An improved column generation algorithm for minimum sum-of-squares clustering

Aloise, Daniel; Hansen, Pierre; Liberti, Leo

doi:10.1007/s10107-010-0349-7

Cited by 85 publications

(51 citation statements)

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“…Depending on the problem structure, there are a few exact solution algorithms. Algorithms designed specifically for minimizing the sum of squares in clustering problems [14] are of particular interest as they are structurally very similar to (7). Although that problem is simpler than the problem stated in (7), it can be used as a reference in terms of solution time and complexity, or it could even be modified to solve (7).…”

Section: Methodsmentioning

confidence: 99%

Hydrological scenario reduction for stochastic optimization in hydrothermal power systems

Aravena

Gil

2014

Appl Stoch Models Bus & Ind

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Most of the methods developed for hydrothermal power system planning are based on scenario-based stochastic programming and therefore represent the stochastic hydro variable (water inflows) as a finite set of hydrological scenarios. As the level of detail in the models grows and the associated optimization problems become more complex, the need to reduce the number of scenarios without distorting the nature of the stochastic variable is arising. In this paper, we propose a scenario reduction method for discrete multivariate distributions based on transforming the moment-matching technique into a combinatorial optimization problem. The method is applied to hydro inflow data from the Chilean Central Interconnected System and is benchmarked against results for the optimal operation of the Chilean Central Interconnected System determined with the selected subsets and the complete set of historical hydrological scenarios. Simulation results show that the proposed scenario-reduction method could adequately approximate the probability distribution of the objective function of the operational planning problem.

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Section: Methodsmentioning

confidence: 99%

Hydrological scenario reduction for stochastic optimization in hydrothermal power systems

Aravena

Gil

2014

Appl Stoch Models Bus & Ind

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“…This approach extends an exact algorithm which uses column generation [31]. It allows must-link, cannot-link and all constraints that are anti-monotone.…”

Section: Related Workmentioning

confidence: 98%

Constrained clustering by constraint programming

Dao

Duong

Vrain

2017

Artificial Intelligence

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Constrained Clustering allows to make the clustering task more accurate by integrating user constraints, which can be instance-level or cluster-level constraints. Few works consider the integration of different kinds of constraints, they are usually based on declarative frameworks and they are often exact methods, which either enumerate all the solutions satisfying the user constraints, or find a global optimum when an optimization criterion is specified. In a previous work, we have proposed a model for Constrained Clustering based on a Constraint Programming framework. It is declarative, allowing a user to integrate user constraints and to choose an optimization criterion among several ones. In this article we present a new and substantially improved model for Constrained Clustering, still based on a Constraint Programming framework. It differs from our earlier model in the way partitions are represented by means of variables and constraints. It is also more flexible since the number of clusters does not need to be set beforehand; only a lower and an upper bound on the number of clusters have to be provided. In order to make the model-based approach more efficient, we propose new global optimization constraints with dedicated filtering algorithms. We show that such a framework can easily be embedded in a more general process and we illustrate this on the problem of finding the optimal Pareto front of a bi-criterion constrained clustering task. We compare our approach with existing exact approaches, based either on a branch-and-bound approach or on graph coloring on twelve datasets. Experiments show that the model outperforms exact approaches in most cases.

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“…However, in practice their approach might be difficult to use as it requires a predetermined set of candidate clusters from which the algorithm searches for the best subset. In [90,96] the authors use an integer programming and column generation based approach in order to exactly solve the minimum sum of squares clustering problem. Constrained clustering has also been approached, again in a different clustering setting, by constraint programming (CP) [97,24].…”

Section: Constrained Clusteringmentioning

confidence: 99%