optimization under the maximum satisfiability (MaxSAT) paradigm.  ...  In this work, we focus on the so-called extension enforcement problem in abstract argumentation as a recently proposed form of argumentation dynamics.  ...  A solution τ is optimal for ϕ if COST(ϕ, τ ) ≤ COST(ϕ, τ ) holds for any solution τ to ϕ. Given ϕ, the Partial MaxSAT problem asks to find an optimal solution to ϕ.  ... 
doi:10.1613/jair.5415 fatcat:dfcx5xtnnvdkpiqwhglf4z64hy

Prospect of Meta-Heuristics Methods and Applications in Electric Power System

Truong Hoang Khoa Pandian M Vasant, Balbir Singh Mahinder Singh
2015 International Journal of Swarm Intelligence and Evolutionary Computation  
The methods based on artificial intelligence and hybrid approaches are very suitable for complex optimization problems. However, their search often results in a near global optimal solution [2, 4] .  ...  Most of these works require formulation of mathematical models with extensive use of computational intelligencebased optimization techniques to solve many technical problems.  ...  The methods based on artificial intelligence and hybrid approaches are very suitable for complex optimization problems. However, their search often results in a near global optimal solution [2, 4] .  ... 
doi:10.4172/2090-4908.1000124 fatcat:d6pm5p3exrasvgn7mz5h6c5mzu

Special issue on: robust combinatorial optimization

Arie M. C. A. Koster, Michael Poss
2018 EURO Journal on Computational Optimization  
Also, extensions in which the decisions can be adjusted (two-stage or adjustable robust optimization), depending on the realization of the uncertain parameters have been successfully studied.  ...  For optimization problems involving discrete decisions, the situation is more complex. Efficient exact or approximate solution algorithms for such problems must exploit the combinatorial B Arie M. C.  ...  Also, extensions in which the decisions can be adjusted (two-stage or adjustable robust optimization), depending on the realization of the uncertain parameters have been successfully studied.  ... 
doi:10.1007/s13675-018-0102-1 fatcat:zqsbowdfvvgkvhjpjn2neu77rm

An improved hybrid algorithm for solving the generalized vehicle routing problem

Petrică C. Pop, Oliviu Matei, Corina Pop Sitar
2013 Neurocomputing  
Areas of expertise Combinatorial Optimization -is concerned with optimization problems where the set of feasible solutions is discrete or can be reduced to a discrete one, and the goal is to find the best  ...  Metaheuristic Algorithms -are providing sub-optimal solutions for complex optimization problems in reasonable time.  ...  Within this research project we are studying the selective coloring problem which consists on finding a coloring of the nodes of a graph whose nodes are partitioned in n clusters such that we select exactly  ... 
doi:10.1016/j.neucom.2012.03.032 fatcat:l6voovmyxrdupg7vko34hgxbda
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