Uncertainties in design variables and problem parameters are inevitable and must be considered in an optimization task, if reliable optimal solutions are to be found. Besides the sampling techniques, there exist a number of reliability-based probabilistic optimization techniques for systematically handling such uncertainties. In this paper, first we present a brief review of these classical probabilistic procedures. Thereafter, we discuss different optimization tasks in which these classical reliability-based optimization procedures will, in general, have difficulties in finding true optimal solutions. These probabilistic techniques are borrowed from classical literature and are extended to constitute efficient reliability-based single and multi-objective evolutionary algorithms for solving such difficult problems. Due to the global perspective of evolutionary algorithms, first, we demonstrate the proposed methodology is better able to solve reliability based optimization problems having multiple local-global solutions. Second, we suggest introducing an additional objective of maximizing the reliability index along with optimizing the usual objective function and find a number of Pareto-optimal solutions trading-off between the objective value and corresponding reliability index, thereby allowing the designers to find solutions corresponding to different reliability requirements for a better application. Finally, the concept of single-objective reliability-based optimization is extended to multi-objective optimization of finding a reliable frontier, instead of a single reliable solution. These optimization tasks are illustrated by solving a number of test problems and a well-studied automobile design problem. Results are also compared with a couple of standard classical reliability-based methodologies. This paper demonstrates how classical reliability-based concepts can be used in single and multi-objective evolutionary algorithms to enhance their scope in handling uncertainties, a matter which is common in most real-world problem solving tasks.
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