Multicriteria Optimization in Engineering and in the Sciences

1. Front Matter

   Pages i-xiv

   PDF

2. Fundamentals of Multicriteria Optimization

   • Wolfram Stadler

   Pages 1-25

3. Numerically Analyzing Linear Multicriteria Optimization Problems

   • Jerald P. Dauer

   Pages 27-47

4. Applications of Multicriteria Optimization in Approximation Theory

   • J. Jahn, W. Krabs

   Pages 49-75

5. Welfare Economics and the Vector Maximum Problem

   • N. Schulz

   Pages 77-116

6. Multicriterion Optimization in Resources Planning

   • Jared L. Cohon, Giuseppe Scavone, Rajendra Solanki

   Pages 117-160

7. Renewable Resource Management

   • Thomas L. Vincent

   Pages 161-186

8. Competition, Kin Selection, and Evolutionary Stable Strategies

   • M. Mirmirani, G. Oster

   Pages 187-223

9. Multicriteria Optimization Methods for Design of Aircraft Control Systems

   • Albert A. Schy, Daniel P. Giesy

   Pages 225-262

10. Multicriteria Truss Optimization

    • Juhani Koski

    Pages 263-307

11. Multicriteria Optimization Techniques for Highly Accurate Focusing Systems

    • Hans A. Eschenauer

    Pages 309-354

12. Natural Structural Shapes (A Unified Optimal Design Philosophy)

    • Wolfram Stadler

    Pages 355-390

13. Back Matter

    Pages 391-405

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We are rarely asked to. make decisions based on only one criterion; most often, decisions are based on several usually confticting, criteria. In nature, if the design of a system evolves to some final, optimal state, then it must include a balance for the interaction of the system with its surroundings­ certainly a design based on a variety of criteria. Furthermore, the diversity of nature's designs suggests an infinity of such optimal states. In another sense, decisions simultaneously optimize a finite number of criteria, while there is usually an infinity of optimal solutions. Multicriteria optimization provides the mathematical framework to accommodate these demands. Multicriteria optimization has its roots in mathematical economics, in particular, in consumer economics as considered by Edgeworth and Pareto. The critical question in an exchange economy concerns the "equilibrium point" at which each of N consumers has achieved the best possible deal for hirnself or herself. Ultimately, this is a collective decision in which any further gain by one consumer can occur only at the expense of at least one other consumer. Such an equilibrium concept was first introduced by Edgeworth in 1881 in his book on mathematical psychics. Today, such an optimum is variously called "Pareto optimum" (after the Italian-French welfare economist who continued and expanded Edgeworth's work), "effi. cient," "nondominated," and so on.

• design
• Mathematica
• multi-objective optimization
• optimization

• San Francisco State University, San Francisco, USA

  Wolfram Stadler

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