scholarly journals Combinatorial two-stage minmax regret problems under interval uncertainty

2020 ◽  
Author(s):  
Marc Goerigk ◽  
Adam Kasperski ◽  
Paweł Zieliński
Keyword(s):  
Combinatorial Optimization ◽  
Shortest Path ◽  
Feasible Solution ◽  
Optimization Problems ◽  
Interval Uncertainty ◽  
Combinatorial Optimization Problems ◽  
Second Stage ◽  
Minmax Regret ◽  
Uncertainty Set ◽  
Two Stages

AbstractIn this paper a class of combinatorial optimization problems is discussed. It is assumed that a feasible solution can be constructed in two stages. In the first stage the objective function costs are known while in the second stage they are uncertain and belong to an interval uncertainty set. In order to choose a solution, the minmax regret criterion is used. Some general properties of the problem are established and results for two particular problems, namely the shortest path and the selection problem, are shown.

scholarly journals Robust two-stage combinatorial optimization problems under convex second-stage cost uncertainty

2021 ◽  
Author(s):  
Marc Goerigk ◽  
Adam Kasperski ◽  
Paweł Zieliński
Keyword(s):  
Combinatorial Optimization ◽  
Approximation Algorithms ◽  
Network Optimization ◽  
Optimization Problems ◽  
Two Stage ◽  
Shortest Path Problems ◽  
Combinatorial Optimization Problems ◽  
Second Stage ◽  
Uncertainty Set ◽  
Basic Network

AbstractIn this paper a class of robust two-stage combinatorial optimization problems is discussed. It is assumed that the uncertain second-stage costs are specified in the form of a convex uncertainty set, in particular polyhedral or ellipsoidal ones. It is shown that the robust two-stage versions of basic network optimization and selection problems are NP-hard, even in a very restrictive cases. Some exact and approximation algorithms for the general problem are constructed. Polynomial and approximation algorithms for the robust two-stage versions of basic problems, such as the selection and shortest path problems, are also provided.

scholarly journals Minmax regret combinatorial optimization problems: an Algorithmic Perspective

2011 ◽  
Vol 45 (2) ◽  
pp. 101-129 ◽  
Author(s):  
Alfredo Candia-Véjar ◽  
Eduardo Álvarez-Miranda ◽  
Nelson Maculan
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problems ◽  
Combinatorial Optimization Problems ◽  
Minmax Regret

Study on Free Search for Combinatorial Optimization Problem

2013 ◽  
Vol 411-414 ◽  
pp. 1904-1910
Author(s):  
Kai Zhong Jiang ◽  
Tian Bo Wang ◽  
Zhong Tuan Zheng ◽  
Yu Zhou
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problem ◽  
Feasible Solution ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Search Process ◽  
Standard Data ◽  
Combinatorial Optimization Problems ◽  
Free Search

An algorithm based on free search is proposed for the combinatorial optimization problems. In this algorithm, a feasible solution is converted into a full permutation of all the elements and a transformation of one solution into another solution can be interpreted the transformation of one permutation into another permutation. Then, the algorithm is combined with intersection elimination. The discrete free search algorithm greatly improves the convergence rate of the search process and enhances the quality of the results. The experiment results on TSP standard data show that the performance of the proposed algorithm is increased by about 2.7% than that of the genetic algorithm.

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