On risk-averse maximum weighted subgraph problems

Rysz, Maciej; Mirghorbani, Mohammad; Krokhmal, Pavlo A.; Pasiliao, Eduardo L.

doi:10.1007/s10878-014-9718-0

Cited by 14 publications

(6 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The newly proposed dynamic candidate set approach remarkably increases the efficiency of the original naive RDS. It is applicable not only for MCFPC but also for any combinatorial optimization problem defined on graphs with hereditary properties, which can be solved using a RDS algorithm [42, 51].…”

Section: Introductionmentioning

confidence: 99%

Minimum cost flow problem with conflicts

2021

View full text Add to dashboard Cite

The minimum cost flow problem with conflicts is a recent extension of the ordinary minimum cost flow problem. It includes flow compatibility restrictions in addition to flow balance equalities and capacity constraints: at most one of the conflicting arcs can have positive flow. In this work we study this extension of the minimum cost flow problem, which can be faced in many real‐world applications. We give mixed‐integer programming formulations of the problem after briefly analyzing its complexity and propose two exact solution algorithms. One of them is a branch‐and‐bound procedure with combinatorial branching rules based on conflicts in an optimal solution of the relaxations. The other one is a Russian Doll Search method exploring the maximal stable sets of the conflict graph, which is obtained from the original network with the purpose of representing the conflict relations among arcs. Also, a set of preprocessing procedures is introduced with the aim of reducing the size of the problem. We can say that the new algorithms are very efficient according to the results of extensive computational experiments realized on a large set of test problems.

show abstract

Section: Introductionmentioning

confidence: 99%

Minimum cost flow problem with conflicts

2021

View full text Add to dashboard Cite

show abstract

“…Rysz et al. () study a class of problems that aim at determining a subgraph with the largest sum of stochastic weights and a given hereditary property. The uncertainty is here associated with node weights rather than the possible failure of links.…”

Section: Networkmentioning

confidence: 99%

“…() (Benders decomposition algorithms), Rysz et al. () (branch and bound—B&B), and Yezerska et al. () (B&B).…”

Section: Networkmentioning

confidence: 99%

Conditional value‐at‐risk beyond finance: a survey

Filippi

Guastaroba

Speranza

2019

Int Trans Operational Res

View full text Add to dashboard Cite

A large number of problems involve making decisions in an uncertain environment and, hence, with unknown outcomes. Optimization models aimed at controlling the trade‐off between risk and return in finance have been widely studied since the seminal work by Markowitz in 1952. In financial applications, shortfall or quantile risk measures are receiving ever‐increasing attention. Conditional value‐at‐risk (CVaR) is arguably the most popular of such measures. In the last decades, optimization models aimed at controlling risk have been applied to several application domains different from financial optimization. This survey provides an overview of the main contributions where CVaR is incorporated into an optimization approach and applied to a context different from financial engineering. The literature is classified following an application‐oriented perspective. The applications cover classical areas studied in operational research—such as supply chain management, scheduling, and networks—and less classical areas such as energy and medicine. For each area, concise paper excerpts are provided that convey the main ideas of the problems studied, and analyze how the CVaR has been used to cope with different sources of uncertainty. Finally, some open research directions are outlined.

show abstract

“…There are several other real world subgraph problems which are either equivalent to or very closely related to the MWS (sometimes called heaviest subgraphs in the literature (Hassin and Rubinstein 1994; Macambira 2002; Vassilevska et al 2010; Álvarez-Miranda et al 2013; Williams and Williams 2013; Rysz etal. 2013).…”

Section: Related Workmentioning

confidence: 99%

Sequential Monte Carlo for Maximum Weight Subgraphs with Application to Solving Image Jigsaw Puzzles

2014

View full text Add to dashboard Cite

We consider a problem of finding maximum weight subgraphs (MWS) that satisfy hard constraints in a weighted graph. The constraints specify the graph nodes that must belong to the solution as well as mutual exclusions of graph nodes, i.e., pairs of nodes that cannot belong to the same solution. Our main contribution is a novel inference approach for solving this problem in a sequential monte carlo (SMC) sampling framework. Usually in an SMC framework there is a natural ordering of the states of the samples. The order typically depends on observations about the states or on the annealing setup used. In many applications (e.g., image jigsaw puzzle problems), all observations (e.g., puzzle pieces) are given at once and it is hard to define a natural ordering. Therefore, we relax the assumption of having ordered observations about states and propose a novel SMC algorithm for obtaining maximum a posteriori estimate of a high-dimensional posterior distribution. This is achieved by exploring different orders of states and selecting the most informative permutations in each step of the sampling. Our experimental results demonstrate that the proposed inference framework significantly outperforms loopy belief propagation in solving the image jigsaw puzzle problem. In particular, our inference quadruples the accuracy of the puzzle assembly compared to that of loopy belief propagation.

show abstract

On risk-averse maximum weighted subgraph problems

Cited by 14 publications

References 27 publications

Minimum cost flow problem with conflicts

Minimum cost flow problem with conflicts

Conditional value‐at‐risk beyond finance: a survey

Sequential Monte Carlo for Maximum Weight Subgraphs with Application to Solving Image Jigsaw Puzzles

Contact Info

Product

Resources

About