Decision environments involve the need to solve problems with varying degrees of uncertainty as well as multiple, potentially conflicting objectives. chance constraints consider the uncertainty encountered. Codes inco...
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Decision environments involve the need to solve problems with varying degrees of uncertainty as well as multiple, potentially conflicting objectives. chance constraints consider the uncertainty encountered. Codes incorporating chance constraints into a mathematical programming model are not available on a widespread basis owing to the non-linear form of the chance constraints. Therefore, accurate linear approximations would be useful to analyse this class of problems with efficient linear codes. This paper presents an approximation formula for chance constraints which can be used in either the single- or multiple-objective case. The approximation presented will place a bound on the chance constraint at least as tight as the true non-linear form, thus overachieving the chance constraint at the expense of other constraints or objectives.
The water distribution system is considered. It is assumed that the system comprises water reservoir network and agricultural users. The control problem consists in (i) optimal satisfying an agricultural user needs, (...
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The water distribution system is considered. It is assumed that the system comprises water reservoir network and agricultural users. The control problem consists in (i) optimal satisfying an agricultural user needs, (ii) avoiding floods and ecological losses. To solve the problem formulated, the following methods are applied: - the multilevel structure approach, - the chance-constrained approach and linear decision rules, - Frank-Wolfe algorithm for solution of upper level task and so called “radial” algorithm (proposed for multiplicative goal functions) for lower level tasks solution. Numerical results for different structures of a three-reservoir system are presented. Two types of decision rules are discussed and compared for all the structures considered.
First, it is shown why Blau's dilemma [4] of negative information value persists even when his problem is reformulated in more general ‘newsboy’ fashion provided that the chance constraint is understood as being...
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First, it is shown why Blau's dilemma [4] of negative information value persists even when his problem is reformulated in more general ‘newsboy’ fashion provided that the chance constraint is understood as being imposed posterior (rather than prior) to obtaining the information. Second, it is shown that, under prior imposition of the chance constraint, information value must be non-negative. Formulations for general CCP's given each assumption as to the point of constraint imposition are examined, and the 'newsboy' results obtained for Blau's dilemma are shown to obtain in general.
A new technique is developed for solving the voltampere reactive (VAR) compensation problem under uncertain operating conditions. The technique employs chance-constrained programming (CCP), and transforms the problem ...
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A new technique is developed for solving the voltampere reactive (VAR) compensation problem under uncertain operating conditions. The technique employs chance-constrained programming (CCP), and transforms the problem into a standard linear programming problem. In providing optimal allocation of VAR support, busbars with unacceptably high probability of violating voltage limits are identified and assigned appropriate chance-constraints. Two cases are considered using the new technique. In the first case, capacitive compensation is evaluated for peak load conditions. Inductive compensation is considered in the second case, assuming light load conditions. The method in its general form can be applied in cases where there is uncertainty with respect to equipment cost and/or the coefficients of the voltage-magnitude/reactive power relationships. Normal distributions are not necessary conditions and, if desired, dependent variates can be assumed. The method has been applied to the AEP 30-busbar test system for both heavy and light load conditions, and sample results are presented in the paper.
In Ref. 1, existence and optimality conditions were given for control systems whose dynamics are determined by a linear stochastic differential equation with linear feedback controls; moreover, the state variables sat...
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In Ref. 1, existence and optimality conditions were given for control systems whose dynamics are determined by a linear stochastic differential equation with linear feedback controls; moreover, the state variables satisfy probability constraints. Here, for the simplest case of such a model, the Ornstein-Uhlenbeck velocity process, we evaluate the necessary conditions derived in Ref. 1 and compute a time-optimal control such that a given threshold value γ > 0 is crossed with probability of at least 1 − α.
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