A simulated annealing approach for reliability‐based chance‐constrained programming

Abstract

The chance-constrained programming (CCP) is a well-known and widely used stochastic programming approach. In the CCP approach, determining the confidence levels of the constraints at the beginning of solution process is a critical issue for optimality. On one hand, it is possible to obtain better solutions at different confidence levels. On the other hand, the decision makers prefer to simplify their choices instead of grappling with the details such as determining confidence levels for all chance constraints. Reliability is an effective tool that enables the decision maker to look over the system integrity. In this paper, the CCP is considered as a reliability-based nonlinear multiobjective model, and a simulated annealing (SA) algorithm is developed to solve the model. The SA represents different solution alternatives at the different reliability degrees to the decision makers by performing different confidence levels. Thus, the decision makers have the opportunity to make more effective decisions.

An algorithm to solve a quantile optimization problem with loss function having a separable structure, and its application to an aerospace problem

“…Therefore, metaheuristic methods are suitable to solve them. For example, the simulated annealing method was applied to solve a problem with probabilistic constraints in the case of normal random parameters in the work of Sakalli …”

“…For example, the simulated annealing method was applied to solve a problem with probabilistic constraints in the case of normal random parameters in the work of Sakalli. 13 For solving stochastic programming problems with quantile criterion, the confidence method was developed. 14 This method reduces the original stochastic programming problem to a minimax problem, where a set of realizations of the random parameters and an optimization strategy are selected.…”