Abstract
Uncertainties in design variables and problem parameters are inevitable and must be considered in an optimization task including multi-objective optimization, if reliable optimal solutions are to be found. Sampling techniques become computationally expensive if a large reliability is desired. In this paper, first we present a brief review of statistical reliability-based optimization procedures. Thereafter, for the first time, we extend and apply multi-objective evolutionary algorithms for solving two different reliability-based optimization problems for which evolutionary approaches have a clear niche in finding a set of reliable, instead of optimal, solutions. The use of an additional objective of maximizing the reliability index in a multi-objective evolutionary optimization procedure allows a number of trade-off solutions to be found, thereby allowing the designers to find solutions corresponding to different reliability requirements. Next, the concept of single-objective reliability-based optimization is extended to multi-objective optimization of finding a reliable frontier, instead of an optimal frontier. These optimization tasks are illustrated by solving test problems and a well-studied engineering design problem. The results should encourage the use of evolutionary optimization methods to more such reliability-based optimization problems.
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Deb, K., Padmanabhan, D., Gupta, S., Mall, A.K. (2007). Reliability-Based Multi-objective Optimization Using Evolutionary Algorithms. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds) Evolutionary Multi-Criterion Optimization. EMO 2007. Lecture Notes in Computer Science, vol 4403. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70928-2_9
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DOI: https://doi.org/10.1007/978-3-540-70928-2_9
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