Chapter

Evolutionary Multi-Criterion Optimization

Volume 4403 of the series Lecture Notes in Computer Science pp 66-80

Reliability-Based Multi-objective Optimization Using Evolutionary Algorithms

  • Kalyanmoy DebAffiliated withKanpur Genetic Algorithms Laboratory (KanGAL), Indian Institute of Technology Kanpur, Kanpur, PIN 208 016
  • , Dhanesh PadmanabhanAffiliated withIndia Science Laboratory, GM R&D, Bangalore, PIN 560066
  • , Sulabh GuptaAffiliated withKanpur Genetic Algorithms Laboratory (KanGAL), Indian Institute of Technology Kanpur, Kanpur, PIN 208 016
  • , Abhishek Kumar MallAffiliated withKanpur Genetic Algorithms Laboratory (KanGAL), Indian Institute of Technology Kanpur, Kanpur, PIN 208 016

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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.