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A factor graph based genetic algorithm

B. Hoda Helmi, Adel T. Rahmani, Martin Pelikan (2014)

International Journal of Applied Mathematics and Computer Science

We propose a new linkage learning genetic algorithm called the Factor Graph based Genetic Algorithm (FGGA). In the FGGA, a factor graph is used to encode the underlying dependencies between variables of the problem. In order to learn the factor graph from a population of potential solutions, a symmetric non-negative matrix factorization is employed to factorize the matrix of pair-wise dependencies. To show the performance of the FGGA, encouraging experimental results on different separable problems...

A smoothing SAA method for a stochastic mathematical program with complementarity constraints

Jie Zhang, Li-wei Zhang, Yue Wu (2012)

Applications of Mathematics

A smoothing sample average approximation (SAA) method based on the log-exponential function is proposed for solving a stochastic mathematical program with complementarity constraints (SMPCC) considered by Birbil et al. (S. I. Birbil, G. Gürkan, O. Listes: Solving stochastic mathematical programs with complementarity constraints using simulation, Math. Oper. Res. 31 (2006), 739–760). It is demonstrated that, under suitable conditions, the optimal solution of the smoothed SAA problem converges almost...

A stochastic programming approach to managing liquid asset portfolios

Helgard Raubenheimer, Machiel F. Kruger (2010)


Maintaining liquid asset portfolios involves a high carry cost and is mandatory by law for most financial institutions. Taking this into account a financial institution's aim is to manage a liquid asset portfolio in an “optimal” way, such that it keeps the minimum required liquid assets to comply with regulations. In this paper we propose a multi-stage dynamic stochastic programming model for liquid asset portfolio management. The model allows for portfolio rebalancing decisions over a multi-period...

A two-stage stochastic optimization model for a gas sale retailer

F. Maggioni, Maria Teresa Vespucci, E. Allevi, Marida Bertocchi, M. Innorta (2008)


The paper deals with a new stochastic optimization model, named OMoGaS–SV (Optimization Modelling for Gas Seller–Stochastic Version), to assist companies dealing with gas retail commercialization. Stochasticity is due to the dependence of consumptions on temperature uncertainty. Due to nonlinearities present in the objective function, the model can be classified as an NLP mixed integer model, with the profit function depending on the number of contracts with the final consumers, the typology of...

Approximative solutions of stochastic optimization problems

Petr Lachout (2010)


The aim of this paper is to present some ideas how to relax the notion of the optimal solution of the stochastic optimization problem. In the deterministic case, ε -minimal solutions and level-minimal solutions are considered as desired relaxations. We call them approximative solutions and we introduce some possibilities how to combine them with randomness. Relations among random versions of approximative solutions and their consistency are presented in this paper. No measurability is assumed, therefore,...

Augmented Lagrangian method for recourse problem of two-stage stochastic linear programming

Saeed Ketabchi, Malihe Behboodi-Kahoo (2013)


In this paper, the augmented Lagrangian method is investigated for solving recourse problems and obtaining their normal solution in solving two-stage stochastic linear programming problems. The objective function of stochastic linear programming problem is piecewise linear and non-differentiable. Therefore, to use a smooth optimization methods, the objective function is approximated by a differentiable and piecewise quadratic function. Using quadratic approximation, it is required to obtain the...

Bound-based decision rules in multistage stochastic programming

Daniel Kuhn, Panos Parpas, Berç Rustem (2008)


We study bounding approximations for a multistage stochastic program with expected value constraints. Two simpler approximate stochastic programs, which provide upper and lower bounds on the original problem, are obtained by replacing the original stochastic data process by finitely supported approximate processes. We model the original and approximate processes as dependent random vectors on a joint probability space. This probabilistic coupling allows us to transform the optimal solution of the...

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