63,861 research outputs found

    Stochastic Constraint Programming

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    To model combinatorial decision problems involving uncertainty and probability, we introduce stochastic constraint programming. Stochastic constraint programs contain both decision variables (which we can set) and stochastic variables (which follow a probability distribution). They combine together the best features of traditional constraint satisfaction, stochastic integer programming, and stochastic satisfiability. We give a semantics for stochastic constraint programs, and propose a number of complete algorithms and approximation procedures. Finally, we discuss a number of extensions of stochastic constraint programming to relax various assumptions like the independence between stochastic variables, and compare with other approaches for decision making under uncertainty.Comment: Proceedings of the 15th Eureopean Conference on Artificial Intelligenc

    A New Index of Environmental Quality

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    An optimal weighting scheme is proposed to construct a new index of environmental quality for different countries using an approach that relies on consistent tests for stochastic dominance efficiency. The test statistics and the estimators are computed using mixed integer programming methods. The variables that are considered include countries’ greenhouse emissions, water pollution and forest benefits, as from the dataset of the World Bank. First, the stochastic efficient weighting for each set of variables is calculated to build three sub-indices (for greenhouse emissions, water pollution and land without forests) and then an overall risk index of environmental quality is constructed. One main result is that land without forest contributes the most (with around 70%), greenhouse emissions contribute with around 20% and water pollution contributes less (with around 10%). Finally, countries are ranked according to their index of environmental quality and their rankings are compared with those of the Kyoto Protocol.Environmental Quality; Emissions; Water Pollution; Nonparametric Stochastic Dominance, Mixed Integer Programming

    Concavity and Efficient Points of Discrete Distributions in Probabilistic Programming

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    We consider stochastic programming problems with probabilistic constraints involving integer-valued random variables. The concept of a p-efficient point of a probability distribution is used to derive various equivalent problem formulations. Next we introduce the concept of r-concave discrete probability distributions and analyse its relevance for problems under consideration. These notions are used to derive lower and upper bounds for the optimal value of probabilistically constrained stochastic programming problems with discrete random variables. The results are illustrated with numerical examples

    An Algorithmic Theory of Integer Programming

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    We study the general integer programming problem where the number of variables nn is a variable part of the input. We consider two natural parameters of the constraint matrix AA: its numeric measure aa and its sparsity measure dd. We show that integer programming can be solved in time g(a,d)poly(n,L)g(a,d)\textrm{poly}(n,L), where gg is some computable function of the parameters aa and dd, and LL is the binary encoding length of the input. In particular, integer programming is fixed-parameter tractable parameterized by aa and dd, and is solvable in polynomial time for every fixed aa and dd. Our results also extend to nonlinear separable convex objective functions. Moreover, for linear objectives, we derive a strongly-polynomial algorithm, that is, with running time g(a,d)poly(n)g(a,d)\textrm{poly}(n), independent of the rest of the input data. We obtain these results by developing an algorithmic framework based on the idea of iterative augmentation: starting from an initial feasible solution, we show how to quickly find augmenting steps which rapidly converge to an optimum. A central notion in this framework is the Graver basis of the matrix AA, which constitutes a set of fundamental augmenting steps. The iterative augmentation idea is then enhanced via the use of other techniques such as new and improved bounds on the Graver basis, rapid solution of integer programs with bounded variables, proximity theorems and a new proximity-scaling algorithm, the notion of a reduced objective function, and others. As a consequence of our work, we advance the state of the art of solving block-structured integer programs. In particular, we develop near-linear time algorithms for nn-fold, tree-fold, and 22-stage stochastic integer programs. We also discuss some of the many applications of these classes.Comment: Revision 2: - strengthened dual treedepth lower bound - simplified proximity-scaling algorith

    A learning-based algorithm to quickly compute good primal solutions for Stochastic Integer Programs

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    We propose a novel approach using supervised learning to obtain near-optimal primal solutions for two-stage stochastic integer programming (2SIP) problems with constraints in the first and second stages. The goal of the algorithm is to predict a "representative scenario" (RS) for the problem such that, deterministically solving the 2SIP with the random realization equal to the RS, gives a near-optimal solution to the original 2SIP. Predicting an RS, instead of directly predicting a solution ensures first-stage feasibility of the solution. If the problem is known to have complete recourse, second-stage feasibility is also guaranteed. For computational testing, we learn to find an RS for a two-stage stochastic facility location problem with integer variables and linear constraints in both stages and consistently provide near-optimal solutions. Our computing times are very competitive with those of general-purpose integer programming solvers to achieve a similar solution quality

    A chance-constrained stochastic approach to intermodal container routing problems

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    We consider a container routing problem with stochastic time variables in a sea-rail intermodal transportation system. The problem is formulated as a binary integer chance-constrained programming model including stochastic travel times and stochastic transfer time, with the objective of minimising the expected total cost. Two chance constraints are proposed to ensure that the container service satisfies ship fulfilment and cargo on-time delivery with pre-specified probabilities. A hybrid heuristic algorithm is employed to solve the binary integer chance-constrained programming model. Two case studies are conducted to demonstrate the feasibility of the proposed model and to analyse the impact of stochastic variables and chance-constraints on the optimal solution and total cost

    A heuristic approach for provider selection and task allocation model in telecommunication networks under stochastic QOS guaranties

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    In this study, we model provider selection and task allocation problem as an expected cost minimization problem with stochastic chance constraints. Two important parameters of Quality of Service (QoS), delay and jitter are considered as random variables to capture stochastic nature of telecom network environment. As solution methodology, stochastic model is converted into its deterministic equivalent and then a novel heuristic algorithm is proposed to solve resulting nonlinear mixed integer programming model. Finally, performance of solution procedure is tested by several randomly generated scenarios

    Decomposition and duality based approaches to stochastic integer programming

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    Stochastic Integer Programming is a variant of Linear Programming which incorporates integer and stochastic properties (i.e. some variables are discrete, and some properties of the problem are randomly determined after the first-stage decision). A Stochastic Integer Program may be rewritten as an equivalent Integer Program with a characteristic structure, but is often too large to effectively solve directly. In this thesis we develop new algorithms which exploit convex duality and scenario-wise decomposition of the equivalent Integer Program to find better dual bounds and faster optimal solutions. A major attraction of this approach is that these algorithms will be amenable to parallel computation

    Wind-pv-thermal power aggregator in electricity market

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    This paper addresses the aggregation of wind, photovoltaic and thermal units with the aim to improve bidding in an electricity market. Market prices, wind and photovoltaic powers are assumed as data given by a set of scenarios. Thermal unit modeling includes start-up costs, variables costs and bounds due to constraints of technical operation, such as: ramp up/down limits and minimum up/down time limits. The modeling is carried out in order to develop a mathematical programming problem based in a stochastic programming approach formulated as a mixed integer linear programming problem. A case study comparison between disaggregated and aggregated bids for the electricity market of the Iberian Peninsula is presented to reveal the advantage of the aggregation
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