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Optimization and Anti-Optimization of Structures Under Uncertainty




Imperial College Press, London



Isaac Elishakoff and Makoto Ohsaki



Optimization and Anti-Optimization of Structures Under Uncertainty

Year of Publication











Krishna B. Misra



Review published in IJPE, Vol. 7, No. 6, November 2011, p. 538



The book consists of the following 9 chapters followed by Authors’ Preface:



09 Pages

Chapter 1


16 Pages

Chapter 2

Optimization or Making the Best in presence of Certainty/Uncertainty

30 Pages

Chapter 3

General Formulation of Anti-Optimization

30 Pages

Chapter 4

Anti-Optimization in Static Problems

36 Pages

Chapter 5

Anti-Optimization in Buckling

32 Pages

Chapter 6

Anti-Optimization in Vibration

66 Pages

Chapter 7

Anti-Optimization via FEM-based Inverse Analysis

16 Pages

Chapter 8

Anti-Optimization and Probabilistic Design

46 Pages

Chapter 9

Hybrid Optimization with Anti-Optimization under Uncertainty or Making the Best out of the Worst

54 Pages

Chapter 10

Concluding Remarks

16 Pages


43 Pages


04 Pages

Author Index

12 Pages



Civil engineers, or rather the structural engineers, know very well that howsoever one may try to design a structure as a deterministic problem with precise data, model and analysis, there will always exist certain 978-1-84816-477-2amount of uncertainty in their designs. In fact, non-deterministic analysis may be more realistic way of treating the problem rather than solving a problem that can often be called as pseudo-deterministic. In fact deterministic design is contained as a special case of probabilistic design. The way safety factors are used and interpreted leads one to believe that probabilistic approach tends to lead an analyst to more realistic way of looking to the problem. In fact advent of fuzzy sets approach among the non-deterministic category is a way out to consider uncertainty problem. The first author calls safety factor approach as an uncertainty unknown but bounded. On the other hand worst case approach is too conservative but simpler to use. The authors opt for anti-optimization or worst case scenario approach.


However, the authors suggest an approach what they call as optimization and anti-optimization or rather optimization with anti-optimization. Such a hybrid approach they feel would be less conservative than worst case analysis and more acceptable to engineers and researchers. They advocate use of healthy dose of optimism represented by optimization and pessimism represented by anti-optimization. The structural optimization is usually minimization of an objective function such as cost, weight or volume subject to constraints on mechanical performances. Alternatively, it could be maximization of mechanical performance subject to upper bound for cost, weight or volume. In anti-optimization problem the response property which is supposed to give worst value if maximized with respect to uncertain parameters. Uncertainty may exist in material parameters, cross sectional geometry, external loads etc. Although the state of art has matured but people still consider probabilistic approach with apprehensions or rather consider it an intellectual exercise. The present book assumes importance since it combines best of two approaches and promotes hybrid path to the design problem.


As the list of contents indicates, chapters 4-7 apply the anti-optimization approach to static problems, buckling, vibration, FEM-based Inverse analysis. Chapter 8 compares anti-optimization and probabilistic design and chapter 9 provides the hybrid approach. Chapter 10 outlines the authors’ motivation to write this book. There is long list of useful bibliography at the end.


The students and teachers pursuing reliability of structures will find this book of interest. In general, the book would be very useful for structural engineers particularly those dealing with design.


Krishna B. Misra

Review published in the International Journal of Performability Engineering, Vol. 7, No. 6, November 2011, p. 538.

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