Optimization of Stochastic Problems with Probability Functions via Differential Evolution
Abstract: Chance constrained programming, quantile/Value-at-Risk (VaR) optimization and integral quantile / Conditional Value-at-Risk (CVaR) optimization problems as Stochastic Programming Problems with Probability Functions (SPP-PF) are one of the most widely studied optimization problems in recent years. As a rule real-life SPP-PF is nonsmooth nonconvex optimization problem with complex geometry of objective function. Moreover, often it cannot be formulated in normative mathematical programming form. Differential evolution based approach together with Monte Carlo sampling technique of the chance constraint(s) evaluation for solution of SPP-PF is proposed in this study. Convergence of differential evolution algorithm and some practical implementation aspects of the proposed approach are discussed. The several case studies such as the blending problem, the quantile linear programming problem, optimization of runway area demonstrate the effectiveness of the proposed approach.
Keywords: stochastic programming; probability function; differential evolution; global optimization; Monte Carlo sampling.
Category 1: Stochastic Programming
Category 2: Global Optimization (Stochastic Approaches )
Category 3: Applications -- Science and Engineering (Basic Sciences Applications )
Entry Submitted: 11/23/2017
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