Abstract
This study presents a newly developed methodology to transform the chance-constrained problem into a deterministic problem and then solving this multiobjective deterministic problem with the proposed method. Chance-constrained problem contains independent gamma random variables that are denoted as a i j . Two methods are proposed to obtain the deterministic equivalent of chance-constrained problem. The first of the methods is directly based on using the distribution, and the second consists of normalizing probabilistic constraints using Lyapunov’s central limit theorem. An algorithm which uses the Global Criterion Method is developed to solve the multiobjective deterministic equivalent of chance-constrained problem. The methodology is applied to a real-life engineering problem that consists of an IoT device and its data sending process. Using Lyapunov’s central limit theorem for large numbers of random variables is found to be more appropriate.
Highlights
Most decision problems, whether real world or hypothetical, can be defined with a mathematical programming model
One possible reason for this uncertainty is the randomness of these factors, and stochastic programming is a branch of mathematical programming that theoretically and empirically focuses on “conditional extremum problems under incomplete information about random coefficients” [1]
By assuming that all initial data exhibit the same basic characteristics, the deterministic approach ignores the probabilistic properties of complicated systems
Summary
Whether real world or hypothetical, can be defined with a mathematical programming model. Developed an algorithm for stochastic goal programming which assumes that the random variable coefficients are normally distributed with known means and variances In doing so, he transformed the stochastic problem into an equivalent deterministic quadratic programming problem. Jagannathan [7] obtained equivalent equations for chance-constrained programming models based on coefficient matrices with normally distributed elements and dependent random right-hand side elements. To the best of our knowledge, there is not any study that proposes an algorithm for solving multiobjective chanceconstraint problems with gamma random variables by directly using the distribution and using Lyapunov’s central limit theorem and Global Criterion Method. We consider a multiobjective chanceconstrained stochastic programming problem, where the technologic coefficients aij are independent gamma random variables with known means and variances. We compared the objective functions of models obtained from these exact and approximate methods
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